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Grade 4 math worksheets

Build your own math worksheets from 35,000+ problems for grades 3 to 12, from fractions to AP Calculus. Every problem comes with step-by-step solutions.

Multi-step problems with addition and subtraction

Learning goals

  • Represents a multi-step addition or subtraction problem with equations.
  • Orders dependent calculations in a multi-step word problem.
  • Computes intermediate and final sums and differences in a word problem.
  • Checks a multi-step whole-number word problem by estimation.

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Multi-step problems with addition and subtraction 1
A bakery has \(1500\) fresh rolls in the morning. It sells \(900\) rolls before noon and then bakes \(400\) more. Caio writes: Step 1: \(1500-900=600\) Step 2: \(600+400=1000\) Explain what the \(600\) represents. How many rolls are in the bakery after the additional baking?

Hints

- Identify the two quantities used in the first subtraction. - Sold rolls are no longer in the bakery. - The second step adds the rolls baked later.

Solution

1. The calculation \(1500-900=600\) subtracts the rolls sold from the starting amount. 2. Therefore, \(600\) represents the rolls remaining after the morning sales. 3. Adding the newly baked rolls gives \(600+400=1000\) rolls.

Answer

The \(600\) represents the rolls left after the morning sales. After baking more, the bakery has \(1000\) rolls.
Multi-step problems with addition and subtraction 2
An old school building was constructed in \(1894\). A celebration was held for its \(125\)th anniversary. a) In what year was the celebration held? b) How many years after that celebration was \(2025\), and how old was the building in \(2025\)?

Hints

- First locate the anniversary year from the construction year and anniversary number. - Use that anniversary as the reference point for part b. - The building’s later age can be related to its age at the anniversary.

Solution

1. The \(125\)th-anniversary year was \(1894+125=2019\). 2. The year \(2025\) was \(2025-2019=6\) years after the celebration. 3. The building’s age in \(2025\) was therefore \(125+6=131\) years.

Answer

a) \(2019\) b) \(6\) years after the celebration; the building was \(131\) years old
Multi-step problems with addition and subtraction 3
\(18\) students sign up for a field trip. Then \(7\) cancel, and \(4\) new students join. Elena adds \(7+4\) and subtracts the result from \(18\). Explain her mistake and find how many students are signed up now.

Hints

- Which event makes the group smaller? Which makes it larger? - Try showing both changes with people joining and leaving a group.

Solution

1. Cancellations decrease the count, but new sign-ups increase it. Elena treats both changes as decreases. 2. After cancellations, \(18 - 7 = 11\) students remain. 3. Adding the new students gives \(11 + 4 = 15\).

Answer

\(15\) students. Cancellations decrease the count and new sign-ups increase it: \(18 - 7 + 4 = 15\).
Multi-step problems with addition and subtraction 4
Volunteers collect \(18\) cans of food in the morning and another \(27\) cans in the afternoon. They give \(16\) cans to a shelter. How many cans are left? Show both steps.

Hints

- Which counts tell you about cans coming in and cans going out? - Which amount represents cans leaving the collection? - Check whether the final count is less than the total collected.

Solution

1. Find the total collected: \(18 + 27 = 45\) cans. 2. Subtract the donated cans: \(45 - 16 = 29\).

Answer

\(18 + 27 = 45\) cans collected; \(45 - 16 = 29\) cans left.
Multi-step problems with addition and subtraction 5
Tim is \(34\,\text{in}\) tall. His sister Julia is \(4\,\text{in}\) taller than he is. Tim's and Julia's heights add to their father's height. Their mother is \(5\,\text{in}\) shorter than their father. How tall are Julia, their father, and their mother?

Hints

- Find Julia's height from Tim's height first. - Use both children's heights to find their father's height. - Use the father's height to find the mother's height.

Solution

1. Julia is \(34\,\text{in} + 4\,\text{in} = 38\,\text{in}\) tall. 2. Their father is \(34\,\text{in} + 38\,\text{in} = 72\,\text{in}\), or \(6\,\text{ft}\), tall. 3. Their mother is \(72\,\text{in} - 5\,\text{in} = 67\,\text{in}\), or \(5\,\text{ft}\ 7\,\text{in}\), tall.

Answer

Julia is \(38\,\text{in}\) tall, their father is \(6\,\text{ft}\) tall, and their mother is \(5\,\text{ft}\ 7\,\text{in}\) tall.
Multi-step problems with addition and subtraction 6
The Sunny Scoop ice cream shop has this menu: <table><tr><th>Ice cream</th><th>Price</th><th>Drinks</th><th>Price</th></tr><tr><td>Fruit sundae</td><td>\(\$6\)</td><td>Apple juice</td><td>\(\$2\)</td></tr><tr><td>Chocolate sundae</td><td>\(\$7\)</td><td>Bottled water</td><td>\(\$1\)</td></tr><tr><td>Vanilla sundae</td><td>\(\$5\)</td><td>Iced tea</td><td>\(\$3\)</td></tr><tr><td>Strawberry sundae</td><td>\(\$8\)</td><td>Lemonade</td><td>\(\$2\)</td></tr></table> a) Leonie buys a vanilla sundae and an iced tea. How much does she pay? b) If Leonie pays with \(\$10\), how much change does she get? c) Jonas has \(\$10\). He wants a chocolate sundae and a drink. Which drinks can he afford?

Hints

- Find Leonie's total cost before trying to find her change. - For Jonas, use the sundae price to find what remains in his budget. - Compare his remaining amount with the drink prices in the table.

Solution

1. Leonie's sundae and tea cost \(\$5 + \$3 = \$8\). 2. Her change is \(\$10 - \$8 = \$2\). 3. Jonas has \(\$10 - \$7 = \$3\) left after the chocolate sundae. All four drinks cost no more than \(\$3\), so he can afford any one of them.

Answer

a) \(\$8\) b) \(\$2\) c) Apple juice, bottled water, iced tea, or lemonade.
Multi-step problems with addition and subtraction 7
Two signs along a bike trail both point the same way: first to Cedar Grove, then to Pine Junction. The second sign is farther along the trail than the first. Sign 1: Cedar Grove \(54\,\text{miles}\), Pine Junction \(92\,\text{miles}\). Sign 2: Cedar Grove \(38\,\text{miles}\). How far should Sign 2 say it is to Pine Junction? Explain how you know.

Hints

- Follow the order of the towns along the trail. - What part of the route stays the same between the signs? - Use the distance shown for Cedar Grove on the second sign.

Solution

1. On Sign 1, Pine Junction is \(92-54=38\,\text{miles}\) beyond Cedar Grove. 2. That distance between the towns stays the same. On Sign 2, Pine Junction must be \(38+38=76\,\text{miles}\) away.

Answer

Sign 2 should say \(76\,\text{miles}\) to Pine Junction.
Multi-step problems with addition and subtraction 8
A highway sign lists the distances to three towns ahead: Pine City: \(155\,\text{miles}\) Lakeview: \(82\,\text{miles}\) Riverdale: \(15\,\text{miles}\) a) What is the distance from Riverdale to Lakeview? b) What is the distance from Lakeview to Pine City? c) Which of those two sections is longer, and by how many miles?

Hints

- Imagine the three towns in order along one line. - Subtract the smaller sign distance from the larger sign distance to find each section. - Compare the two section lengths and subtract to find the difference.

Solution

1. Find the distance from Riverdale to Lakeview: \(82 - 15 = 67\,\text{miles}\). 2. Find the distance from Lakeview to Pine City: \(155 - 82 = 73\,\text{miles}\). 3. Since \(73 > 67\), the Lakeview-to-Pine City section is longer. 4. Find the difference: \(73 - 67 = 6\,\text{miles}\).

Answer

a) The distance is \(67\,\text{miles}\). b) The distance is \(73\,\text{miles}\). c) The Lakeview-to-Pine City section is longer by \(6\,\text{miles}\).
Multi-step problems with addition and subtraction 9
A sporting goods store lists these prices: <table> <tr><td>Inline skates</td><td>\(\$59\)</td></tr> <tr><td>Helmet</td><td>\(\$24\)</td></tr> <tr><td>Knee pads</td><td>\(\$12\)</td></tr> <tr><td>Elbow pads</td><td>\(\$9\)</td></tr> </table> Sarah receives \(\$100\) for her birthday and buys the inline skates and helmet. a) How much does she pay for those two items? b) How much money remains? c) Is the remaining money enough to buy both the knee pads and elbow pads? Explain.

Hints

- Add the prices of the skates and helmet. - Subtract that total from \(\$100\). - Add the prices of the knee pads and elbow pads. - Compare the pad cost with the money remaining.

Solution

1. The skates and helmet cost \(\$59 + \$24 = \$83\). 2. The money remaining is \(\$100 - \$83 = \$17\). 3. The knee pads and elbow pads cost \(\$12 + \$9 = \$21\). 4. Since \(\$21 > \$17\), the remaining money is not enough.

Answer

a) \(\$83\) b) \(\$17\) c) No. The pads cost \(\$21\), but Sarah has only \(\$17\) left.
Multi-step problems with addition and subtraction 10
A truck driver travels \(840\) miles from Monday through Thursday. The driver travels \(195\) miles on Monday, \(210\) miles on Tuesday, and \(185\) miles on Wednesday. The remaining distance is traveled on Thursday. On which day does the driver travel the farthest? How many more miles is that than the distance traveled on Wednesday?

Hints

- First find the distance traveled on Thursday. - Compare all four daily distances. - Subtract Wednesday's distance from the greatest distance.

Solution

1. Add the distances from Monday through Wednesday: \(195 + 210 + 185 = 590\) miles. 2. Find Thursday's distance: \(840 - 590 = 250\) miles. 3. Compare \(195\), \(210\), \(185\), and \(250\). Thursday has the greatest distance. 4. Find the difference between Thursday and Wednesday: \(250 - 185 = 65\) miles.

Answer

The driver travels farthest on Thursday, at \(250\) miles. That is \(65\) miles farther than Wednesday.
Multi-step problems with addition and subtraction 11
A \(\$1{,}000{,}000\) grant is divided among three programs in each plan. Complete the table so that each row totals exactly \(\$1{,}000{,}000\). <table> <tr><th>Program 1</th><th>Program 2</th><th>Program 3</th></tr> <tr><td>\(\$450{,}000\)</td><td>\(\$250{,}000\)</td><td>?</td></tr> <tr><td>\(\$125{,}000\)</td><td>?</td><td>\(\$375{,}000\)</td></tr> <tr><td>?</td><td>\(\$660{,}000\)</td><td>\(\$140{,}000\)</td></tr> </table>

Hints

- Add the two known amounts in each row. - Subtract that sum from \(\$1{,}000{,}000\). - Check that all three amounts in each row total \(\$1{,}000{,}000\).

Solution

1. In row 1, the known amounts total \(450{,}000 + 250{,}000 = 700{,}000\). The missing amount is \(1{,}000{,}000 - 700{,}000 = 300{,}000\). 2. In row 2, the known amounts total \(125{,}000 + 375{,}000 = 500{,}000\). The missing amount is \(1{,}000{,}000 - 500{,}000 = 500{,}000\). 3. In row 3, the known amounts total \(660{,}000 + 140{,}000 = 800{,}000\). The missing amount is \(1{,}000{,}000 - 800{,}000 = 200{,}000\).

Answer

Row 1: \(\$300{,}000\) Row 2: \(\$500{,}000\) Row 3: \(\$200{,}000\)
Multi-step problems with addition and subtraction 12
A warehouse receives \(345\) packages on Monday and \(287\) packages on Tuesday. a) How many packages have arrived altogether? b) A large order requires \(900\) packages. How many more packages are needed after Tuesday’s delivery?

Hints

- First decide which operation finds the total delivered. - Then find the difference between the required number and the number already delivered.

Solution

1. Add the two deliveries: \(345+287=632\). A total of \(632\) packages have arrived. 2. Subtract the amount received from the amount needed: \(900-632=268\). 3. The warehouse needs \(268\) more packages.

Answer

a) \(632\) packages b) \(268\) more packages
Multi-step problems with addition and subtraction 13
Park Elementary offers several after-school sports clubs. The table shows how many students are enrolled in each club. <table><tr><th>Club</th><th>Boys</th><th>Girls</th></tr><tr><td>Basketball</td><td>\(24\)</td><td>\(18\)</td></tr><tr><td>Gymnastics</td><td>\(12\)</td><td>\(35\)</td></tr><tr><td>Swimming</td><td>\(22\)</td><td>\(26\)</td></tr></table> How many more girls than boys are enrolled in the three clubs altogether?

Hints

- Find one total for all girls and one total for all boys. - Use every row of the table in each total. - Compare the two totals only after both have been found.

Solution

1. The total number of girls is \(18+35+26=79\). 2. The total number of boys is \(24+12+22=58\). 3. The difference is \(79-58=21\).

Answer

There are \(21\) more girls than boys enrolled in the three clubs altogether.
Multi-step problems with addition and subtraction 14
A snack stand by a lake sells popsicles on weekends. The table shows the number of each flavor sold on Saturday and Sunday. <table><tr><th>Flavor</th><th>Saturday</th><th>Sunday</th></tr><tr><td>Chocolate</td><td>\(156\)</td><td>\(213\)</td></tr><tr><td>Strawberry</td><td>\(98\)</td><td>\(145\)</td></tr><tr><td>Vanilla</td><td>\(112\)</td><td>\(128\)</td></tr></table> How many more chocolate popsicles than strawberry popsicles were sold over the entire weekend?

Hints

- Combine Saturday and Sunday sales for each of the two flavors named in the question. - Keep the two weekend totals separate until both are known. - The final question asks for the difference between those totals.

Solution

1. Chocolate sales for the weekend were \(156+213=369\). 2. Strawberry sales for the weekend were \(98+145=243\). 3. The difference is \(369-243=126\).

Answer

The stand sold \(126\) more chocolate popsicles than strawberry popsicles over the weekend.
Multi-step problems with addition and subtraction 15
A public library added books to its collection. The table groups the new books by age level, type, and how the library received them. <table> <tr><th></th><th colspan="2">Children (ages 12 and under)</th><th colspan="2">Teens (ages 13 and older)</th></tr> <tr><td></td><td>Nonfiction</td><td>Fiction</td><td>Nonfiction</td><td>Fiction</td></tr> <tr><td>Purchased</td><td>\(1450\)</td><td>\(2380\)</td><td>\(870\)</td><td>\(1560\)</td></tr> <tr><td>Donated</td><td>\(320\)</td><td>\(540\)</td><td>\(150\)</td><td>\(420\)</td></tr> </table> a) How many children’s fiction books were added altogether? b) How many teen nonfiction books were added altogether? c) Which age level received more books altogether?

Hints

- Notice that each age level has two columns. - Identify which columns belong to children and which belong to teens. - For part c), add all four entries for each age level, and then compare the totals.

Solution

1. Add the purchased and donated children’s fiction books: \(2380 + 540 = 2920\). 2. Add the purchased and donated teen nonfiction books: \(870 + 150 = 1020\). 3. Find the children’s total: \(1450 + 2380 + 320 + 540 = 4690\). 4. Find the teen total: \(870 + 1560 + 150 + 420 = 3000\). 5. Since \(4690 > 3000\), the children’s collection received more books.

Answer

a) \(2920\) children’s fiction books b) \(1020\) teen nonfiction books c) The children’s collection
Multi-step problems with addition and subtraction 16
A technology museum celebrates its \(125\)th anniversary on September 20, 2025. On that date, the museum director is exactly \(62\) years old. a) In what year did the museum open? b) How old was the director when the museum celebrated its \(100\)th anniversary?

Hints

- First find the year the museum opened. - In what year did the museum celebrate its \(100\)th anniversary? - How many years passed between the \(100\)th and \(125\)th anniversaries?

Solution

1. Find the opening year: \(2025 - 125 = 1900\). 2. Find the year of the \(100\)th anniversary: \(1900 + 100 = 2000\). 3. Find the number of years from the \(100\)th anniversary to the \(125\)th anniversary: \(2025 - 2000 = 25\) years. 4. Find the director’s age in \(2000\): \(62 - 25 = 37\).

Answer

a) The museum opened in \(1900\). b) The director was \(37\) years old.
Multi-step problems with addition and subtraction 17
On his \(75\)th birthday in \(2023\), Grandpa Henry also celebrated exactly \(50\) years since his first day working at the same cabinet shop. a) In what year was Henry born? b) How old was he when he started working at the shop?

Hints

- Find the birth year by counting back from the birthday in \(2023\). - How many years before \(2023\) was his first day at the shop? - The anniversary falls on his birthday. How does that help with his exact age?

Solution

1. Henry was born in \(2023-75=1948\). 2. He started at the shop in \(2023-50=1973\). 3. Because his first day was on his birthday, his age then was \(75-50=25\) years.

Answer

a) \(1948\) b) \(25\) years old
Multi-step problems with addition and subtraction 18
The table shows the populations of three towns in \(2010\) and \(2020\), with projections for \(2030\). <table><thead><tr><th>Town</th><th>2010</th><th>2020</th><th>2030 projection</th></tr></thead><tbody><tr><td>Pineville</td><td>\(45{,}600\)</td><td>\(48{,}200\)</td><td>\(51{,}000\)</td></tr><tr><td>Oakton</td><td>\(32{,}100\)</td><td>\(30{,}900\)</td><td>\(29{,}500\)</td></tr><tr><td>Lakeview</td><td>\(54{,}300\)</td><td>\(56{,}700\)</td><td>\(55{,}200\)</td></tr></tbody></table> a) Which town's population decreases in both periods? b) How many more people is that town projected to lose from \(2020\) to \(2030\) than it lost from \(2010\) to \(2020\)?

Hints

- Find the row that gets smaller from one column to the next both times. - Compare the change in that row for each ten-year period. - The final question asks for the difference between those two changes.

Solution

1. Oakton is the only town with a decrease in both periods. 2. Its population fell by \(32{,}100-30{,}900=1200\) from \(2010\) to \(2020\). 3. It is projected to fall by \(30{,}900-29{,}500=1400\) from \(2020\) to \(2030\). 4. The projected decrease is \(1400-1200=200\) people greater.

Answer

a) Oakton b) \(200\) more people
Multi-step problems with addition and subtraction 19
A state forestry department tracks newly planted trees in three forest districts. <table> <thead> <tr> <th>District</th> <th>Evergreen trees</th> <th>Deciduous trees</th> </tr> </thead> <tbody> <tr> <td>Oak Forest</td> <td>\(125{,}000\)</td> <td>\(88{,}500\)</td> </tr> <tr> <td>Pine Ridge</td> <td>\(94{,}200\)</td> <td>\(112{,}000\)</td> </tr> <tr> <td>Beech Grove</td> <td>\(108{,}600\)</td> <td>\(95{,}400\)</td> </tr> </tbody> </table> a) How many trees were planted in Pine Ridge altogether? b) How many evergreen trees were planted in the three districts altogether? c) In which district is the difference between the numbers of evergreen and deciduous trees greatest?

Hints

- For part a), add only the two entries in one row. - For part b), add the entries in one column. - For part c), find the difference in each row and compare the results.

Solution

1. Add the two entries for Pine Ridge: \(94{,}200 + 112{,}000 = 206{,}200\). 2. Add the evergreen entries: \(125{,}000 + 94{,}200 + 108{,}600 = 327{,}800\). 3. Find the difference in each district. Oak Forest: \(125{,}000 - 88{,}500 = 36{,}500\). Pine Ridge: \(112{,}000 - 94{,}200 = 17{,}800\). Beech Grove: \(108{,}600 - 95{,}400 = 13{,}200\). The greatest difference is in Oak Forest.

Answer

a) \(206{,}200\) trees b) \(327{,}800\) evergreen trees c) Oak Forest
Multi-step problems with addition and subtraction 20
The table shows the number of visitors to four large amusement parks in 2022 and 2023. <table> <thead> <tr> <th>Amusement park</th> <th>2022</th> <th>2023</th> </tr> </thead> <tbody> <tr> <td>Sunshine Park</td> <td>\(245{,}000\)</td> <td>\(261{,}000\)</td> </tr> <tr> <td>Adventure World</td> <td>\(198{,}500\)</td> <td>\(192{,}000\)</td> </tr> <tr> <td>Wildlife West</td> <td>\(312{,}400\)</td> <td>\(315{,}000\)</td> </tr> <tr> <td>Water Paradise</td> <td>\(156{,}700\)</td> <td>\(168{,}200\)</td> </tr> </tbody> </table> a) Which park had the most visitors in 2023? b) By how many visitors did attendance at Water Paradise increase from 2022 to 2023? c) Is the combined 2023 attendance at Sunshine Park and Adventure World greater than or less than the 2023 attendance at Wildlife West?

Hints

- For part a), find the greatest entry in the correct column. - Use subtraction to find the increase in part b). - For part c), add two entries first, and then compare the sum with a third entry.

Solution

1. Compare the entries in the 2023 column. The greatest value is \(315{,}000\), for Wildlife West. 2. Subtract the 2022 attendance from the 2023 attendance for Water Paradise: \(168{,}200 - 156{,}700 = 11{,}500\). 3. Add the 2023 attendance at Sunshine Park and Adventure World: \(261{,}000 + 192{,}000 = 453{,}000\). 4. Compare the result with Wildlife West: \(453{,}000 > 315{,}000\), so the combined attendance is greater.

Answer

a) Wildlife West b) \(11{,}500\) visitors c) Greater than
Multi-step problems with addition and subtraction 21
A state had \(435{,}600\) elementary school students in 2021. In 2022, enrollment increased by \(12{,}850\) students. For 2023, enrollment was projected to decrease by \(9420\) students from the 2022 level. a) What was the projected enrollment for 2023? b) How many more students were projected for 2023 than were enrolled in 2021?

Hints

- Decide whether enrollment increases or decreases at each step. - Work from one year to the next in order. - For part b, compare the 2023 result with the original 2021 value.

Solution

1. Find the 2022 enrollment: \(435{,}600+12{,}850=448{,}450\). 2. Subtract the projected decrease: \(448{,}450-9420=439{,}030\). 3. Compare the 2023 projection with 2021: \(439{,}030-435{,}600=3430\).

Answer

a) The projected 2023 enrollment was \(439{,}030\) students. b) That is \(3430\) more students than in 2021.
Multi-step problems with addition and subtraction 22
Three large school districts report their elementary school enrollment: - Cedar Point School District has \(84{,}320\) students. - Meadow Run School District has \(15{,}650\) fewer students than Cedar Point. - Brookstone School District has \(7480\) more students than Meadow Run. How many elementary school students are enrolled in the three districts altogether?

Hints

- Determine the two enrollments that are not given directly before finding the total. - Keep track of which district each “fewer than” or “more than” statement compares. - Check that all three district enrollments are included in the final sum.

Solution

1. Meadow Run’s enrollment is \(84{,}320-15{,}650=68{,}670\). 2. Brookstone’s enrollment is \(68{,}670+7480=76{,}150\). 3. The three enrollments total \(84{,}320+68{,}670+76{,}150=229{,}140\).

Answer

The three districts have \(229{,}140\) elementary school students altogether.
Multi-step problems with addition and subtraction 23
A state education department plans for \(950{,}000\) elementary school seats in Grades 1 through 4. Current enrollment is: - Grade 1: \(234{,}500\) students - Grade 2: \(241{,}200\) students - Grade 3: \(238{,}900\) students - Grade 4: \(232{,}150\) students How many seats will remain open if every enrolled student receives a seat?

Hints

- First find the total enrollment across all four grades. - Compare the total enrollment with the total number of seats. - The word “altogether” signals that addition is needed first.

Solution

1. Find the total enrollment: \(234{,}500+241{,}200+238{,}900+232{,}150=946{,}750\). 2. Subtract the enrollment from the available seats: \(950{,}000-946{,}750=3250\).

Answer

\(3250\) seats will remain open.
Multi-step problems with addition and subtraction 24
Two fruit crates are weighed at a wholesale market. Crate A, filled with apples, has a total mass of \(12{,}450\,\text{g}\). The empty crate has a mass of \(1120\,\text{g}\). Crate B, filled with pears, has a total mass of \(15{,}200\,\text{g}\). The empty crate has a mass of \(1450\,\text{g}\). Which fruit has the greater mass, and what is the difference in grams?

Hints

- Find the mass of the fruit in each crate by subtracting the empty crate's mass. - Compare the two fruit masses. - Subtract to find the difference.

Solution

1. Start with the filled mass of Crate A, \(12{,}450\,\text{g}\). Subtract the empty crate's mass, \(1120\,\text{g}\). The apples have a mass of \(11{,}330\,\text{g}\). 2. Start with the filled mass of Crate B, \(15{,}200\,\text{g}\). Subtract the empty crate's mass, \(1450\,\text{g}\). The pears have a mass of \(13{,}750\,\text{g}\). 3. The pears have the greater mass because \(13{,}750\,\text{g} > 11{,}330\,\text{g}\). 4. Subtract \(11{,}330\,\text{g}\) from \(13{,}750\,\text{g}\). The difference is \(2420\,\text{g}\).

Answer

The pears have a greater mass by \(2420\,\text{g}\).
Multi-step problems with addition and subtraction 25
A small truck may have a maximum total mass of \(14{,}250\,\text{kg}\). The empty truck has a mass of \(10{,}150\,\text{kg}\). Two machines with a combined mass of \(1240\,\text{kg}\) and a tool pallet with a mass of \(980\,\text{kg}\) are loaded. How many more kilograms can be added without exceeding the limit?

Hints

- Add the empty truck and all items already loaded. - Compare the current mass with the maximum allowed mass. - Subtract to find the remaining capacity.

Solution

1. Find the combined mass of the machines and tool pallet: \(1240\,\text{kg} + 980\,\text{kg} = 2220\,\text{kg}\). 2. Add \(2220\,\text{kg}\) to the empty truck's mass of \(10{,}150\,\text{kg}\). The truck's current mass is \(12{,}370\,\text{kg}\). 3. Subtract the current mass from the limit. Start with \(14{,}250\,\text{kg}\) and subtract \(12{,}370\,\text{kg}\). The remaining capacity is \(1880\,\text{kg}\).

Answer

The truck can carry \(1880\,\text{kg}\) more.
Multi-step problems with addition and subtraction 26
A horse trailer may have a maximum total mass of \(2000\,\text{kg}\). The empty trailer has a mass of \(840\,\text{kg}\). One horse with a mass of \(565\,\text{kg}\) is already inside. What is the greatest combined mass the second horse and the remaining equipment can have?

Hints

- First find how much cargo the empty trailer can carry. - The first horse uses part of that capacity. - Subtract the first horse's mass from the total payload capacity.

Solution

1. Find the trailer's total payload capacity: \(2000\,\text{kg} - 840\,\text{kg} = 1160\,\text{kg}\). 2. Subtract the first horse's mass: \(1160\,\text{kg} - 565\,\text{kg} = 595\,\text{kg}\).

Answer

The second horse and equipment can have a combined mass of at most \(595\,\text{kg}\).
Multi-step problems with addition and subtraction 27
A wildlife reserve in Africa has \(4870\) white rhinos and \(2450\) black rhinos. During the year, \(156\) calves were born and \(89\) rhinos died. How many rhinos are now living in the reserve?

Hints

- First find the total starting population. - Decide which change increases the population and which decreases it. - Work through the changes one step at a time.

Solution

1. Find the starting population: \(4870+2450=7320\). 2. Add the calves born: \(7320+156=7476\). 3. Subtract the rhinos that died: \(7476-89=7387\).

Answer

There are now \(7387\) rhinos living in the reserve.
Multi-step problems with addition and subtraction 28
A wildlife charity prints \(3600\) rhino fact cards for its Asian wildlife campaign. Of these, \(2750\) show greater one-horned rhinos, \(760\) show Sumatran rhinos, and the rest show Javan rhinos. The charity prints \(18{,}500\) rhino fact cards for its African wildlife campaign. a) How many Asian campaign cards show Javan rhinos? b) How many more cards are printed for the African campaign than for the Asian campaign?

Hints

- Find how many Asian cards belong to the two named groups. - What remains from the Asian total? - For part b), compare the two overall campaign totals.

Solution

1. The two known kinds of Asian cards total \(2750+760=3510\). 2. There are \(3600-3510=90\) Javan rhino cards. 3. The African campaign has \(18{,}500-3600=14{,}900\) more cards.

Answer

a) \(90\) Javan rhino cards b) \(14{,}900\) more cards
Multi-step problems with addition and subtraction 29
Two caterpillars crawl directly toward each other along a straight garden path. They begin \(120\,\text{cm}\) apart. After one hour, the first caterpillar has crawled \(48\,\text{cm}\), and the second has crawled \(55\,\text{cm}\). How far apart are they now?

Hints

- Both caterpillars reduce the same starting gap because they move toward each other. - Determine how much of the gap has been closed after one hour. - A simple line sketch can help you check which distances should be combined.

Solution

1. Together, the caterpillars close \(48+55=103\,\text{cm}\) of the starting gap. 2. The remaining distance is \(120-103=17\,\text{cm}\).

Answer

The caterpillars are \(17\,\text{cm}\) apart.
Multi-step problems with addition and subtraction 30
Class 3A collects \(145\,\text{kg}\) of paper for a recycling project. Class 3B collects \(20\,\text{kg}\) more than Class 3A. Class 3C collects \(15\,\text{kg}\) less than Classes 3A and 3B combined. How many kilograms of paper does Class 3C collect?

Hints

- First find how much Class 3B collects. - Then combine the amounts for Classes 3A and 3B. - Use “less than” to determine the final operation.

Solution

1. Find the amount collected by Class 3B: \(145 + 20 = 165\,\text{kg}\). 2. Find the combined amount for Classes 3A and 3B: \(145 + 165 = 310\,\text{kg}\). 3. Subtract \(15\,\text{kg}\): \(310 - 15 = 295\,\text{kg}\).

Answer

Class 3C collects \(295\,\text{kg}\) of paper.
Multi-step problems with addition and subtraction 31
Birch Trail is \(185\,\text{m}\) long and is extended by \(55\,\text{m}\) at each end. Alder Trail is \(230\,\text{m}\) long and is extended by \(40\,\text{m}\) at one end and \(35\,\text{m}\) at the other. Which trail is longer after the extensions, and by how many meters?

Hints

- Find each trail's new length separately. - Remember that Birch Trail is extended at both ends by the same amount. - Subtract the shorter final length from the longer final length.

Solution

1. Find the new length of Birch Trail: \(185 + 55 + 55 = 295\,\text{m}\). 2. Find the new length of Alder Trail: \(230 + 40 + 35 = 305\,\text{m}\). 3. Compare: \(305 > 295\), so Alder Trail is longer. 4. Find the difference: \(305 - 295 = 10\,\text{m}\).

Answer

Alder Trail is longer by \(10\,\text{m}\).
Multi-step problems with addition and subtraction 32
A bakery begins with \(150\,\text{kg}\) of flour. It uses \(45\,\text{kg}\) for bread. The bakery uses \(20\,\text{kg}\) more flour for rolls than for bread. How much flour remains?

Hints

- First find the amount of flour used for rolls. - Add the amounts used for bread and rolls. - Subtract the total used from the starting amount.

Solution

1. Find the flour used for rolls: \(45 + 20 = 65\,\text{kg}\). 2. Find the total amount used: \(45 + 65 = 110\,\text{kg}\). 3. Subtract from the starting amount: \(150 - 110 = 40\,\text{kg}\).

Answer

\(40\,\text{kg}\) of flour remains.
Multi-step problems with addition and subtraction 33
A school event begins with \(350\,\text{L}\) of apple juice. Students drink \(115\,\text{L}\) during the first hour. During the second hour, they drink \(30\,\text{L}\) less than during the first hour. How much juice remains after two hours?

Hints

- First find how much juice is consumed during the second hour. - Add the amounts consumed during both hours. - Subtract the total consumed from the amount delivered.

Solution

1. Find the amount consumed during the second hour: \(115 - 30 = 85\,\text{L}\). 2. Find the total amount consumed: \(115 + 85 = 200\,\text{L}\). 3. Subtract from the starting amount: \(350 - 200 = 150\,\text{L}\).

Answer

\(150\,\text{L}\) of apple juice remains.
Multi-step problems with addition and subtraction 34
An observation tower's base is \(485\,\text{m}\) above sea level. a) The lower observation deck is \(156\,\text{m}\) above the tower's base. The upper deck is \(68\,\text{m}\) above the lower deck. The top of the tower is another \(92\,\text{m}\) above the upper deck. Find the elevation of the tower's top above sea level. b) The top of a nearby bell tower is \(572\,\text{m}\) above sea level. How much higher is the observation tower?

Hints

- Which elevation is already measured from sea level? - Add the successive heights above the tower's base in order. - Compare the two towers using their elevations above the same reference level.

Solution

1. The lower deck's elevation is \(485+156=641\,\text{m}\). 2. The upper deck's elevation is \(641+68=709\,\text{m}\). 3. The tower's top is at \(709+92=801\,\text{m}\) above sea level. 4. The observation tower is \(801-572=229\,\text{m}\) higher than the bell tower.

Answer

a) \(801\,\text{m}\) above sea level b) \(229\,\text{m}\) higher
Multi-step problems with addition and subtraction 35
One library shelf has \(148\) adventure books and \(165\) animal books. Another shelf has \(152\) adventure books and \(159\) animal books. Which shelf has more books in all, and what is the difference?

Hints

- Find the total number of books on each shelf. - Compare the two totals. - Subtract the smaller total from the larger total.

Solution

1. Find the total on the first shelf: \(148 + 165 = 313\). 2. Find the total on the second shelf: \(152 + 159 = 311\). 3. Compare the totals: \(313 > 311\), so the first shelf has more books. 4. Find the difference: \(313 - 311 = 2\).

Answer

The first shelf has more books. It has \(2\) more books than the second shelf.
Multi-step problems with addition and subtraction 36
At a school event, \(125\) cups of apple juice and \(140\) cups of orange juice are sold in the morning. In the afternoon, \(30\) more cups of apple juice are sold than in the morning, but \(45\) fewer cups of orange juice are sold. When are more cups of juice sold in all, and what is the difference?

Hints

- Find the afternoon amount for each kind of juice. - Find the total for each time of day. - Compare the totals and subtract to find the difference.

Solution

1. Find the morning total: \(125 + 140 = 265\) cups. 2. Find the afternoon apple juice sales: \(125 + 30 = 155\) cups. 3. Find the afternoon orange juice sales: \(140 - 45 = 95\) cups. 4. Find the afternoon total: \(155 + 95 = 250\) cups. 5. Compare and subtract: \(265 > 250\) and \(265 - 250 = 15\).

Answer

More juice is sold in the morning. The difference is \(15\) cups.
Multi-step problems with addition and subtraction 37
A collection tank must hold \(15{,}000\,\text{L}\) of water. It receives \(4250\,\text{L}\) on Monday, \(5180\,\text{L}\) on Tuesday, and \(3940\,\text{L}\) on Wednesday. A leak lets \(285\,\text{L}\) drain out. How much more water is needed to fill the tank?

Hints

- First find the total amount that flowed into the tank. - The leak decreases the amount in the tank. - Compare the remaining amount with the tank's target capacity.

Solution

1. Add the water received: \(4250\,\text{L}+5180\,\text{L}+3940\,\text{L}=13{,}370\,\text{L}\). 2. Subtract the leaked water: \(13{,}370\,\text{L}-285\,\text{L}=13{,}085\,\text{L}\). 3. Find the amount still needed: \(15{,}000\,\text{L}-13{,}085\,\text{L}=1915\,\text{L}\).

Answer

\(1915\,\text{L}\)
Multi-step problems with addition and subtraction 38
A soccer stadium has \(2500\) seats. During the first ticket sale, \(845\) tickets are sold. During the second sale, \(125\) more tickets are sold than during the first sale. Sponsors also receive \(210\) complimentary tickets. How many seats remain available?

Hints

- First find the number of tickets sold during the second sale. - Add all sold and complimentary tickets. - Subtract the assigned seats from the stadium capacity.

Solution

1. The second sale includes \(845+125=970\) tickets. 2. The total number of assigned seats is \(845+970+210=2025\). 3. The number of available seats is \(2500-2025=475\).

Answer

\(475\) seats
Multi-step problems with addition and subtraction 39
At an amusement park, the Blue Bolt roller coaster is \(645\,\text{m}\) long. The new Red Dragon coaster is \(278\,\text{m}\) longer than the Blue Bolt. a) How long is the Red Dragon? b) Are \(1500\,\text{m}\) of track enough to build both coasters? Show a calculation to support your answer.

Hints

- Use the phrase “longer than” to find the second coaster's length. - Add the lengths of both coasters. - Compare the total with \(1500\,\text{m}\).

Solution

1. Find the length of the Red Dragon: \(645 + 278 = 923\,\text{m}\). 2. Find the combined length of both coasters: \(645 + 923 = 1568\,\text{m}\). 3. Since \(1568 > 1500\), the available track is not enough. 4. Find the shortage: \(1568 - 1500 = 68\,\text{m}\).

Answer

a) The Red Dragon is \(923\,\text{m}\) long. b) No. The two coasters require \(1568\,\text{m}\) of track, which is \(68\,\text{m}\) more than the amount available.
Multi-step problems with addition and subtraction 40
A school library receives \(145\) books on Monday. On Tuesday, it receives \(67\) more books than on Monday. On Wednesday, it receives \(25\) fewer books than the Monday and Tuesday deliveries combined. How many books arrive on Wednesday?

Hints

- First find Tuesday’s delivery. - Then combine the Monday and Tuesday deliveries. - Read carefully whether Wednesday’s delivery is more or fewer than that combined amount.

Solution

1. Tuesday’s delivery is \(145+67=212\) books. 2. Monday and Tuesday together total \(145+212=357\) books. 3. Wednesday’s delivery is \(357-25=332\) books.

Answer

\(332\) books arrive on Wednesday.
Multi-step problems with addition and subtraction 41
Three fourth-grade classes collect aluminum cans for an environmental project. Class 4A collects \(326\) cans. Class 4B collects \(47\) fewer cans than Class 4A. Class 4C collects \(85\) more cans than Classes 4A and 4B combined. a) How many cans did Class 4C collect? b) Did the three classes collect more than \(1200\) cans altogether? Support your answer with a calculation.

Hints

- Find Class 4B’s amount first, paying attention to “fewer.” - Combine Classes 4A and 4B before finding Class 4C’s amount. - Add all three class amounts to answer part b.

Solution

1. Class 4B collected \(326-47=279\) cans. 2. Classes 4A and 4B collected \(326+279=605\) cans together. 3. Class 4C collected \(605+85=690\) cans. 4. The three classes collected \(605+690=1295\) cans altogether. 5. Since \(1295>1200\), they collected more than \(1200\) cans.

Answer

a) Class 4C collected \(690\) cans. b) Yes. The classes collected \(1295\) cans altogether.
Multi-step problems with addition and subtraction 42
The table shows distances between five fictional towns, in miles. <table><thead><tr><th>Distances in miles</th><th>Pine Ridge</th><th>Cedar Falls</th><th>Lakeview</th><th>Hillcrest</th><th>Brookside</th></tr></thead><tbody><tr><th>Pine Ridge</th><td>---</td><td>65</td><td>30</td><td>70</td><td>115</td></tr><tr><th>Cedar Falls</th><td>65</td><td>---</td><td>50</td><td>130</td><td>175</td></tr><tr><th>Lakeview</th><td>30</td><td>50</td><td>---</td><td>100</td><td>145</td></tr><tr><th>Hillcrest</th><td>70</td><td>130</td><td>100</td><td>---</td><td>45</td></tr><tr><th>Brookside</th><td>115</td><td>175</td><td>145</td><td>45</td><td>---</td></tr></tbody></table> A group travels Brookside \(\rightarrow\) Hillcrest \(\rightarrow\) Lakeview \(\rightarrow\) Pine Ridge \(\rightarrow\) Cedar Falls. How many miles does the group travel altogether?

Hints

- Read the table once for each pair of consecutive towns in the route. - Keep a list of the four route-segment distances before combining them. - Check that every arrow in the route contributes exactly one distance.

Solution

1. The four route segments are \(45\), \(100\), \(30\), and \(65\) miles. 2. The route length is \(45+100+30+65=240\) miles.

Answer

The group travels \(240\) miles altogether.
Multi-step problems with addition and subtraction 43
A delivery van must travel from Harbor City to Riverton with two stops. The table shows distances in miles between five fictional towns. <table><thead><tr><th>Distances in miles</th><th>Harbor City</th><th>Westport</th><th>Greenfield</th><th>Northgate</th><th>Riverton</th></tr></thead><tbody><tr><th>Harbor City</th><td>---</td><td>35</td><td>60</td><td>30</td><td>175</td></tr><tr><th>Westport</th><td>35</td><td>---</td><td>30</td><td>65</td><td>145</td></tr><tr><th>Greenfield</th><td>60</td><td>30</td><td>---</td><td>90</td><td>115</td></tr><tr><th>Northgate</th><td>30</td><td>65</td><td>90</td><td>---</td><td>205</td></tr><tr><th>Riverton</th><td>175</td><td>145</td><td>115</td><td>205</td><td>---</td></tr></tbody></table> Route A: Harbor City \(\rightarrow\) Westport \(\rightarrow\) Greenfield \(\rightarrow\) Riverton Route B: Harbor City \(\rightarrow\) Northgate \(\rightarrow\) Greenfield \(\rightarrow\) Riverton Which route is shorter, and by how many miles?

Hints

- Find a total distance for each route using only consecutive stops. - Compare the two route totals after both have been found. - The final answer asks for both the shorter route and the size of the difference.

Solution

1. Route A is \(35+30+115=180\) miles. 2. Route B is \(30+90+115=235\) miles. 3. Route A is shorter by \(235-180=55\) miles.

Answer

Route A is shorter by \(55\) miles.
Multi-step problems with addition and subtraction 44
A large city library has \(125{,}450\) books in its children’s and young adult section and \(243{,}120\) books in its adult section. It buys \(15{,}230\) new children’s and young adult books and \(22{,}845\) new adult books. How many books does the library have after the purchases?

Hints

- You may update each section separately. - Another method is to find the original library total first. - Both methods should combine all original books and all new books.

Solution

1. The children’s and young adult section then has \(125{,}450+15{,}230=140{,}680\) books. 2. The adult section then has \(243{,}120+22{,}845=265{,}965\) books. 3. The new library total is \(140{,}680+265{,}965=406{,}645\). 4. Another method is to add the original total, \(125{,}450+243{,}120=368{,}570\), and the total purchases, \(15{,}230+22{,}845=38{,}075\). Then \(368{,}570+38{,}075=406{,}645\).

Answer

The library has \(406{,}645\) books after the purchases.
Multi-step problems with addition and subtraction 45
Two wildlife parks compare their animal populations. Greenwood Park has \(156{,}780\) birds and \(42{,}350\) mammals. Lakeside Park has \(189{,}200\) birds and \(12{,}400\) mammals. During the summer: - Greenwood gains \(12{,}450\) birds, while its mammal population decreases by \(3120\). - Lakeside loses \(5600\) birds and gains \(18{,}700\) mammals. Which park has more animals after these changes, and what is the difference?

Hints

- Find the final population of each park separately. - Pay attention to which changes increase and which decrease each population. - Compare the two final totals and subtract to find the difference.

Solution

1. Greenwood’s new total is \(156{,}780+42{,}350+12{,}450-3120=208{,}460\). 2. Lakeside’s new total is \(189{,}200+12{,}400-5600+18{,}700=214{,}700\). 3. Since \(214{,}700>208{,}460\), Lakeside has more animals. 4. The difference is \(214{,}700-208{,}460=6240\) animals.

Answer

Lakeside Park has more animals. It has \(6240\) more animals than Greenwood Park.
Multi-step problems with addition and subtraction 46
A concert sells \(38{,}450\) tickets in Chicago. It sells \(12{,}675\) more tickets in Dallas than in Chicago. It sells \(15{,}340\) fewer tickets in Seattle than in Dallas. How many tickets are sold in the three cities altogether?

Hints

- Translate each comparison into a calculation one step at a time. - Find the number of tickets in each city before finding the total. - Seattle’s amount is compared with Dallas’s amount. - A table may help organize the three values.

Solution

1. Dallas sells \(38{,}450+12{,}675=51{,}125\) tickets. 2. Seattle sells \(51{,}125-15{,}340=35{,}785\) tickets. 3. The total is \(38{,}450+51{,}125+35{,}785=125{,}360\) tickets.

Answer

The concert sells \(125{,}360\) tickets in the three cities altogether.
Multi-step problems with addition and subtraction 47
A truck driver records the distance driven over three days. On Monday, the driver travels \(365\,\text{miles}\). On Tuesday, the driver travels \(145\,\text{miles}\) more than on Monday. On Wednesday, the driver travels \(210\,\text{miles}\) less than on Tuesday. How many miles does the driver travel altogether?

Hints

- Determine Tuesday’s distance from Monday before finding Wednesday’s distance. - Wednesday is compared with Tuesday, not directly with Monday. - Add the three daily distances only after both missing amounts are known.

Solution

1. Tuesday’s distance is \(365+145=510\,\text{miles}\). 2. Wednesday’s distance is \(510-210=300\,\text{miles}\). 3. The three-day total is \(365+510+300=1175\,\text{miles}\).

Answer

The driver travels \(1175\,\text{miles}\) altogether.
Multi-step problems with addition and subtraction 48
A wildlife park has \(240\) visitors on Friday. On Saturday, it has \(65\) more visitors than on Friday. On Sunday, it has \(120\) fewer visitors than on Saturday. How many visitors come to the park over the three days altogether?

Hints

- Find the Saturday attendance first. - Use Saturday's attendance to find Sunday's attendance. - Add the attendance for Friday, Saturday, and Sunday.

Solution

1. Find the Saturday attendance: \(240 + 65 = 305\). 2. Find the Sunday attendance: \(305 - 120 = 185\). 3. Add the attendance for all three days: \(240 + 305 + 185 = 730\).

Answer

The wildlife park has \(730\) visitors over the three days altogether.
Multi-step problems with addition and subtraction 49
Lucas wants to read a \(900\)-page book during vacation. He reads \(215\) pages in the first week. In the second week, he reads \(40\) fewer pages than in the first week. In the third week, he reads \(250\) pages. How many pages must Lucas read in the fourth week to finish the book?

Hints

- First find how many pages Lucas reads in the second week. - Add the pages read during the first three weeks. - Subtract that total from \(900\).

Solution

1. Find the pages read in the second week: \(215 - 40 = 175\). 2. Find the total read in the first three weeks: \(215 + 175 + 250 = 640\). 3. Subtract from the total number of pages: \(900 - 640 = 260\).

Answer

Lucas must read \(260\) pages in the fourth week.
Multi-step problems with addition and subtraction 50
Three ribbons are sewn together for a festival decoration. The red ribbon is \(245\,\text{cm}\) long. The blue ribbon is \(60\,\text{cm}\) shorter than the red ribbon but \(30\,\text{cm}\) longer than the green ribbon. The seams use a total of \(25\,\text{cm}\) of ribbon. How long is the finished decoration?

Hints

- Use the red ribbon to find the blue ribbon. - Use the blue ribbon to find the green ribbon. - Add all three lengths, then subtract the amount used in the seams.

Solution

1. Find the length of the blue ribbon: \(245 - 60 = 185\,\text{cm}\). 2. Find the length of the green ribbon: \(185 - 30 = 155\,\text{cm}\). 3. Add the three ribbon lengths: \(245 + 185 + 155 = 585\,\text{cm}\). 4. Subtract the ribbon used in the seams: \(585 - 25 = 560\,\text{cm}\).

Answer

The finished decoration is \(560\,\text{cm}\) long.
Multi-step problems with addition and subtraction 51
Use the month lengths below to compare the first half of a year (January through June) with the second half (July through December). <table><tr><th>Months</th><th>Days in order</th></tr><tr><td>January–June</td><td>\(31,28,31,30,31,30\)</td></tr><tr><td>July–December</td><td>\(31,31,30,31,30,31\)</td></tr></table> In a leap year, February has \(29\) days instead of \(28\). a) How many days are in the first half of a non-leap year? b) How many days are in the second half? c) Which half is longer, and by how many days? d) How does that difference change in a leap year?

Hints

- Add the first six month lengths, then the last six. - Compare the two totals for the non-leap year. - Which month's length changes for a leap year, and which half contains it?

Solution

1. The first half has \(31+28+31+30+31+30=181\) days. 2. The second half has \(31+31+30+31+30+31=184\) days. 3. The second half has \(184-181=3\) more days. 4. In a leap year, the first half has \(182\) days and the second still has \(184\), so the difference becomes \(2\) days.

Answer

a) \(181\) days b) \(184\) days c) The second half, by \(3\) days d) The second half is longer by only \(2\) days.
Multi-step problems with addition and subtraction 52
The table shows the tons of paper recycled in three cities during two consecutive years. <table> <tr><th>City</th><th>Year 1</th><th>Year 2</th></tr> <tr><td>Oakton</td><td>\(12{,}450\,\text{tons}\)</td><td>\(15{,}800\,\text{tons}\)</td></tr> <tr><td>Pineville</td><td>\(8900\,\text{tons}\)</td><td>\(12{,}150\,\text{tons}\)</td></tr> <tr><td>Maple City</td><td>\(5650\,\text{tons}\)</td><td>\(9400\,\text{tons}\)</td></tr> </table> a) Which city had the greatest increase in recycled paper from Year 1 to Year 2? b) How many more tons of paper were recycled across all three cities in Year 2 than in Year 1?

Hints

- How can you find the difference between two values? - Find the increase for each city, and then compare the increases. - Can you find the overall increase without first finding both yearly totals? - Line up place values carefully when adding large numbers.

Solution

1. Find the increase for each city. Oakton: \(15{,}800 - 12{,}450 = 3350\) tons. Pineville: \(12{,}150 - 8900 = 3250\) tons. Maple City: \(9400 - 5650 = 3750\) tons. Maple City has the greatest increase. 2. Find the total for Year 1: \(12{,}450 + 8900 + 5650 = 27{,}000\) tons. 3. Find the total for Year 2: \(15{,}800 + 12{,}150 + 9400 = 37{,}350\) tons. 4. Subtract the totals: \(37{,}350 - 27{,}000 = 10{,}350\) tons. The same result comes from adding the three city increases.

Answer

a) Maple City, with an increase of \(3750\) tons b) \(10{,}350\) tons
Multi-step problems with addition and subtraction 53
Three fictional museums summarized their attendance for two years. <table> <tr><th>Museum</th><th>Visitors in 2022</th><th>Visitors in 2023</th></tr> <tr><td>Harbor Science Center</td><td>\(215{,}400\)</td><td>\(248{,}900\)</td></tr> <tr><td>Maple Art Museum</td><td>\(178{,}250\)</td><td>\(165{,}300\)</td></tr> <tr><td>Riverbend History Museum</td><td>\(324{,}800\)</td><td>\(352{,}150\)</td></tr> </table> a) Find the total attendance at all three museums for each year. b) Find the difference between the two yearly totals. Was there an overall increase or decrease?

Hints

- Treat each year as its own total across all three rows. - One museum changes in a different direction from the other two, so use the actual yearly totals rather than judging row by row. - Compare the two yearly totals after both are known.

Solution

1. The 2022 total is \(215{,}400+178{,}250+324{,}800=718{,}450\). 2. The 2023 total is \(248{,}900+165{,}300+352{,}150=766{,}350\). 3. The difference is \(766{,}350-718{,}450=47{,}900\). 4. Because the 2023 total is greater, attendance increased overall by \(47{,}900\) visitors.

Answer

a) 2022: \(718{,}450\) visitors 2023: \(766{,}350\) visitors b) An increase of \(47{,}900\) visitors
Multi-step problems with addition and subtraction 54
A bookstore has three locations. The table shows how many books each location sold in April and May. <table> <tr><th>Location</th><th>April</th><th>May</th></tr> <tr><td>Downtown</td><td>\(12{,}450\)</td><td>\(11{,}800\)</td></tr> <tr><td>Station</td><td>\(8920\)</td><td>\(10{,}250\)</td></tr> <tr><td>Westside</td><td>\(4130\)</td><td>\(4560\)</td></tr> </table> a) At which location were fewer books sold in May than in April? By how many books did sales decrease there? b) How many books were sold at all three locations over both months altogether?

Hints

- Compare the two entries in each row to find where the May value is smaller. - For part b), every sales entry in the table must be included. - You can first find a total for each month and then add the two totals.

Solution

1. Compare April and May at each location. Only Downtown decreased, from \(12{,}450\) books to \(11{,}800\) books. 2. Find the decrease: \(12{,}450 - 11{,}800 = 650\) books. 3. Add the April sales: \(12{,}450 + 8920 + 4130 = 25{,}500\). 4. Add the May sales: \(11{,}800 + 10{,}250 + 4560 = 26{,}610\). 5. Add the monthly totals: \(25{,}500 + 26{,}610 = 52{,}110\) books.

Answer

a) Downtown; sales decreased by \(650\) books. b) \(52{,}110\) books
Multi-step problems with addition and subtraction 55
An orchard stores \(325\,\text{kg}\) of apples and \(180\,\text{kg}\) of pears. In the morning, \(115\,\text{kg}\) of apples are delivered to a store. In the afternoon, \(95\,\text{kg}\) of newly harvested pears are added. How many kilograms of fruit are in storage at the end of the day?

Hints

- Subtract the apples that are delivered. - Add the newly harvested pears. - Add the final amounts of apples and pears.

Solution

1. Find the apples remaining: \(325 - 115 = 210\,\text{kg}\). 2. Find the new amount of pears: \(180 + 95 = 275\,\text{kg}\). 3. Add the final amounts: \(210 + 275 = 485\,\text{kg}\).

Answer

There are \(485\,\text{kg}\) of fruit in storage at the end of the day.
Multi-step problems with addition and subtraction 56
An old castle was completed in \(1580\). a) A new tower was added exactly \(120\) years later. In what year was it added? b) A gatehouse was restored \(75\) years after the tower was added. In what year was the gatehouse restored? c) How many years passed from the castle’s completion to the gatehouse restoration?

Hints

- Add the first elapsed time to the castle’s completion year. - Use the tower year as the starting point for the next event. - To find the total elapsed time, compare the first and last years.

Solution

1. Find the year the tower was added: \(1580 + 120 = 1700\). 2. Find the year the gatehouse was restored: \(1700 + 75 = 1775\). 3. Find the total elapsed time: \(1775 - 1580 = 195\) years.

Answer

a) The tower was added in \(1700\). b) The gatehouse was restored in \(1775\). c) \(195\) years passed.
Multi-step problems with addition and subtraction 57
A warehouse shipped \(67{,}804\), \(123{,}900\), \(8560\), and \(204{,}050\) packages during four different periods. a) Find the difference between the greatest and least shipment totals. b) Add the two least shipment totals. Then subtract that sum from the greatest shipment total.

Hints

- Order the four totals before doing any calculations. - For part a, subtract the least total from the greatest. - For part b, identify and add the two least totals first. - Keep place values aligned when adding and subtracting.

Solution

1. Order the totals: \(8560 < 67{,}804 < 123{,}900 < 204{,}050\). 2. For a), subtract the least total from the greatest: \(204{,}050 - 8560 = 195{,}490\). 3. For b), add the two least totals: \(8560 + 67{,}804 = 76{,}364\). 4. Subtract that sum from the greatest total: \(204{,}050 - 76{,}364 = 127{,}686\).

Answer

a) \(195{,}490\) b) \(127{,}686\)
Multi-step problems with addition and subtraction 58
Four fourth-grade classes collect paper for a recycling contest: - Class 4A: \(345{,}600\,\text{g}\) - Class 4B: \(120{,}850\,\text{g}\) - Class 4C: \(402{,}300\,\text{g}\) - Class 4D: \(98{,}760\,\text{g}\) a) What is the difference between the greatest and least amounts collected? b) The two classes with the least amounts combine their paper. How many more grams would they need to equal the amount collected by Class 4C?

Hints

- Identify the greatest and least amounts for part a. - For part b, identify and add the two least amounts. - Subtract their combined amount from Class 4C's amount.

Solution

1. The greatest amount is \(402{,}300\,\text{g}\), and the least amount is \(98{,}760\,\text{g}\). 2. Find the difference for part a: \(402{,}300\,\text{g} - 98{,}760\,\text{g} = 303{,}540\,\text{g}\). 3. The two least amounts are \(98{,}760\,\text{g}\) and \(120{,}850\,\text{g}\). 4. Combine them: \(98{,}760\,\text{g} + 120{,}850\,\text{g} = 219{,}610\,\text{g}\). 5. Find the amount still needed: \(402{,}300\,\text{g} - 219{,}610\,\text{g} = 182{,}690\,\text{g}\).

Answer

a) The difference is \(303{,}540\,\text{g}\). b) The two classes need \(182{,}690\,\text{g}\) more.
Multi-step problems with addition and subtraction 59
An orchard harvests \(4250\,\text{kg}\) of apples, pears, and plums altogether. The apples and pears together have a mass of \(3120\,\text{kg}\). The orchard harvests \(1845\,\text{kg}\) of apples. How many kilograms of each type of fruit are harvested?

Hints

- Use the combined apple-and-pear amount to find the pears. - Subtract the apple-and-pear amount from the total to find the plums. - Add all three amounts to check.

Solution

1. The apple harvest is \(1845\,\text{kg}\). 2. Find the pear harvest: \(3120\,\text{kg} - 1845\,\text{kg} = 1275\,\text{kg}\). 3. Find the plum harvest: \(4250\,\text{kg} - 3120\,\text{kg} = 1130\,\text{kg}\). 4. Check: \(1845\,\text{kg} + 1275\,\text{kg} + 1130\,\text{kg} = 4250\,\text{kg}\).

Answer

The orchard harvests \(1845\,\text{kg}\) of apples, \(1275\,\text{kg}\) of pears, and \(1130\,\text{kg}\) of plums.
Multi-step problems with addition and subtraction 60
An adult elephant has a mass of \(6200\,\text{kg}\), which is \(3850\,\text{kg}\) more than a rhinoceros. A hippopotamus has a mass that is \(540\,\text{kg}\) less than the rhinoceros. What are the masses of the rhinoceros and the hippopotamus? Which of the three animals has the least mass?

Hints

- The elephant's mass is greater, so subtract to find the rhinoceros's mass. - Then subtract again to find the hippopotamus's mass. - Compare all three masses.

Solution

1. Find the rhinoceros's mass: \(6200\,\text{kg} - 3850\,\text{kg} = 2350\,\text{kg}\). 2. Find the hippopotamus's mass: \(2350\,\text{kg} - 540\,\text{kg} = 1810\,\text{kg}\). 3. Compare the masses: \(1810\,\text{kg} < 2350\,\text{kg} < 6200\,\text{kg}\), so the hippopotamus has the least mass.

Answer

The rhinoceros has a mass of \(2350\,\text{kg}\), and the hippopotamus has a mass of \(1810\,\text{kg}\). The hippopotamus has the least mass.
Multi-step problems with addition and subtraction 61
An elementary school collects recyclable materials for a project. The table shows how many pounds of paper and plastic were collected during four months. <table> <thead> <tr> <th>Month</th> <th>Paper (lb)</th> <th>Plastic (lb)</th> </tr> </thead> <tbody> <tr> <td>March</td> <td>\(456\)</td> <td>\(212\)</td> </tr> <tr> <td>April</td> <td>\(512\)</td> <td>\(198\)</td> </tr> <tr> <td>May</td> <td>\(489\)</td> <td>\(245\)</td> </tr> <tr> <td>June</td> <td>\(534\)</td> <td>\(221\)</td> </tr> </tbody> </table> During which month was the greatest total weight of material collected? How many more pounds was that than in the month with the least total weight?

Hints

- First find the total amount collected in each month. - Compare the monthly totals to find the greatest and least. - What is the difference between those two totals?

Solution

1. Find the total for each month. March: \(456 + 212 = 668\) pounds. April: \(512 + 198 = 710\) pounds. May: \(489 + 245 = 734\) pounds. June: \(534 + 221 = 755\) pounds. 2. The greatest total is \(755\) pounds in June, and the least total is \(668\) pounds in March. 3. Find the difference: \(755 - 668 = 87\) pounds.

Answer

The greatest total was collected in June. It was \(87\) pounds more than the March total.
Multi-step problems with addition and subtraction 62
Write a word problem that can be solved with these two steps: 1) \(1200+500=1700\) 2) \(1700-800=900\) Write your word problem and its answer.

Hints

- Choose a situation in which something is added first and removed later. - Possible contexts include inventory, animals, or books. - Use the given numbers exactly in the story. - End with a question whose answer is \(900\).

Solution

1. A valid problem must begin with a quantity of \(1200\), increase it by \(500\), and then decrease the new quantity by \(800\). 2. The intermediate quantity is \(1700\), and the final quantity is \(900\). 3. The context, units, and wording may vary, but both operations and all three quantities must match the story.

Answer

Answers will vary. Example: A toy store has \(1200\) marbles. It receives \(500\) more and then sells \(800\). The store has \(900\) marbles left.
Multi-step problems with addition and subtraction 63
A hiking group starts at a mountain lodge \(4650\,\text{ft}\) above sea level. The entire trail is \(7\) miles long. The hikers climb \(2080\,\text{ft}\) to a viewpoint, then descend \(715\,\text{ft}\) to a lake. What is the lake’s elevation above sea level?

Hints

- Identify how far the hikers move upward. - A descent decreases the current elevation. - Decide whether every number in the problem is needed.

Solution

1. Find the viewpoint’s elevation: \(4650\,\text{ft} + 2080\,\text{ft} = 6730\,\text{ft}\). 2. Subtract the descent: \(6730\,\text{ft} - 715\,\text{ft} = 6015\,\text{ft}\). 3. The total trail length is not needed to determine the elevation.

Answer

The lake is \(6015\,\text{ft}\) above sea level.
Multi-step problems with addition and subtraction 64
In spring, the water in a reservoir is \(110\,\text{ft}\) below the top of the dam. After heavy rain, the water level rises \(40\,\text{ft}\). During a later dry period, it falls \(23\,\text{ft}\). How far below the top of the dam is the water after the dry period? Explain with calculations.

Hints

- When the water rises, does its distance below the top increase or decrease? - Treat the top of the dam as a fixed reference point. - Decide which operation matches each change in the water level.

Solution

1. When the water rises, its distance below the top becomes smaller: \(110\,\text{ft} - 40\,\text{ft} = 70\,\text{ft}\). 2. When the water falls, its distance below the top becomes larger: \(70\,\text{ft} + 23\,\text{ft} = 93\,\text{ft}\).

Answer

The water is \(93\,\text{ft}\) below the top of the dam.
Multi-step problems with addition and subtraction 65
A remotely operated underwater robot with a mass of \(150\,\text{kg}\) is exploring the ocean floor. It begins \(412\,\text{m}\) below the surface, descends another \(289\,\text{m}\) to collect a sample, and later rises \(154\,\text{m}\). What is the robot’s current depth below the surface?

Hints

- A descent increases the depth below the surface. - A rise decreases the depth below the surface. - Decide which information is actually needed.

Solution

1. After descending, the robot’s depth is \(412\,\text{m} + 289\,\text{m} = 701\,\text{m}\). 2. After rising, its depth is \(701\,\text{m} - 154\,\text{m} = 547\,\text{m}\). 3. The robot’s mass is not needed to calculate its depth.

Answer

The robot is \(547\,\text{m}\) below the surface.
Multi-step problems with addition and subtraction 66
Last year, a library put \(710\) books on display. This year, it has two display sections. The fiction section has \(240\) fewer books than last year's display. The nonfiction section has \(130\) more books than the fiction section. How many books are in each section this year?

Hints

- Compare the fiction section with last year's display. - Which section's count must you know before finding the other? - Check whether nonfiction should be larger or smaller than fiction.

Solution

1. The fiction section has \(710 - 240 = 470\) books. 2. The nonfiction section has \(470 + 130 = 600\) books.

Answer

Fiction: \(470\) books. Nonfiction: \(600\) books.
Multi-step problems with addition and subtraction 67
Three deliveries bring \(1000\) notebooks to a district warehouse altogether. The first delivery has \(350\) notebooks. The second has \(100\) fewer notebooks than the first. How many notebooks are in the third delivery?

Hints

- Determine the second delivery from its comparison with the first. - Combine the two known deliveries before using the overall total. - Check that all three delivery amounts add to \(1000\).

Solution

1. The second delivery has \(350-100=250\) notebooks. 2. The first two deliveries contain \(350+250=600\) notebooks. 3. The third delivery has \(1000-600=400\) notebooks.

Answer

The third delivery contains \(400\) notebooks.
Multi-step problems with addition and subtraction 68
A public library opened in \(1974\) and was first expanded in \(1999\). a) How many years after opening did the expansion occur? b) In \(2012\), how old was the library, and how many years had passed since the expansion? c) In \(2024\), how many years older was the library than it had been at the time of the expansion?

Hints

- Use the opening year to establish the library’s age at the expansion. - Later parts compare later ages with that earlier milestone rather than asking three unrelated date differences. - Keep “age of the library” and “years since the expansion” distinct.

Solution

1. The expansion occurred \(1999-1974=25\) years after opening. 2. In \(2012\), the library was \(2012-1974=38\) years old. 3. The time from the expansion to \(2012\) was \(38-25=13\) years. 4. In \(2024\), the library was \(2024-1974=50\) years old. 5. Compared with its age at expansion, it was \(50-25=25\) years older.

Answer

a) \(25\) years after opening b) \(38\) years old, and \(13\) years after the expansion c) \(25\) years older than at the time of the expansion
Multi-step problems with addition and subtraction 69
A giant tortoise was born in \(1888\) and lived for \(134\) years. An elephant in the same wildlife park was born when the tortoise was \(56\) years old. The elephant lived for \(71\) years. a) In what year did the tortoise die? b) In what year was the elephant born? c) In what year did the elephant die? Did it die before or after the tortoise?

Hints

- First find the tortoise’s birth and death years. - Use the tortoise’s age to find the elephant’s birth year. - Add the elephant’s lifespan to its birth year. - Compare the two death years.

Solution

1. Find the tortoise’s death year: \(1888 + 134 = 2022\). 2. Find the elephant’s birth year: \(1888 + 56 = 1944\). 3. Find the elephant’s death year: \(1944 + 71 = 2015\). 4. Since \(2015 < 2022\), the elephant died before the tortoise.

Answer

a) The tortoise died in \(2022\). b) The elephant was born in \(1944\). c) The elephant died in \(2015\), before the tortoise.
Multi-step problems with addition and subtraction 70
An elementary school celebrated its \(125\)th anniversary in \(2024\). a) In what year was the school founded? b) A nearby school opened in \(1875\). How many years older is the nearby school?

Hints

- To find the founding year, work backward from \(2024\). - First find when the school was founded. - Then compare that year with \(1875\).

Solution

1. Subtract the school's age from the anniversary year: \(2024 - 125 = 1899\). The first school was founded in \(1899\). 2. Compare the founding years: \(1899 - 1875 = 24\). 3. The nearby school is \(24\) years older.

Answer

a) The school was founded in \(1899\). b) The nearby school is \(24\) years older.
Multi-step problems with addition and subtraction 71
A school garden covers \(8000\,\text{ft}^2\). A lawn uses \(3500\,\text{ft}^2\), and a pond uses \(450\,\text{ft}^2\). The rest of the garden contains vegetable beds. Find the area of the vegetable beds.

Hints

- Find the combined area of the lawn and pond. - What part of the full garden area remains?

Solution

1. The lawn and pond take up \(3500+450=3950\,\text{ft}^2\). 2. The vegetable beds take up \(8000-3950=4050\,\text{ft}^2\).

Answer

\(4050\,\text{ft}^2\)
Multi-step problems with addition and subtraction 72
Mia and Leo earn points in a game. Mia earns \(140\) points in the first round and \(260\) points in the second round. Leo starts with \(320\) points but loses \(150\) points in the second round. The calculation tree shows how to compare Mia’s total with Leo’s remaining points. a) Find the values for the empty boxes in the calculation tree. b) What is the final difference in the bottom box?
Figure for problem 531712

Hints

- On the left side of the tree, which two numbers are added? - On the right side, what number is subtracted from \(320\)? - After finding the two middle results, subtract to find the bottom result.

Solution

1. Find Mia’s total: \(140 + 260 = 400\). 2. Find Leo’s remaining points: \(320 - 150 = 170\). 3. Find the difference: \(400 - 170 = 230\).

Answer

a) The middle boxes are \(400\) on the left and \(170\) on the right. b) The final difference is \(230\) points.
Multi-step problems with addition and subtraction 73
A school library begins the week with \(145\) books on a shelf. On Monday, \(18\) books are checked out and \(22\) are returned. On Tuesday, a donated box containing \(10\) mystery books, \(4\) nonfiction books, and \(1\) graphic novel is added, while \(7\) damaged books are removed. On Wednesday, \(12\) more books are returned than are checked out. On Thursday, a class checks out \(24\) books and a teacher returns \(3\). Fifteen students read in the library without checking out books. On Friday, \(31\) books are returned and \(19\) are checked out. How many books are on the shelf at the end of the week?

Hints

- Determine the net change for each day. - Decide which details affect the number of books on the shelf. - “Twelve more returned than checked out” means a net increase of \(12\). - Update the running total one day at a time.

Solution

1. After Monday, there are \(145-18+22=149\) books. 2. The donation contains \(10+4+1=15\) books. After Tuesday, there are \(149+15-7=157\) books. 3. Wednesday gives a net increase of \(12\), so there are \(157+12=169\) books. 4. The students who only read do not change the shelf total. After Thursday, there are \(169-24+3=148\) books. 5. After Friday, there are \(148+31-19=160\) books.

Answer

\(160\) books
Multi-step problems with addition and subtraction 74
An orchard harvests \(52{,}480\,\text{kg}\) of apples. It harvests \(14{,}650\,\text{kg}\) fewer pears than apples and \(9320\,\text{kg}\) fewer plums than pears. The orchard sells \(95{,}000\,\text{kg}\) of fruit to grocery stores. The rest will be made into juice. How many kilograms of fruit remain for juice?

Hints

- Find the amount of each type of fruit. - Add the three harvested amounts. - Subtract the amount sold from the total harvest.

Solution

1. Find the mass of the pears: \(52{,}480\,\text{kg} - 14{,}650\,\text{kg} = 37{,}830\,\text{kg}\). 2. Start with \(37{,}830\,\text{kg}\) of pears and subtract \(9320\,\text{kg}\). The mass of the plums is \(28{,}510\,\text{kg}\). 3. Find the total harvest: \(52{,}480\,\text{kg} + 37{,}830\,\text{kg} + 28{,}510\,\text{kg} = 118{,}820\,\text{kg}\). 4. Subtract the amount sold: \(118{,}820\,\text{kg} - 95{,}000\,\text{kg} = 23{,}820\,\text{kg}\).

Answer

\(23{,}820\,\text{kg}\) of fruit remain for juice.
Multi-step problems with addition and subtraction 75
Three school districts collect paper during a countywide recycling drive. Pine Valley District collects \(18{,}560\,\text{kg}\). Meadow Creek District collects \(4230\,\text{kg}\) more than Pine Valley. Hillview District collects \(3150\,\text{kg}\) less than Meadow Creek. A recycling center has a container that holds \(60{,}000\,\text{kg}\). Will all the collected paper fit? If not, how many kilograms will not fit?

Hints

- Determine each district’s collection amount from the comparisons. - Combine the three amounts before making the capacity decision. - If the collection exceeds capacity, the difference between those two quantities is the amount that will not fit.

Solution

1. Meadow Creek collects \(18{,}560+4230=22{,}790\,\text{kg}\). 2. Hillview collects \(22{,}790-3150=19{,}640\,\text{kg}\). 3. The total is \(18{,}560+22{,}790+19{,}640=60{,}990\,\text{kg}\). 4. Since \(60{,}990>60{,}000\), all the paper will not fit. 5. The excess is \(60{,}990-60{,}000=990\,\text{kg}\).

Answer

No. \(990\,\text{kg}\) of paper will not fit in the container.
Multi-step problems with addition and subtraction 76
A nursery grows \(320\) red tulips and \(280\) yellow tulips. It grows \(150\) fewer daffodils than the total number of tulips. a) How many daffodils does the nursery grow? b) Suppose the nursery grew \(50\) more yellow tulips while the number of daffodils stayed \(150\) below the total number of tulips. By how much would the number of daffodils change? Explain without fully recalculating.

Hints

- First find the total number of tulips. - Read carefully what the daffodil count is \(150\) fewer than. - In part b, consider what happens when one quantity increases while a fixed difference is maintained.

Solution

1. Find the total number of tulips: \(320 + 280 = 600\). 2. Find the number of daffodils: \(600 - 150 = 450\). 3. In part b, the difference of \(150\) stays fixed. Increasing the tulip total by \(50\) therefore increases the daffodil count by \(50\).

Answer

a) The nursery grows \(450\) daffodils. b) The number of daffodils would increase by \(50\) because the tulip total increases by \(50\) while the difference remains fixed.
Multi-step problems with addition and subtraction 77
One crate has \(45\,\text{kg}\) more apples than a second crate. Then \(28\,\text{kg}\) of apples are removed from the first crate, and an unknown mass is removed from the second crate. Afterward, the first crate still has \(32\,\text{kg}\) more apples than the second crate. How many kilograms of apples were removed from the second crate?

Hints

- Track how each removal affects the difference between the two crates, not just the individual masses. - Removing from the larger crate and removing from the smaller crate change the difference in opposite directions. - Compare the original and final differences to check your reasoning.

Solution

1. If only the first removal occurred, the original \(45\,\text{kg}\) difference would decrease to \(45-28=17\,\text{kg}\). 2. The actual final difference is \(32\,\text{kg}\), which is \(32-17=15\,\text{kg}\) greater. 3. Removing apples from the second crate increases the first crate’s lead by exactly the amount removed, so \(15\,\text{kg}\) were removed from the second crate.

Answer

\(15\,\text{kg}\) of apples were removed from the second crate.

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