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Divide decimals by whole numbers

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5108525
A case of \(12\) identical bags of flour weighs \(12.6\) lb altogether. a) Find the weight of one bag. b) What would \(100\) of these bags weigh, not including the pallet?

Hints

- Describe what the total weight and number of bags tell you. - Find the weight of one bag before finding the weight of \(100\) bags. - Think about how multiplying by \(100\) changes place value.

Solution

1. For a), divide the total weight by the number of bags: \(12.6\div12=1.05\) lb. 2. For b), \(1.05\times100=105\) lb.

Answer

a) \(1.05\) lb b) \(105\) lb
5116775
Divide and give each result in the unit shown in parentheses. a) \(4.5\,\text{m} \div 6\) in \(\text{cm}\) b) \(0.12\,\text{km} \div 8\) in \(\text{m}\)

Hints

- You can divide as though the numbers were whole numbers and then place the decimal point. - How many centimeters are in one meter? - How many meters are in one kilometer? - You may also convert to the requested unit before dividing.

Solution

1. For part a, \(4.5\,\text{m} \div 6 = 0.75\,\text{m}\). Since \(0.75\,\text{m} = 75\,\text{cm}\), the result is \(75\,\text{cm}\). 2. For part b, \(0.12\,\text{km} \div 8 = 0.015\,\text{km}\). Since \(0.015\,\text{km} = 15\,\text{m}\), the result is \(15\,\text{m}\).

Answer

a) \(75\,\text{cm}\) b) \(15\,\text{m}\)
5169625
A school art club orders \(8\) identical paintbrush sets. The total cost is \(\$62.00\). How much does one paintbrush set cost?

Hints

- Divide the total cost by the number of identical sets. - Keep the decimal point aligned as you divide. - Multiply your quotient by \(8\) to check it.

Solution

1. Divide the total cost by the number of sets: \(\$62.00 \div 8 = \$7.75\). 2. Check: \(8 \times \$7.75 = \$62.00\).

Answer

One paintbrush set costs \(\$7.75\).
5169635
Nine friends rent bicycles for a group ride. The total rental bill is \(\$110.70\). How much should each friend pay if they split the bill equally?

Hints

- Divide the total bill by the number of friends. - Keep the decimal point aligned during the division. - Multiply the amount per person by \(9\) to check your answer.

Solution

1. Divide the total bill equally among the nine friends: \(\$110.70 \div 9 = \$12.30\). 2. Check: \(9 \times \$12.30 = \$110.70\).

Answer

Each friend should pay \(\$12.30\).
5209285
A gardener has a \(13.5\)-meter irrigation hose and cuts it into \(6\) equal pieces. Use decimal division to find the length of each piece in meters.

Hints

- The answer should be a little more than \(2\,\text{m}\). - Divide as you would with whole numbers, placing the decimal point in the quotient correctly. - Check by multiplying your quotient by \(6\).

Solution

1. Divide the total length by the number of equal pieces: \(13.5 \div 6\). 2. Using decimal division, \(13.5 \div 6 = 2.25\). 3. Each piece is \(2.25\,\text{m}\) long.

Answer

Each piece is \(2.25\,\text{m}\) long.
5108975
A shipment of \(25\) identical bags of flour weighs \(312.5\) lb altogether. A second shipment has \(40\) bags from another supplier and weighs \(480\) lb altogether. a) Find the weight of one bag in each shipment. b) Which bag is heavier? Give the difference in ounces.

Hints

- Divide each shipment's total weight by its number of bags. - Compare the two unit weights. - Convert the difference from pounds to ounces.

Solution

1. First shipment: \(312.5\div25=12.5\) lb per bag. 2. Second shipment: \(480\div40=12\) lb per bag. 3. The first bag is heavier by \(12.5-12=0.5\) lb. 4. Since \(1\,\text{lb}=16\,\text{oz}\), \(0.5\times16=8\) oz.

Answer

a) First shipment: \(12.5\) lb per bag; second shipment: \(12\) lb per bag b) The first bag is heavier by \(8\) oz.
5108985
A sports club has \(12.5\) cups of juice concentrate to divide equally among \(50\) bottles for a tournament. a) How many cups of concentrate go in each bottle? b) A coach suggests using \(0.3\) cup per bottle. Explain mathematically why there is not enough concentrate for that plan.

Hints

- Divide the total amount equally among the bottles. - For part b), find the total amount needed if every bottle gets the proposed amount.

Solution

1. For a), divide the concentrate equally: \(12.5\div50=0.25\) cup per bottle. 2. For b), \(0.3\times50=15\) cups would be needed. 3. Since \(15>12.5\), the club does not have enough concentrate.

Answer

a) \(0.25\) cup per bottle b) The plan would require \(15\) cups, but only \(12.5\) cups are available.
5169615
Six students are buying a farewell gift for their teacher. The gift costs \(\$112.50\). If they share the cost equally, how much does each student pay? Estimate first.

Hints

- Choose a nearby dollar amount that is easy to divide by \(6\). - You can express the total cost in cents before dividing. - Write the quotient as a dollar amount with two decimal places.

Solution

1. Estimate with a nearby compatible number: \(\$120 \div 6 = \$20\). 2. Divide the exact cost by \(6\): \(\$112.50 \div 6 = \$18.75\). 3. The exact amount is close to the estimate, so it is reasonable.

Answer

An estimate is \(\$20\) per student. Each student pays exactly \(\$18.75\).
5179415
A teacher buys \(5\) notebooks for \(\$2.40\) each and \(4\) identical pens. The total cost is \(\$22.00\). How much does one pen cost?

Hints

- Find the total cost of the notebooks first. - Subtract that amount from the full bill. - Divide the remaining amount equally among the four pens.

Solution

1. The notebooks cost \(5 \times \$2.40 = \$12.00\). 2. The four pens cost \(\$22.00 - \$12.00 = \$10.00\). 3. One pen costs \(\$10.00 \div 4 = \$2.50\).

Answer

One pen costs \(\$2.50\).
5180645
Lucas buys \(5\) notebooks and \(3\) highlighters. He pays with \(\$10.00\) and receives \(\$2.50\) in change. Each highlighter costs \(\$1.50\). How much does one notebook cost?

Hints

- First find the total amount Lucas spends. - How much do the three highlighters cost altogether? - Subtract the highlighter cost to find the cost of all five notebooks. - Then divide to find the cost of one notebook.

Solution

1. Find the total amount spent: \(\$10.00 - \$2.50 = \$7.50\). 2. Find the cost of the three highlighters: \(3 \times \$1.50 = \$4.50\). 3. Find the cost of all five notebooks: \(\$7.50 - \$4.50 = \$3.00\). 4. Divide by the number of notebooks: \(\$3.00 \div 5 = \$0.60\).

Answer

One notebook costs \(\$0.60\).
5195215
A package of \(6\) pencils costs \(\$4.20\). An art project needs \(15\) pencils at the same price per pencil. How much do the \(15\) pencils cost?

Hints

- Find the price of one pencil. - Multiply the unit price by \(15\). - Check that six times the unit price equals \(\$4.20\).

Solution

1. One pencil costs \(\$4.20 \div 6 = \$0.70\). 2. Fifteen pencils cost \(15 \times \$0.70 = \$10.50\).

Answer

The \(15\) pencils cost \(\$10.50\).
5200905
A store offers juice in two ways: - Offer A: \(3\) bottles cost \(\$3.90\). - Offer B: \(1\) bottle costs \(\$1.45\). a) Find the price per bottle for Offer A. b) Which offer costs less per bottle, and what is the difference?

Hints

- Divide Offer A’s total price by the number of bottles. - Compare the two unit prices. - Subtract the smaller unit price from the larger one.

Solution

1. Offer A costs \(\$3.90 \div 3 = \$1.30\) per bottle. 2. Since \(\$1.30 < \$1.45\), Offer A costs less per bottle. 3. The difference is \(\$1.45 - \$1.30 = \$0.15\).

Answer

a) Offer A costs \(\$1.30\) per bottle. b) Offer A costs less by \(\$0.15\) per bottle.
5211505
The Weber family buys \(2\) loaves of bread for \(\$4\) each and a bag of \(10\) rolls. Mr. Weber pays with \(\$20\) and receives \(\$7\) in change. How much does one roll cost?

Hints

- How much does the entire purchase cost after accounting for the change? - How much do the two loaves cost? - What is the total cost of the rolls? - Divide that amount by ten to find the price of one roll.

Solution

1. Find the total cost of the purchase: \(\$20 - \$7 = \$13\). 2. Find the cost of the two loaves: \(2 \times \$4 = \$8\). 3. Find the cost of all ten rolls: \(\$13 - \$8 = \$5.00\). 4. Divide by the number of rolls: \(\$5.00 \div 10 = \$0.50\).

Answer

One roll costs \(\$0.50\).
5213165
At one office-supply store, \(4\) identical binders cost \(\$8.40\) altogether. At another store, \(3\) of the same binders cost \(\$6.60\) altogether. At which store is one binder less expensive? Justify your answer with calculations.

Hints

- Find the price of one binder at each store. - You can change each dollar amount to cents before dividing. - Compare the two unit prices.

Solution

1. Find the unit price at the first store: \(840\text{ cents} \div 4 = 210\text{ cents}\), or \(\$2.10\). 2. Find the unit price at the second store: \(660\text{ cents} \div 3 = 220\text{ cents}\), or \(\$2.20\). 3. Compare the unit prices: \(\$2.10 < \$2.20\).

Answer

One binder is less expensive at the first store because it costs \(\$2.10\), compared with \(\$2.20\) at the second store.

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