Free Math Worksheets

- What does one-eighth mean as an operation? - What number do you divide by to find one-eighth of a set? - Could \(32 \div 8\) help you calculate \(320 \div 8\)?

1. Find one-eighth of the total: \(320 \div 8 = 40\). 2. Therefore, \(40\) guinea pigs have completely white fur.

There are \(40\) white guinea pigs.

- The whole circle represents all \(100\) students. - Multiply \(100\) by each fraction shown by the circle sectors.

1. Soccer represents \(\frac{1}{2}\) of the students: \(\frac{1}{2} \times 100 = 50\). 2. Swimming represents \(\frac{1}{4}\) of the students: \(\frac{1}{4} \times 100 = 25\). 3. Tennis also represents \(\frac{1}{4}\) of the students: \(\frac{1}{4} \times 100 = 25\).

Soccer: \(50\) students; swimming: \(25\) students; tennis: \(25\) students

- First find the weight of one-fifth of the flour. - After finding one part, how can you find two parts? - Which operation divides the total into equal groups?

1. Find one-fifth of the flour: \(600\,\text{lb} \div 5 = 120\,\text{lb}\). 2. Find two-fifths: \(2 \times 120\,\text{lb} = 240\,\text{lb}\).

The bakery uses \(240\,\text{lb}\) of flour during the morning.

- The largest sector represents the most popular snack. - Add fractions with the same denominator by adding their numerators. - Multiply the class size by the pretzel fraction.

1. The largest sector is apple, representing \(\frac{1}{2}\) of the class. 2. Add the banana and granola-bar fractions: \(\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}\). 3. Pretzel represents \(\frac{1}{4}\) of the class. Compute \(\frac{1}{4} \times 24 = 6\) students.

1. Apple 2. \(\frac{1}{4}\) 3. \(6\) students

- Multiply \(32\) by the fraction for each fruit. - Look for two sectors whose fractions add to \(\frac{1}{4}\). - Two eighths are equivalent to one-fourth.

1. Apples represent \(\frac{1}{2}\) of the class: \(\frac{1}{2} \times 32 = 16\) students. 2. Pears represent \(\frac{1}{8}\) of the class: \(\frac{1}{8} \times 32 = 4\) students. 3. Pears and strawberries each represent \(\frac{1}{8}\). Together, \(\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}\).

a) \(16\) students b) \(4\) students c) Pears and strawberries

- Count how many of the \(8\) sections are not shaded. - Divide the total trail length by \(8\) to find the length of one section. - Multiply the length of one section by the number of sections remaining.

1. The group has completed \(5\) of the \(8\) sections, so \(8-5=3\) sections remain. 2. Each section is \(24\div8=3\,\text{km}\) long. 3. The remaining distance is \(3\times3\,\text{km}=9\,\text{km}\).

The group still needs to hike \(9\,\text{km}\).

- Compare the sector sizes for part a). - Add the fractions for comics and nonfiction. - Multiply the total number of books by the combined fraction.

1. Adventure is the largest sector, representing \(\frac{1}{2}\) of the books. 2. Comics and nonfiction each represent \(\frac{1}{4}\). Together they represent \(\frac{1}{2}\) of the box, so \(\frac{1}{2} \times 60 = 30\) books.

a) Adventure b) \(30\) books

- Compare each sector with the whole circle. - Find one-half of \(24\) for part a). - For part b), write the campground votes over the total votes and simplify.

1. The farm sector represents one-half of the class. Compute \(\frac{1}{2} \times 24 = 12\) students. 2. The campground received \(3\) of the \(24\) votes. The fraction is \(\frac{3}{24} = \frac{1}{8}\).

a) \(12\) students b) \(\frac{1}{8}\)

- Count the total number of equal squares and the number of blue-shaded squares. - Write the shaded part as a fraction of the whole grid. - Divide the total area by the denominator, then multiply by the numerator.

1. The grid has \(4\) rows and \(6\) columns, so it contains \(4\times6=24\) equal squares. 2. There are \(10\) blue-shaded squares, so the shaded fraction is \(\frac{10}{24}=\frac{5}{12}\). 3. Find \(\frac{5}{12}\) of \(72\,\text{cm}^2\): \(72\div12=6\), and \(5\times6\,\text{cm}^2=30\,\text{cm}^2\).

The blue-shaded area is \(30\,\text{cm}^2\).

- How many times do you need to find half of the original amount? - Write down the result of the first step before finding half again. - Include the unit in your answer.

1. Find the forest area: \(\frac{1}{2} \times 960\,\text{acres} = 480\,\text{acres}\). 2. Find half of the forest area: \(\frac{1}{2} \times 480\,\text{acres} = 240\,\text{acres}\).

The protected oak grove covers \(240\,\text{acres}\).

- How can you find one-fourth of the total number of marbles? - After finding how many marbles were given away, how can you find how many remain? - What number do you divide by to find one-fourth?

1. Find one-fourth of \(36\): \(\frac{1}{4} \times 36 = 9\). 2. Subtract the marbles he gives away: \(36 - 9 = 27\).

Leon keeps \(27\) marbles.

- What does it mean to hike one-eighth of a trail? - First find the distance the family hiked before stopping. - How can you use the total distance and the distance already hiked to find the distance remaining?

1. Find one-eighth of the trail: \(\frac{1}{8} \times 8\,\text{mi} = 1\,\text{mi}\). 2. Subtract the distance already hiked: \(8\,\text{mi} - 1\,\text{mi} = 7\,\text{mi}\).

The family has \(7\,\text{mi}\) left to hike.

- Can you divide the total number of flowers into four equal groups? - How many flowers are in one of those groups? - After finding the number of tulips, how can you find the number of flowers that remain?

1. Find the number of tulips: \(\frac{1}{4} \times 32 = 8\). 2. Subtract the tulips from the total number of flowers: \(32 - 8 = 24\).

There are \(24\) daffodils in the bouquet.

- First find how many marbles each person gives away. - For the same total, is one-third greater or less than one-fourth? - If one person gives away more marbles, will that person have more or fewer left?

1. Lucas gives away \(\frac{1}{4} \times 24 = 6\) marbles, so he has \(24 - 6 = 18\) marbles left. 2. Sarah gives away \(\frac{1}{3} \times 24 = 8\) marbles, so she has \(24 - 8 = 16\) marbles left. 3. Since \(18 > 16\), Lucas has more marbles left.

Lucas has more marbles left. Lucas has \(18\) marbles, and Sarah has \(16\) marbles.

- First find one-fifth of \(40\). - What does one-fifth mean when the seats are divided into equal groups? - After finding the number of occupied seats, how can you find the number available?

1. Find the number of occupied seats: \(\frac{1}{5} \times 40 = 8\). 2. Subtract the occupied seats from the total: \(40 - 8 = 32\).

There are \(32\) seats still available.

- How can you divide the total weight into eight equal parts? - After finding the weight of one part, how can you find the weight of several parts? - Calculate the two fractional weights separately, and then compare them.

1. Find one-eighth of the bar: \(\frac{1}{8} \times 16\,\text{oz} = 2\,\text{oz}\). 2. Find three-eighths of the bar: \(3 \times 2\,\text{oz} = 6\,\text{oz}\). 3. Two-eighths weigh \(2 \times 2\,\text{oz} = 4\,\text{oz}\). One-fourth weighs \(\frac{1}{4} \times 16\,\text{oz} = 4\,\text{oz}\). 4. Both fractions give the same weight, so the student is correct.

a) One-eighth weighs \(2\,\text{oz}\). b) Three-eighths weigh \(6\,\text{oz}\). c) Yes. Both two-eighths and one-fourth weigh \(4\,\text{oz}\).

- First find the weight of the packaging alone. - What operation can you use to find one-eighth of a quantity? - What do you get when you subtract the packaging weight from the total weight?

1. Find the weight of the packaging: \(\frac{1}{8} \times 32\,\text{lb} = 4\,\text{lb}\). 2. Subtract the packaging weight from the total weight: \(32\,\text{lb} - 4\,\text{lb} = 28\,\text{lb}\).

The contents weigh \(28\,\text{lb}\).

- What does one-sixth mean in this calculation? - First find how many bulbs have already been planted. - What operation can you use to find the number remaining?

1. Find the number of bulbs already planted: \(\frac{1}{6} \times 480 = 80\). 2. Subtract the planted bulbs from the total: \(480 - 80 = 400\).

There are \(400\) flower bulbs left to plant.

- First find exactly how much Tim spends. - Then find exactly how much Sarah spends. - Compare the two amounts.

1. Find the amount Tim spends: \(\frac{1}{2} \times \$40 = \$20\). 2. Find the amount Sarah spends: \(\frac{1}{4} \times \$60 = \$15\). 3. Since \(\$20 > \$15\), Tim spends more.

Tim spends more. He spends \(\$20\), while Sarah spends \(\$15\).

- First find how many meters Paul has run. - Then find how many meters Anna has run. - What operation finds how much farther one distance is than another?

1. Find Paul's distance: \(\frac{3}{4} \times 400\,\text{m} = 300\,\text{m}\). 2. Find Anna's distance: \(\frac{1}{2} \times 400\,\text{m} = 200\,\text{m}\). 3. Find the difference: \(300\,\text{m} - 200\,\text{m} = 100\,\text{m}\).

Paul has run \(100\,\text{m}\) farther than Anna.

- Imagine dividing the rope into equal-length pieces. - What does the denominator tell you about the number of equal parts? - What does the numerator tell you about the number of parts being used? - How are \(\frac{1}{6}\) and \(\frac{5}{6}\) related?

1. Find one-sixth of the rope: \(\frac{1}{6} \times 24\,\text{ft} = 4\,\text{ft}\). 2. Find five-sixths of the rope: \(5 \times 4\,\text{ft} = 20\,\text{ft}\). 3. Compare the lengths: \(20\,\text{ft} \div 4\,\text{ft} = 5\). The shorter piece fits into the longer piece \(5\) times because \(\frac{5}{6}\) is five times \(\frac{1}{6}\).

a) \(4\,\text{ft}\) b) \(20\,\text{ft}\) c) \(5\) times, because \(\frac{5}{6}\) is five times \(\frac{1}{6}\).

- First find the length of one-fourth of the cord. - After finding one-fourth, how can you find three-fourths? - What operation finds the amount left from the original length?

1. Find one-fourth of the cord: \(24\,\text{in} \div 4 = 6\,\text{in}\). 2. Find three-fourths: \(3 \times 6\,\text{in} = 18\,\text{in}\). 3. The sister is correct because \(\frac{3}{4}\) of \(24\,\text{in}\) is \(18\,\text{in}\). 4. Find the remaining length: \(24\,\text{in} - 18\,\text{in} = 6\,\text{in}\).

Yes. \(\frac{3}{4}\) of \(24\,\text{in}\) is \(18\,\text{in}\), and \(6\,\text{in}\) remain.

- Convert the total goal to meters. - Find the distance of half a lap. - Subtract the distance already completed from the goal.

1. Convert the goal distance: \(2\,\text{km} = 2000\,\text{m}\). 2. Seven full laps cover \(7 \times 200\,\text{m} = 1400\,\text{m}\). 3. Half a lap covers \(\frac{1}{2} \times 200\,\text{m} = 100\,\text{m}\). 4. Sarah has run \(1400\,\text{m} + 100\,\text{m} = 1500\,\text{m}\). 5. She has \(2000\,\text{m} - 1500\,\text{m} = 500\,\text{m}\) left.

Sarah still needs to run \(500\,\text{m}\).

- What fraction of the whole roll is the \(20\,\text{yd}\) piece? - How much does that fraction of the total ribbon weigh? - How can you find the weight of the ribbon that remains?

1. The cut piece is \(\frac{20}{80} = \frac{1}{4}\) of the total length. 2. Find the weight of the cut piece: \(\frac{1}{4} \times 24\,\text{oz} = 6\,\text{oz}\). 3. Subtract the cut piece's weight: \(24\,\text{oz} - 6\,\text{oz} = 18\,\text{oz}\).

The ribbon remaining on the roll weighs \(18\,\text{oz}\).

- First find one-fourth of the total amount of flour. - Check whether the question asks for the amount used or the amount remaining. - Imagine dividing the flour into four equal groups.

1. Find the flour used: \(\frac{1}{4} \times 32\,\text{oz} = 8\,\text{oz}\). 2. Subtract from the full bag: \(32\,\text{oz} - 8\,\text{oz} = 24\,\text{oz}\).

\(24\,\text{oz}\) of flour remain in the bag.

- Find each student's cut length separately. - How can you find one-eighth of a number? - Compare the two final lengths.

1. Find the length Lucas cuts: \(\frac{1}{8} \times 16\,\text{ft} = 2\,\text{ft}\). 2. Find the length Sarah cuts: \(\frac{1}{2} \times 6\,\text{ft} = 3\,\text{ft}\). 3. Since \(3\,\text{ft} > 2\,\text{ft}\), Sarah cuts the longer piece.

Sarah cuts the longer piece: \(3\,\text{ft}\) compared with Lucas's \(2\,\text{ft}\).

- Look at the angles in the circle. Which familiar fractions, such as one-half or one-fourth, do you recognize? - After identifying a fraction, use it to find that part of the total weight. - Compare the size of the cherry slice with the pear slice.

1. The apple slice is one-half of the circle, so apples are \(\frac{1}{2}\) of the harvest. 2. The pear slice is one-fourth of the circle, so pears are \(\frac{1}{4}\) of the harvest. 3. Find the pear weight: \(\frac{1}{4} \times 80\,\text{lb} = 20\,\text{lb}\). 4. The cherry slice is one-half the size of the pear slice, so cherries are \(\frac{1}{8}\) of the harvest. 5. Find the cherry weight: \(\frac{1}{8} \times 80\,\text{lb} = 10\,\text{lb}\).

a) \(\frac{1}{2}\) b) \(20\,\text{lb}\) c) \(10\,\text{lb}\)

- Find each fraction as a number of dots. - Do not compare only the fractions because the total numbers of dots are different.

1. Find the shaded dots in Field A: \(\frac{3}{4} \times 40 = 30\). 2. Find the shaded dots in Field B: \(\frac{2}{5} \times 60 = 24\). 3. Compare and subtract: \(30 - 24 = 6\). Field A has \(6\) more shaded dots.

Field A has more shaded dots. It has \(30\) shaded dots compared with \(24\) in Field B, so it has \(6\) more.

- First find the number of groups that are not working. - Then use the number of working groups to find the number of working lights.

1. One-sixth of the \(84\) groups are not working: \(\frac{1}{6} \times 84 = 14\) groups. 2. The number of working groups is \(84 - 14 = 70\). 3. Each working group has \(5\) lights, so \(70 \times 5 = 350\) lights are working.

\(350\) lights are working.

- How can you find a fraction of a number? - First find how many miles each rider has completed. - How can you find the distance remaining from the total route? - Compare the two remaining distances.

1. Find Leon's completed distance: \(\frac{1}{4} \times 80\,\text{mi} = 20\,\text{mi}\). 2. Find Leon's remaining distance: \(80\,\text{mi} - 20\,\text{mi} = 60\,\text{mi}\). 3. Find Mia's completed distance: \(\frac{3}{8} \times 80\,\text{mi} = 30\,\text{mi}\). 4. Find Mia's remaining distance: \(80\,\text{mi} - 30\,\text{mi} = 50\,\text{mi}\). 5. Since \(60\,\text{mi} > 50\,\text{mi}\), Leon has the longer distance left.

Leon has \(60\,\text{mi}\) left, and Mia has \(50\,\text{mi}\) left. Leon has the longer distance remaining.