Dividing Fractions: math practice, Grade 6 – download the PDF

1 Counting pieces ★★★

Compute each quotient. Think of how many pieces fit.

1. \( 6 \div \dfrac{1}{2} \)
2. \( 3 \div \dfrac{1}{5} \)
3. \( 8 \div \dfrac{1}{4} \)

2 Reciprocals ★★★

Write the reciprocal of each number.

1. \( \dfrac{3}{5} \)
2. \( 7 \)
3. \( \dfrac{1}{9} \)
4. \( 2\dfrac{1}{2} \)

3 Sharing a fraction ★★★

Compute.

1. \( \dfrac{1}{2} \div 3 \)
2. \( \dfrac{3}{4} \div 2 \)
3. \( \dfrac{6}{7} \div 3 \)

4 Loaves of bread ★★★

A baker has 2 pounds of flour. Each small loaf needs \( \dfrac{1}{4} \) pound. How many loaves can she make?

5 True or false? ★★★

Say whether each statement is true or false, and justify.

1. \( 3 \div \dfrac{1}{6} = 18 \)
2. \( \dfrac{1}{3} \div 2 = \dfrac{2}{3} \)
3. The reciprocal of \( \dfrac{4}{9} \) is \( \dfrac{9}{4} \).

6 Using the bar model ★★★

The bar below is cut into sixths, and 4 sixths are colored, which is \( \dfrac{2}{3} \) of the bar.

How many pieces of size \( \dfrac{1}{6} \) fit in \( \dfrac{2}{3} \)? Write the division sentence.

7 Garden hose breaks ★★★

Maya has 9 feet of garden hose and wants pieces of \( \dfrac{3}{4} \) foot each for plant labels. Write the division and compute the number of pieces.

8 Fraction divided by a fraction ★★★

Compute \( \dfrac{3}{5} \div \dfrac{3}{10} \) and check by multiplication.

9 Three quotients ★★★

Compute and simplify.

1. \( \dfrac{5}{6} \div \dfrac{2}{3} \)
2. \( \dfrac{7}{8} \div \dfrac{1}{4} \)
3. \( \dfrac{4}{9} \div \dfrac{8}{3} \)

10 Find the mistake ★★★

Mia wrote \( \dfrac{2}{5} \div 3 = \dfrac{2}{5} \times 3 = \dfrac{6}{5} \). Explain her mistake and give the correct answer.

11 Ribbon for gift bows ★★★

A ribbon is \( \dfrac{9}{10} \) meter long. Each bow needs \( \dfrac{3}{20} \) meter. How many bows can be made? Give the bow length in centimeters too.

12 Jumps on a number line ★★★

Use the number line to compute \( 2 \div \dfrac{2}{3} \). How many jumps of \( \dfrac{2}{3} \) go from 0 to 2?

13 Mixed numbers ★★★

Compute. Turn each mixed number into a fraction first.

1. \( 1\dfrac{1}{2} \div \dfrac{3}{4} \)
2. \( 2\dfrac{1}{4} \div \dfrac{3}{2} \)
3. \( 3 \div 1\dfrac{1}{2} \)

14 Missing factor ★★★

Use division to find the missing number.

1. \( \square \times \dfrac{2}{5} = 6 \)
2. \( \dfrac{3}{4} \times \square = \dfrac{9}{10} \)

15 Pizza night ★★★

After dinner, \( \dfrac{5}{6} \) of a pizza is left. Five friends share it equally. What fraction of the whole pizza does each friend eat?

16 Hiking speed ★★★

A hiker walks \( \dfrac{3}{4} \) mile in \( \dfrac{1}{6} \) hour. Find her speed in miles per hour. Is it a realistic walking speed?

17 Predict, then compute ★★★

Without computing, say whether each quotient is greater than, less than, or equal to its first number. Then compute.

1. \( 5 \div \dfrac{3}{4} \)
2. \( \dfrac{2}{3} \div \dfrac{5}{4} \)
3. \( \dfrac{7}{8} \div 1 \)

18 Height of a fish tank ★★★

A fish tank shaped like a rectangular prism has a base area of \( \dfrac{3}{4} \) square foot and holds \( \dfrac{9}{8} \) cubic foot of water. Since volume = base area × height, find the height in feet and in inches.

19 Friendship bracelets ★★★

Lena has \( 7\dfrac{1}{2} \) meters of cord. Each bracelet uses \( \dfrac{3}{4} \) meter.

1. How many bracelets can she make?
2. She buys \( 2\dfrac{1}{4} \) more meters of cord. How many bracelets can she make in all?

20 Write your own problem ★★★

Write a word problem (with a context of your choice) that is solved by \( \dfrac{4}{5} \div \dfrac{1}{10} \). Then solve it and check your answer.

21 Find the unknown number ★★★

1. A number divided by \( \dfrac{2}{3} \) gives \( \dfrac{9}{4} \). What is the number?
2. \( \dfrac{5}{6} \) divided by a number gives \( \dfrac{5}{3} \). What is the number?