The People’s Share

GED Math

Fractions Practice

Simplifying, comparing, adding, subtracting, multiplying and dividing fractions and mixed numbers. 176 problems, with the answer key at the end.

← Math · Family 3

Practice for family 3. Quizzes 8 to 12 explain each of these skills; this sheet is for doing them until they are quick. 176 problems in four parts, each section starting with its plainest version.

Part One

Naming fractions

The same amount can have many names. These sections are about finding the simplest one, and moving between the forms.

1.Simplifying

Divide the top and the bottom by the same number until nothing but 1 divides both.

Example12⁄18 = 2⁄3, dividing both by 6.

Simplify each fraction.

  1. 1.Simplify 5⁄10
  2. 2.Simplify 6⁄12
  3. 3.Simplify 6⁄18
  4. 4.Simplify 18⁄20
  5. 5.Simplify 12⁄20
  6. 6.Simplify 16⁄24
  7. 7.Simplify 6⁄24
  8. 8.Simplify 5⁄30
  9. 9.Simplify 9⁄30
  10. 10.Simplify 8⁄48
  11. 11.Simplify 44⁄48
  12. 12.Simplify 12⁄54
  13. 13.Simplify 9⁄63
  14. 14.Simplify 16⁄88

2.Equivalent fractions

Whatever you multiply the bottom by, multiply the top by the same.

Example3⁄4 = ?⁄20: 4 became 20 by × 5, so 3 × 5 = 15.

Find the missing number.

  1. 15.1⁄5 = 6⁄?
  2. 16.1⁄8 = 4⁄?
  3. 17.1⁄2 = ?⁄8
  4. 18.2⁄9 = 6⁄?
  5. 19.1⁄2 = ?⁄10
  6. 20.1⁄12 = 4⁄?
  7. 21.1⁄2 = ?⁄14
  8. 22.1⁄8 = ?⁄16
  9. 23.3⁄4 = ?⁄20
  10. 24.2⁄11 = ?⁄22
  11. 25.1⁄4 = ?⁄24
  12. 26.5⁄7 = 25⁄?
  13. 27.3⁄4 = ?⁄28
  14. 28.3⁄10 = ?⁄60

3.Improper fractions to mixed numbers

Divide the top by the bottom. The whole number is how many times it goes; the remainder goes over the same bottom.

Example17⁄5: 17 ÷ 5 = 3, remainder 2, so 3 2⁄5.

Write each as a mixed number.

  1. 29.Write 5⁄2 as a mixed number
  2. 30.Write 9⁄2 as a mixed number
  3. 31.Write 11⁄6 as a mixed number
  4. 32.Write 11⁄3 as a mixed number
  5. 33.Write 19⁄5 as a mixed number
  6. 34.Write 22⁄5 as a mixed number
  7. 35.Write 29⁄6 as a mixed number
  8. 36.Write 40⁄7 as a mixed number
  9. 37.Write 47⁄9 as a mixed number
  10. 38.Write 48⁄7 as a mixed number

4.Mixed numbers to improper fractions

Multiply the whole number by the bottom, add the top, and keep the bottom.

Example2 3⁄4 = (2 × 4 + 3) over 4 = 11⁄4.

Write each as an improper fraction.

  1. 39.Write 2 1⁄2 as an improper fraction
  2. 40.Write 7 1⁄5 as an improper fraction
  3. 41.Write 1 2⁄7 as an improper fraction
  4. 42.Write 5 2⁄7 as an improper fraction
  5. 43.Write 6 4⁄7 as an improper fraction
  6. 44.Write 7 7⁄8 as an improper fraction
  7. 45.Write 1 1⁄8 as an improper fraction
  8. 46.Write 6 5⁄9 as an improper fraction
  9. 47.Write 2 7⁄10 as an improper fraction
  10. 48.Write 3 3⁄10 as an improper fraction

5.Which is larger?

Put both over the same bottom, then compare the tops. Or cross-multiply: the larger product sits above the larger fraction.

Example3⁄4 and 5⁄7: 21 against 20, so 3⁄4 > 5⁄7.

Write >, <, or = in the box.

  1. 49.9⁄10  □  4⁄5
  2. 50.2⁄3  □  1⁄2
  3. 51.1⁄2  □  8⁄9
  4. 52.3⁄10  □  1⁄4
  5. 53.2⁄5  □  1⁄2
  6. 54.2⁄3  □  7⁄11
  7. 55.1⁄7  □  1⁄3
  8. 56.2⁄3  □  1⁄4
  9. 57.7⁄8  □  3⁄4
  10. 58.1⁄7  □  1⁄2
  11. 59.4⁄5  □  2⁄3
  12. 60.6⁄7  □  1⁄3
  13. 61.1⁄3  □  2⁄7
  14. 62.1⁄3  □  5⁄6

Part Two

Adding and subtracting

Pieces can only be added when they are the same size. Every section here comes down to that.

6.Same bottom

Add or subtract the tops. The bottom stays.

Example2⁄9 + 4⁄9 = 2⁄3.

Give each answer in simplest form.

  1. 63.2⁄5 + 3⁄5
  2. 64.4⁄5 + 4⁄5
  3. 65.2⁄6 + 1⁄6
  4. 66.4⁄7 + 5⁄7
  5. 67.3⁄7 + 4⁄7
  6. 68.5⁄7 + 5⁄7
  7. 69.2⁄8 + 7⁄8
  8. 70.5⁄6 − 3⁄6
  9. 71.5⁄7 − 3⁄7
  10. 72.5⁄9 − 1⁄9

7.Different bottoms

Change both to the same bottom first, then add or subtract the tops.

Example3⁄4 + 1⁄6 = 9⁄12 + 2⁄12 = 11⁄12.

Give each answer in simplest form.

  1. 73.1⁄3 + 1⁄2
  2. 74.2⁄3 + 3⁄4
  3. 75.3⁄4 + 1⁄5
  4. 76.1⁄2 + 1⁄6
  5. 77.3⁄4 + 1⁄8
  6. 78.3⁄4 − 1⁄3
  7. 79.1⁄2 − 1⁄4
  8. 80.3⁄4 − 2⁄3
  9. 81.1⁄8 + 5⁄9
  10. 82.1⁄2 − 1⁄5
  11. 83.1⁄10 + 3⁄5
  12. 84.9⁄10 + 4⁄9
  13. 85.3⁄5 − 1⁄7
  14. 86.5⁄8 − 1⁄3
  15. 87.5⁄8 − 3⁄5
  16. 88.1⁄3 − 2⁄9
  17. 89.5⁄9 − 1⁄5
  18. 90.5⁄6 − 1⁄9

8.Adding mixed numbers

Add the whole numbers, add the fractions, then trade any extra whole out of the fraction.

Example2 1⁄3 + 1 3⁄4 = 3 13⁄12 = 4 1⁄12.

Add.

  1. 91.4 1⁄2 + 1 1⁄2
  2. 92.3 1⁄4 + 5 1⁄4
  3. 93.6 1⁄2 + 2 1⁄2
  4. 94.6 1⁄5 + 6 1⁄2
  5. 95.5 5⁄7 + 1 1⁄4
  6. 96.6 1⁄7 + 4 1⁄7
  7. 97.3 2⁄7 + 4 2⁄3
  8. 98.5 1⁄6 + 3 3⁄7
  9. 99.6 3⁄8 + 3 1⁄3
  10. 100.4 1⁄4 + 1 7⁄8

9.Subtracting mixed numbers, with borrowing

When the top fraction is too small, borrow 1 whole from the whole number and add it to the fraction as a full set of pieces.

Example3 1⁄4 − 1 2⁄3 = 2 15⁄12 − 1 8⁄12 = 1 7⁄12.

Subtract.

  1. 101.4 1⁄3 − 2 1⁄2
  2. 102.3 1⁄2 − 1 3⁄4
  3. 103.5 1⁄4 − 3 4⁄5
  4. 104.6 1⁄4 − 1 2⁄3
  5. 105.6 2⁄5 − 3 1⁄2
  6. 106.5 2⁄7 − 3 1⁄3
  7. 107.6 4⁄7 − 3 2⁄3
  8. 108.4 1⁄4 − 2 2⁄7
  9. 109.4 3⁄7 − 1 7⁄8
  10. 110.6 1⁄3 − 3 7⁄8

Part Three

Multiplying and dividing

No common bottom needed. Multiply straight across; to divide, flip the second fraction and multiply.

10.Multiplying

Top times top, bottom times bottom, then simplify.

Example2⁄3 × 9⁄10 = 18⁄30 = 3⁄5.

Multiply. Simplify each answer.

  1. 111.1⁄2 × 1⁄3
  2. 112.2⁄3 × 1⁄2
  3. 113.1⁄3 × 1⁄2
  4. 114.4⁄5 × 1⁄2
  5. 115.1⁄6 × 1⁄4
  6. 116.5⁄6 × 2⁄5
  7. 117.6⁄7 × 1⁄2
  8. 118.1⁄8 × 3⁄5
  9. 119.1⁄8 × 2⁄7
  10. 120.1⁄4 × 4⁄11
  11. 121.1⁄3 × 7⁄11
  12. 122.5⁄8 × 1⁄11
  13. 123.3⁄4 × 7⁄12
  14. 124.5⁄12 × 3⁄4

11.“Of” means times

A fraction of a number: divide by the bottom, multiply by the top.

Example2⁄3 of 24: 24 ÷ 3 = 8, and 8 × 2 = 16.

Find each amount.

  1. 125.1⁄2 of 12
  2. 126.3⁄8 of 16
  3. 127.1⁄3 of 27
  4. 128.3⁄4 of 32
  5. 129.5⁄7 of 35
  6. 130.9⁄10 of 50
  7. 131.8⁄9 of 63
  8. 132.3⁄10 of 70
  9. 133.5⁄8 of 72
  10. 134.3⁄8 of 96

12.Dividing

Keep the first, flip the second, multiply.

Example3⁄4 ÷ 2⁄5 = 3⁄4 × 5⁄2 = 1 7⁄8.

Divide. Simplify each answer.

  1. 135.1⁄2 ÷ 1⁄2
  2. 136.1⁄3 ÷ 1⁄2
  3. 137.1⁄5 ÷ 3⁄5
  4. 138.3⁄7 ÷ 4⁄5
  5. 139.3⁄8 ÷ 1⁄5
  6. 140.1⁄3 ÷ 7⁄8
  7. 141.4⁄9 ÷ 3⁄4
  8. 142.3⁄5 ÷ 7⁄9
  9. 143.1⁄2 ÷ 9⁄10
  10. 144.4⁄5 ÷ 1⁄10
  11. 145.1⁄9 ÷ 4⁄11
  12. 146.5⁄11 ÷ 1⁄2
  13. 147.1⁄12 ÷ 4⁄11
  14. 148.1⁄12 ÷ 2⁄7

13.Dividing with whole numbers

Write the whole number over 1 first.

Example6 ÷ 3⁄4 = 6⁄1 × 4⁄3 = 8.

Divide.

  1. 149.1⁄3 ÷ 2
  2. 150.3 ÷ 1⁄4
  3. 151.4 ÷ 1⁄2
  4. 152.1⁄4 ÷ 5
  5. 153.6 ÷ 2⁄3
  6. 154.3⁄7 ÷ 2
  7. 155.3⁄7 ÷ 4
  8. 156.7 ÷ 1⁄5
  9. 157.7 ÷ 1⁄8
  10. 158.9 ÷ 1⁄3

14.Mixed numbers

Change each mixed number to an improper fraction first. Then multiply or divide.

Example1 1⁄2 × 2 1⁄3 = 3⁄2 × 7⁄3 = 7⁄2 = 3 1⁄2.

Multiply or divide.

  1. 159.1 1⁄2 ÷ 2 2⁄3
  2. 160.1 3⁄4 ÷ 2 1⁄2
  3. 161.3 1⁄3 ÷ 1 3⁄4
  4. 162.2 1⁄3 × 1 1⁄4
  5. 163.3 1⁄2 ÷ 2 1⁄4
  6. 164.1 1⁄5 × 2 4⁄5
  7. 165.5 2⁄3 × 2 1⁄6
  8. 166.3 2⁄3 ÷ 6 3⁄4
  9. 167.6 1⁄4 × 3 2⁄3
  10. 168.1 2⁄5 ÷ 6 1⁄2

Part Four

Fractions in words

The test asks most fraction questions as small stories. Decide first which operation the story needs.

15.Word problems

Answer each question.

  1. 169.A recipe calls for 3⁄4 cup of oil. You are making half the recipe. How much oil do you need?
  2. 170.A board is 8 1⁄2 feet long. You cut off 3 1⁄4 feet. How much is left?
  3. 171.You worked 3 3⁄4 hours on Monday and 5 1⁄3 hours on Tuesday. How many hours in all?
  4. 172.How many 3⁄4-cup servings are in 6 cups of rice?
  5. 173.5⁄6 of the 36 people in a class passed the test on the first try. How many is that?
  6. 174.A bus ride takes 2⁄5 of an hour. How many minutes is that?
  7. 175.A ribbon 7 1⁄2 yards long is cut into pieces 3⁄4 yard long. How many pieces?
  8. 176.A tank is 7⁄8 full. After using 1⁄3 of a tank, how full is it?

Answer Key

Answers are in simplest form, and answers bigger than 1 are written as mixed numbers.

1.Simplifying (1–14)

  1. 1.1⁄2
  2. 2.1⁄2
  3. 3.1⁄3
  4. 4.9⁄10
  5. 5.3⁄5
  6. 6.2⁄3
  7. 7.1⁄4
  8. 8.1⁄6
  9. 9.3⁄10
  10. 10.1⁄6
  11. 11.11⁄12
  12. 12.2⁄9
  13. 13.1⁄7
  14. 14.2⁄11

2.Equivalent fractions (15–28)

  1. 15.30
  2. 16.32
  3. 17.4
  4. 18.27
  5. 19.5
  6. 20.48
  7. 21.7
  8. 22.2
  9. 23.15
  10. 24.4
  11. 25.6
  12. 26.35
  13. 27.21
  14. 28.18

3.Improper fractions to mixed numbers (29–38)

  1. 29.2 1⁄2
  2. 30.4 1⁄2
  3. 31.1 5⁄6
  4. 32.3 2⁄3
  5. 33.3 4⁄5
  6. 34.4 2⁄5
  7. 35.4 5⁄6
  8. 36.5 5⁄7
  9. 37.5 2⁄9
  10. 38.6 6⁄7

4.Mixed numbers to improper fractions (39–48)

  1. 39.5⁄2
  2. 40.36⁄5
  3. 41.9⁄7
  4. 42.37⁄7
  5. 43.46⁄7
  6. 44.63⁄8
  7. 45.9⁄8
  8. 46.59⁄9
  9. 47.27⁄10
  10. 48.33⁄10

5.Which is larger? (49–62)

  1. 49.9⁄10 > 4⁄5
  2. 50.2⁄3 > 1⁄2
  3. 51.1⁄2 < 8⁄9
  4. 52.3⁄10 > 1⁄4
  5. 53.2⁄5 < 1⁄2
  6. 54.2⁄3 > 7⁄11
  7. 55.1⁄7 < 1⁄3
  8. 56.2⁄3 > 1⁄4
  9. 57.7⁄8 > 3⁄4
  10. 58.1⁄7 < 1⁄2
  11. 59.4⁄5 > 2⁄3
  12. 60.6⁄7 > 1⁄3
  13. 61.1⁄3 > 2⁄7
  14. 62.1⁄3 < 5⁄6

6.Same bottom (63–72)

  1. 63.1
  2. 64.1 3⁄5
  3. 65.1⁄2
  4. 66.1 2⁄7
  5. 67.1
  6. 68.1 3⁄7
  7. 69.1 1⁄8
  8. 70.1⁄3
  9. 71.2⁄7
  10. 72.4⁄9

7.Different bottoms (73–90)

  1. 73.5⁄6
  2. 74.1 5⁄12
  3. 75.19⁄20
  4. 76.2⁄3
  5. 77.7⁄8
  6. 78.5⁄12
  7. 79.1⁄4
  8. 80.1⁄12
  9. 81.49⁄72
  10. 82.3⁄10
  11. 83.7⁄10
  12. 84.1 31⁄90
  13. 85.16⁄35
  14. 86.7⁄24
  15. 87.1⁄40
  16. 88.1⁄9
  17. 89.16⁄45
  18. 90.13⁄18

8.Adding mixed numbers (91–100)

  1. 91.6
  2. 92.8 1⁄2
  3. 93.9
  4. 94.12 7⁄10
  5. 95.6 27⁄28
  6. 96.10 2⁄7
  7. 97.7 20⁄21
  8. 98.8 25⁄42
  9. 99.9 17⁄24
  10. 100.6 1⁄8

9.Subtracting mixed numbers, with borrowing (101–110)

  1. 101.1 5⁄6
  2. 102.1 3⁄4
  3. 103.1 9⁄20
  4. 104.4 7⁄12
  5. 105.2 9⁄10
  6. 106.1 20⁄21
  7. 107.2 19⁄21
  8. 108.1 27⁄28
  9. 109.2 31⁄56
  10. 110.2 11⁄24

10.Multiplying (111–124)

  1. 111.1⁄6
  2. 112.1⁄3
  3. 113.1⁄6
  4. 114.2⁄5
  5. 115.1⁄24
  6. 116.1⁄3
  7. 117.3⁄7
  8. 118.3⁄40
  9. 119.1⁄28
  10. 120.1⁄11
  11. 121.7⁄33
  12. 122.5⁄88
  13. 123.7⁄16
  14. 124.5⁄16

11.“Of” means times (125–134)

  1. 125.6
  2. 126.6
  3. 127.9
  4. 128.24
  5. 129.25
  6. 130.45
  7. 131.56
  8. 132.21
  9. 133.45
  10. 134.36

12.Dividing (135–148)

  1. 135.1
  2. 136.2⁄3
  3. 137.1⁄3
  4. 138.15⁄28
  5. 139.1 7⁄8
  6. 140.8⁄21
  7. 141.16⁄27
  8. 142.27⁄35
  9. 143.5⁄9
  10. 144.8
  11. 145.11⁄36
  12. 146.10⁄11
  13. 147.11⁄48
  14. 148.7⁄24

13.Dividing with whole numbers (149–158)

  1. 149.1⁄6
  2. 150.12
  3. 151.8
  4. 152.1⁄20
  5. 153.9
  6. 154.3⁄14
  7. 155.3⁄28
  8. 156.35
  9. 157.56
  10. 158.27

14.Mixed numbers (159–168)

  1. 159.9⁄16
  2. 160.7⁄10
  3. 161.1 19⁄21
  4. 162.2 11⁄12
  5. 163.1 5⁄9
  6. 164.3 9⁄25
  7. 165.12 5⁄18
  8. 166.44⁄81
  9. 167.22 11⁄12
  10. 168.14⁄65

15.Word problems (169–176)

  1. 169.3⁄8 cup
  2. 170.5 1⁄4 feet
  3. 171.9 1⁄12 hours
  4. 172.8 servings
  5. 173.30 people
  6. 174.24 minutes
  7. 175.10 pieces
  8. 176.13⁄24 of a tank