Fraction Division

Grade 5 · fractions · 87 practice problems · read aloud

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Dividing Fractions: Sharing into Equal Groups

Division helps us split things into equal parts. When we divide fractions, we are finding out how many of one fraction fit into another. It's super useful for real-life problems, like figuring out how many servings of a recipe you can make! 🧁

How to Divide Fractions: The "Keep, Change, Flip" Method

  1. KEEP the first fraction just as it is.
  2. CHANGE the division sign (÷) to a multiplication sign (×).
  3. FLIP the second fraction (swap its numerator and denominator).
  4. Multiply the two fractions straight across.
  5. Simplify your answer to its lowest terms.

Let's Try Some Examples!

Example 1: ½ ÷ ¼

  1. Keep: ½
  2. Change: ÷ becomes ×
  3. Flip: ¼ becomes 4/1
  4. Multiply: ½ × 4/1 = (1×4)/(2×1) = 4/2
  5. Simplify: 4/2 = 2

So, ½ ÷ ¼ = 2. This means there are two quarters in one half! 🎯

Example 2: ¾ ÷ ⅖

  1. Keep: ¾
  2. Change: ÷ becomes ×
  3. Flip: ⅖ becomes 5/2
  4. Multiply: ¾ × 5/2 = (3×5)/(4×2) = 15/8
  5. Simplify: 15/8 = 1 ⅞

Watch Out! Common Mistakes

Don't flip the first fraction! Only flip the second fraction (the one you are dividing by).

Don't forget to change the sign! Division must become multiplication for the method to work.

Always simplify! Your teacher will always want your answer in the simplest form.

Tips & Tricks to Remember

🎵 Memory Rhyme: "Dividing fractions, don't ask why, flip the second and multiply!"

✂️ Think of it as cutting: ½ ÷ ¼ means "How many one-quarter pieces can I get from a one-half piece?" The answer is 2!

✅ Check your work: After you find your answer, multiply it by the divisor. You should get back your original dividend.

How to Practice

  • Start with simple problems like 1 ÷ ½.
  • Use graph paper to keep your numbers neatly lined up.
  • Create your own word problems. For example: "I have ¾ of a pizza and want to give friends slices that are ⅛ of a pizza. How many friends can get a slice?"
  • Ask a friend or parent to give you problems to solve. Practice makes perfect!

Practice problems

6 of the 87, worked through step by step — try them before opening the answer.

1 3/4 ÷ 1/2 = ?

Hint: When dividing fractions, think about how many times the second fraction fits into the first one. You can use the reciprocal method with different fractions like 2/3 ÷ 1/4.

Show the answer

Answer: 1.5

  1. Write down the problem. 3/4 ÷ 1/2
  2. Change the division sign to a multiplication sign and find the reciprocal of the second fraction (the divisor). The reciprocal of 1/2 is 2/1. So the problem becomes: 3/4 × 2/1
  3. Multiply the fractions. Multiply the numerators: 3 × 2 = 6 Multiply the denominators: 4 × 1 = 4 This gives us: 6/4
  4. Simplify the resulting fraction. 6/4 can be simplified. Both the numerator (6) and denominator (4) can be divided by 2. 6 ÷ 2 = 3 4 ÷ 2 = 2 So, 6/4 simplifies to 3/2.
  5. Convert the fraction to a decimal. 3/2 means 3 divided by 2. 3 ÷ 2 = 1.5 Therefore, the final answer is 1.5.

To divide fractions, we use the rule: dividing by a fraction is the same as multiplying by its reciprocal.

2 3/4 ÷ 2/3 = ?

Hint: When dividing fractions, think about multiplying by the reciprocal of the second fraction.

Show the answer

Answer: 9/8

  1. Write down the problem. 3/4 ÷ 2/3
  2. Change the division to multiplication by the reciprocal of the second fraction. The reciprocal of a fraction is created by swapping its numerator and denominator. The reciprocal of 2/3 is 3/2. So the problem becomes: 3/4 × 3/2
  3. Multiply the fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerator: 3 × 3 = 9 Denominator: 4 × 2 = 8 This gives us the new fraction: 9/8
  4. Check if the fraction can be simplified. 9/8 is already in its simplest form because 9 and 8 have no common factors other than 1. Therefore, the final answer is 9/8.

To divide fractions, we use the rule: dividing by a fraction is the same as multiplying by its reciprocal.

3 2/3 ÷ 1/4 = ?

Hint: Remember that dividing by a fraction is the same as multiplying by its reciprocal.

Show the answer

Answer: 8/3

  1. Write the problem: 2/3 ÷ 1/4
  2. Change division to multiplication by the reciprocal: 2/3 × 4/1
  3. Multiply the numerators: 2 × 4 = 8
  4. Multiply the denominators: 3 × 1 = 3
  5. Write the result: 8/3

The answer is 8/3.

4 5/6 ÷ 3/4 = ?

Hint: When dividing fractions, remember to multiply by the reciprocal of the second fraction.

Show the answer

Answer: 1 1/9

  1. Write the division problem: 5/6 ÷ 3/4
  2. Change division to multiplication by the reciprocal: 5/6 × 4/3
  3. Multiply numerators: 5 × 4 = 20
  4. Multiply denominators: 6 × 3 = 18
  5. Simplify the fraction: 20/18 = 10/9
  6. Convert to mixed number: 10/9 = 1 1/9

The answer is 1 1/9.

5 5/6 ÷ 2/3 = ?

Hint: Remember that dividing by a fraction is the same as multiplying by its reciprocal. For example, 1/2 ÷ 1/4 becomes 1/2 × 4/1.

Show the answer

Answer: 5/4

  1. Write the division problem: 5/6 ÷ 2/3
  2. Change division to multiplication by the reciprocal of the second fraction: 5/6 × 3/2
  3. Multiply the numerators: 5 × 3 = 15
  4. Multiply the denominators: 6 × 2 = 12
  5. Write the resulting fraction: 15/12
  6. Simplify the fraction by dividing numerator and denominator by 3: 15 ÷ 3 = 5, 12 ÷ 3 = 4
  7. The simplified fraction is 5/4

The answer is 5/4.

6 3/4 ÷ 1/6 = ?

Hint: Remember that dividing by a fraction is the same as multiplying by its reciprocal. For example, 1/2 ÷ 1/4 becomes 1/2 × 4/1.

Show the answer

Answer: 9/2

  1. Write the division problem: 3/4 ÷ 1/6
  2. Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 1/6 is 6/1.
  3. Rewrite the problem as multiplication: 3/4 × 6/1
  4. Multiply the numerators: 3 × 6 = 18
  5. Multiply the denominators: 4 × 1 = 4
  6. Write the result as a fraction: 18/4
  7. Simplify the fraction by dividing numerator and denominator by 2: 18 ÷ 2 = 9, 4 ÷ 2 = 2
  8. The simplified answer is 9/2.
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