Fraction Division Words

Grade 6 · fractions · 100 practice problems · read aloud

🔊 Listen to this explanation

Fraction Division: Sharing and Grouping

Dividing fractions helps us solve real-world problems, like figuring out how many servings of a recipe you can make or how many groups you can form. It's all about splitting things into equal parts!

🚀 The Simple Rule: Keep, Change, Flip!

To divide fractions, you don't actually divide! You multiply by the reciprocal. The reciprocal is just the fraction flipped upside down.

  1. KEEP the first fraction the same.
  2. CHANGE the division sign (÷) to a multiplication sign (×).
  3. FLIP the second fraction (find its reciprocal).
  4. Multiply the fractions as you normally would (numerator × numerator, denominator × denominator).
  5. Simplify your answer to its lowest terms.

📚 Worked Examples

Example 1: ½ ÷ ¼

  1. Keep: ½ stays the same.
  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

Example 2: ¾ ÷ ⅖

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

⚠️ Common Mistakes to Avoid

Flipping the wrong fraction! Only flip the second fraction (the one you are dividing by). The first fraction always stays the same.

Forgetting to change the sign! You must change the division sign to a multiplication sign. If you forget, your answer will be wrong.

Not simplifying! Always check if your final answer can be simplified or written as a mixed number.

💡 Tips & Tricks

Story Connection: Think of it as "How many of the second fraction fit into the first?" For ½ ÷ ¼, you're asking "How many quarters are in a half?" The answer is 2!

Double-Check with Whole Numbers: If you know 6 ÷ 2 = 3, test the rule with fractions: 6/1 ÷ 2/1 = 6/1 × 1/2 = 6/2 = 3. It works!

🎯 How to Practice

  • Start Simple: Practice with whole numbers and unit fractions (like 1/2, 1/3) first.
  • Create Word Problems: Write your own story problems. "I have 3/4 of a pizza and want to give each friend 1/8 of a pizza. How many friends can I feed?"
  • Use Online Games: Find interactive fraction division games to make practice fun.
  • Teach Someone: Explain the "Keep, Change, Flip" rule to a family member. Teaching is a great way to learn!

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 2/3 ÷ 3/4 = ?

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

Show the answer

Answer: 8/9

  1. Write down the problem. 2/3 ÷ 3/4
  2. Change the division sign to a multiplication sign and flip the second fraction (find its reciprocal). The reciprocal of 3/4 is 4/3. So the problem becomes: 2/3 × 4/3
  3. Multiply the fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerators: 2 × 4 = 8 Denominators: 3 × 3 = 9 This gives us: 8/9
  4. Check if the fraction can be simplified. The fraction 8/9 has no common factors other than 1, so it is already in simplest form. Therefore, the final answer is 8/9.

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

2 2/3 ÷ 4/5 = ?

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

Show the answer

Answer: 5/6

  1. Understand that dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 4/5 is 5/4.
  2. Rewrite the division as multiplication: 2/3 ÷ 4/5 = 2/3 × 5/4
  3. Multiply the numerators: 2 × 5 = 10
  4. Multiply the denominators: 3 × 4 = 12
  5. This gives the fraction 10/12
  6. Simplify 10/12 by dividing numerator and denominator by their greatest common factor, which is 2: 10 ÷ 2 = 5 12 ÷ 2 = 6
  7. The simplified fraction is 5/6. Final answer: 5/6

We are dividing two fractions: 2/3 ÷ 4/5.

3 3/4 ÷ 2/5 = ?

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

Show the answer

Answer: 15/8

  1. Write down the problem. 3/4 ÷ 2/5
  2. Change the division to multiplication by the reciprocal of the second fraction. The reciprocal of 2/5 is 5/2. So the problem becomes: 3/4 × 5/2
  3. Multiply the numerators. Numerators: 3 × 5 = 15
  4. Multiply the denominators. Denominators: 4 × 2 = 8
  5. Write the result as a fraction. 15/8
  6. Simplify if possible. 15 and 8 have no common factors other than 1, so 15/8 is already in simplest form. Final Answer: 15/8

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

4 7/9 ÷ 5/11 = ?

Hint: Think about the rule for dividing fractions: you can change the division to multiplication by flipping the second fraction.

Show the answer

Answer: 77/45

  1. Write the problem: 7/9 ÷ 5/11
  2. Change division to multiplication by the reciprocal of the second fraction. The reciprocal of 5/11 is 11/5.
  3. Rewrite: 7/9 × 11/5
  4. Multiply the numerators: 7 × 11 = 77
  5. Multiply the denominators: 9 × 5 = 45
  6. The result is 77/45. Check if it can be simplified: 77 and 45 have no common factors other than 1, so it is already in simplest form. Final answer: 77/45

5 Tane has 7 1/5 meters of rope. He cuts it into pieces that are each 3/5 meter long. How many pieces does he get?

Hint: Think about how many times the smaller piece length fits into the total length. You can convert the mixed number to an improper fraction first.

Show the answer

Answer: 12

  1. Convert the mixed number to an improper fraction. 7 1/5 = (7 × 5 + 1)/5 = (35 + 1)/5 = 36/5.
  2. Write the division problem: 36/5 ÷ 3/5.
  3. To divide fractions, multiply by the reciprocal of the divisor. The reciprocal of 3/5 is 5/3.
  4. Rewrite as multiplication: 36/5 × 5/3.
  5. Multiply the numerators: 36 × 5 = 180.
  6. Multiply the denominators: 5 × 3 = 15.
  7. This gives 180/15.
  8. Simplify by dividing numerator and denominator by 15: 180 ÷ 15 = 12, 15 ÷ 15 = 1, so 12/1 = 12. Final answer: 12 pieces.

6 Matiu has 8 2/5 liters of juice. He pours it into bottles that each hold 4/5 liter. How many bottles can he fill?

Hint: Think about how many times the smaller amount (the bottle size) fits into the larger amount (the total juice). This is a division problem. Start by converting the mixed number into an improper fraction.

Show the answer

Answer: 10 1/2

  1. Convert the mixed number 8 2/5 into an improper fraction. 8 2/5 = (8 × 5 + 2)/5 = (40 + 2)/5 = 42/5.
  2. Write the division problem: 42/5 ÷ 4/5.
  3. To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of 4/5 is 5/4.
  4. Perform the multiplication: 42/5 × 5/4 = (42 × 5) / (5 × 4) = 210/20.
  5. Simplify the fraction. Divide the numerator and denominator by their greatest common factor, which is 10: 210 ÷ 10 = 21, and 20 ÷ 10 = 2. This gives 21/2.
  6. Convert the improper fraction 21/2 into a mixed number: 21 ÷ 2 = 10 with a remainder of 1, so it is 10 1/2. Final Answer: Matiu can fill 10 1/2 bottles.
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