Fraction ÷ Fraction

Grade 6 · fractions · 60 practice problems · read aloud

🔊 Listen to this explanation

Dividing Fractions: A Simple Guide

Dividing fractions helps us solve problems like "How many 1/3-cup servings are in 2/3 of a cup?" or "If a recipe uses 1/2 pound of flour and you have 3 pounds, how many batches can you make?" It's a super useful skill for cooking, building, and other real-life situations! 🧑‍🍳

How to Solve: Step-by-Step

  1. Keep the first fraction as it is.
  2. Change the division sign (÷) to a multiplication sign (×).
  3. Flip the second fraction (find its reciprocal).
  4. Multiply the numerators and denominators.
  5. Simplify your answer if possible.

Remember the rhyme: "Keep, Change, Flip!" 🔄

Worked Examples

Example 1: 2/3 ÷ 1/4

Step 1: Keep 2/3

Step 2: Change ÷ to ×

Step 3: Flip 1/4 to get 4/1

Step 4: Multiply: (2 × 4) / (3 × 1) = 8/3

Step 5: Simplify: 8/3 = 2 ²⁄₃

Example 2: 3/4 ÷ 2/5

Step 1: Keep 3/4

Step 2: Change ÷ to ×

Step 3: Flip 2/5 to get 5/2

Step 4: Multiply: (3 × 5) / (4 × 2) = 15/8

Step 5: Simplify: 15/8 = 1 ⁷⁄₈

Common Mistakes to Avoid

❌ Forgetting to flip the second fraction: This is the most common error! Always flip the fraction after the division sign.

❌ Flipping both fractions: Only flip the second one. The first fraction stays the same.

❌ Not simplifying the final answer: Always check if your answer can be reduced to its simplest form.

Tips & Tricks

Memory Aid: "Keep, Change, Flip" is your best friend! Say it out loud as you work.

Visual Check: Draw a diagram! For 1/2 ÷ 1/4, draw a half, then see how many quarters fit into it (the answer is 2!).

Reasonableness: When you divide fractions, your answer should usually be larger than what you started with. If it's smaller, double-check your work!

How to Practice

  • Start with simple problems like 1/2 ÷ 1/4 before moving to trickier ones.
  • Create your own word problems using food or measurements.
  • Use online math games that focus on fraction division.
  • Practice with a friend and explain the steps to each other—teaching is a great way to learn!

Practice problems

6 of the 60, worked through step by step — try them before opening the answer.

1 (2/3) ÷ (4/5) = ?

Hint: When dividing fractions, multiply the first fraction by the reciprocal of the second fraction. Remember to simplify your answer if possible.

Show the answer

Answer: 5/6

  1. Write down the problem. (2/3) ÷ (4/5)
  2. Change the division to multiplication by the reciprocal of the second fraction. The reciprocal of a fraction is found by swapping its numerator and denominator. The reciprocal of 4/5 is 5/4. So, the problem becomes: (2/3) × (5/4)
  3. Multiply the two fractions. To multiply fractions, multiply the numerators together and multiply the denominators together. Numerator: 2 × 5 = 10 Denominator: 3 × 4 = 12 This gives us the new fraction: 10/12
  4. Simplify the fraction to its lowest terms. Find the greatest common factor (GCF) of 10 and 12. The GCF is 2. Divide both the numerator and the denominator by 2: 10 ÷ 2 = 5 12 ÷ 2 = 6 So, 10/12 simplifies to 5/6. Therefore, the final answer is 5/6.

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

2 (6/7) ÷ (2/3) = ?

Hint: Think about the rule for dividing fractions: you multiply by the reciprocal of the second fraction. What is the reciprocal of 2/3?

Show the answer

Answer: 9/7

  1. Write the problem: (6/7) ÷ (2/3)
  2. Find the reciprocal of the second fraction (2/3). The reciprocal is 3/2.
  3. Change division to multiplication: (6/7) × (3/2)
  4. Multiply the numerators: 6 × 3 = 18
  5. Multiply the denominators: 7 × 2 = 14
  6. Write the result as a fraction: 18/14
  7. Simplify the fraction. Find the greatest common factor (GCF) of 18 and 14, which is 2.
  8. Divide numerator and denominator by 2: 18 ÷ 2 = 9, 14 ÷ 2 = 7
  9. The simplified fraction is 9/7.

The answer is 9/7.

3 Liam is baking cookies and needs 3/4 cup of chocolate chips for each batch. He has 2 1/4 cups of chocolate chips total. How many complete batches of cookies can Liam make?

Hint: When you have a total amount of an ingredient and know how much is needed for each recipe, think about how many times the smaller amount fits into the larger amount. For example, if someone had 5 cups of flour and each recipe needed 1 1/2 cups, you would determine how many full recipes they could complete.

Show the answer

Answer: 3

  1. Understand the problem. Liam uses 3/4 cup of chocolate chips per batch. He has 2 1/4 cups total. We need to find how many complete batches he can make.
  2. Convert the mixed number to an improper fraction. 2 1/4 cups = 2 + 1/4 = 8/4 + 1/4 = 9/4 cups.
  3. Set up the division. We divide total chips by chips per batch: (9/4) ÷ (3/4)
  4. Dividing fractions rule. Dividing by a fraction is the same as multiplying by its reciprocal. So: (9/4) ÷ (3/4) = (9/4) × (4/3)
  5. Multiply the fractions. Multiply numerators: 9 × 4 = 36 Multiply denominators: 4 × 3 = 12 So we have 36/12.
  6. Simplify the fraction. 36 ÷ 12 = 3.
  7. Interpret the result. The answer 3 means Liam can make 3 complete batches. There will be no chocolate chips left over because the division came out exactly to a whole number. Final answer: 3

4 A construction crew is paving a road that is 2 1/4 miles long. Each day they can complete 3/8 of a mile. How many full days will it take them to finish paving the entire road?

Hint: Think about how to determine how many equal parts fit into a whole when working with fractions. Consider a different scenario: if you had 3/4 of a pizza and wanted to share it equally with friends, with each friend getting 1/8 of the pizza, how would you figure out how many friends you could serve?

Show the answer

Answer: 6

  1. We need to divide the total road length by the daily progress to find how many days are needed.
  2. Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4
  3. Set up the division: 9/4 ÷ 3/8
  4. When dividing fractions, multiply by the reciprocal: 9/4 × 8/3
  5. Multiply the numerators: 9 × 8 = 72
  6. Multiply the denominators: 4 × 3 = 12
  7. Simplify the fraction: 72/12 = 6
  8. Since the question asks for full days, and we got exactly 6, the crew needs 6 full days to complete the road.

The answer is 6.

5 A construction crew is paving a road that is 2 1/4 miles long. Each day they can pave exactly 3/8 of a mile. How many complete days will it take them to finish paving the entire road?

Hint: Think about how you would divide a whole amount into equal smaller portions. Consider what operation helps you find how many times one quantity fits into another.

Show the answer

Answer: 6

  1. Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4
  2. Set up the division problem: total road length ÷ daily paving amount = 9/4 ÷ 3/8
  3. To divide fractions, multiply by the reciprocal: 9/4 × 8/3
  4. Multiply numerators: 9 × 8 = 72
  5. Multiply denominators: 4 × 3 = 12
  6. Simplify the fraction: 72/12 = 6
  7. Since the question asks for complete days, and 6 is a whole number,

the answer is 6 complete days. The construction crew will take 6 complete days to pave the road.

6 A factory uses 3/4 of a barrel of oil to produce one batch of plastic containers. If they have 2 1/4 barrels of oil available, how many complete batches of plastic containers can they produce?

Hint: Think about how many times the amount needed for one batch fits into the total amount available. Convert any mixed numbers to improper fractions first.

Show the answer

Answer: 3

  1. Understand the problem. We know: - 1 batch requires 3/4 barrel of oil. - Available oil = 2 1/4 barrels.
  2. Convert mixed number to improper fraction. 2 1/4 = 2 + 1/4 = 8/4 + 1/4 = 9/4 barrels.
  3. Determine how many batches can be made. Number of batches = (Total oil) ÷ (Oil per batch) = (9/4) ÷ (3/4)
  4. Dividing fractions rule: multiply by reciprocal. (9/4) ÷ (3/4) = (9/4) × (4/3)
  5. Simplify. The 4 in numerator and denominator cancels: (9/4) × (4/3) = 9/3 = 3.
  6. Interpret the result. The factory can make 3 complete batches (no remainder). Final Answer: 3
Practise this topic — 10 free problems, no signup →