Amount we have
3/4 = 3/4
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Fractions topic
How to Divide Fractions
Solve a fraction division problem first, then use the steps and visual explanation to understand why the rule works.
- fraction ÷ fraction
- fraction ÷ whole number
- whole number ÷ fraction
- mixed numbers
Interactive tool
Divide fractions step by step
Build the picture first: make equal parts, count groups, then use the rule to check your answer.
Start with the question
3/4 ÷ 1/2
Build the picture in three short moves.
Use the guided buttons below to reveal one idea at a time.
See the division
How many groups of 1/2 fit inside 3/4?
First make both fractions use the same-size pieces. Then count groups of the divisor — not just colored bars.
Step 1 — Make the parts match
These are the same one whole, cut into 4 equal parts.
One group to measure with
1/2 = 2/4
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Step 2 — Count groups of 2/4
The blue amount has 3 equal pieces. Each green group needs 2 pieces.
Next, mark 2/4 as one complete group.
1 full group
1/4 left = 1/2 of one more 2/4 group
You measured1 1/2groups.
3/4 ÷ 1/2 = 1 + 1/2 = 1 1/2
Check with the rule
3/4 ÷ 1/2=3/4 × 2/1=6/4=3/2
The calculation steps
- 1.Keep 3/4.
- 2.Flip the divisor: 1/2 becomes 2/1.
- 3.Change division to multiplication: 3/4 × 2/1.
- 4.Simplify before multiplying: 3/2 × 1/1.
- 5.Multiply across: 6/4.
- 6.Simplify the result: 3/2.
- 7.Write the mixed number: 1 1/2.
What division means
Division asks how many groups fit inside an amount
Before using a shortcut, ask how many groups of the divisor can fit inside the dividend. That question gives the answer meaning and makes the reciprocal step easier to explain.
The rule
Keep, change, flip — then explain why
Keep the first fraction
The amount you start with does not change. Keep the dividend exactly where it is.
Change division to multiplication
Rewrite the division sign as multiplication so the problem can use a multiplication rule.
Flip only the divisor
Turn the second fraction upside down. Do not flip the first fraction.
Multiply and simplify
Multiply across, then reduce the answer and write a mixed number when it is helpful.
Problem types
Match the problem to the first useful step
Fraction ÷ fraction
Keep the first fraction, flip the second fraction, and multiply.
3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2
Fraction ÷ whole number
Write the whole number as a fraction with denominator 1 before flipping it.
3/4 ÷ 2 = 3/4 × 1/2 = 3/8
Whole number ÷ fraction
Write the whole number over 1, then ask how many groups of the fraction fit inside it.
3 ÷ 2/5 = 3/1 × 5/2 = 15/2
Mixed number ÷ fraction
Convert the mixed number to an improper fraction before you flip the divisor.
1 1/2 ÷ 2/3 = 3/2 × 3/2 = 9/4
Learn each case
Fraction ÷ whole number
How to divide a fraction by a whole number
A problem like 3/4 ÷ 2 asks you to share three fourths equally between two groups. The total amount is still three fourths; each group gets a smaller equal share.
3/4 ÷ 2 = 3/4 ÷ 2/1 = 3/4 × 1/2 = 3/8
- 1.Write the whole number as a fraction: 2 becomes 2/1.
- 2.Keep 3/4, change ÷ to ×, and flip only the divisor: 2/1 becomes 1/2.
- 3.Multiply across. Three fourths of one half is three eighths.
For parents: Helpful language: “We are sharing the amount equally.” Do not tell a child to make both parts of the fraction smaller separately—that changes the fraction in a way that does not explain division.
Unit fraction ÷ whole number
Dividing unit fractions by whole numbers
A unit fraction has 1 in the numerator. Start here when you want the meaning to be easy to see: 1/2 ÷ 3 means split one half into three equal shares.
1/2 ÷ 3 = 1/2 × 1/3 = 1/6
- 1.Picture one half of a whole as the amount you have.
- 2.Divide that half into three equal pieces.
- 3.Each piece is one sixth of the original whole, so the answer is 1/6.
For parents: This is a strong first visual model because it shows that dividing by a whole number makes each share smaller. Use the tool’s tape before introducing a harder fraction ÷ fraction problem.
Mixed number ÷ fraction
How to divide mixed fractions
When a problem has a mixed number, convert it to an improper fraction before using the reciprocal rule. That gives you one fraction to work with instead of a whole-number part and a fractional part.
1 1/2 ÷ 2/3 = 3/2 × 3/2 = 9/4 = 2 1/4
- 1.Convert 1 1/2 to an improper fraction: (1 × 2 + 1)/2 = 3/2.
- 2.Keep 3/2, change ÷ to ×, then flip the divisor 2/3 to 3/2.
- 3.Multiply, simplify if possible, and change an improper answer to a mixed number when it helps.
For parents: Convert before you flip. Only the number you are dividing by is flipped; the mixed number is first rewritten because it is the amount you start with.
Practice routine
Practice fraction division with visual feedback
Try one problem at a time. Predict the answer first, then enter it into the visual tool and use the tape and guided steps to check what each group means. The goal is to reason about the groups, not only remember “keep, change, flip.”
TryWhat to noticeAnswer
3/4 ÷ 2Share a fraction between equal groups.3/8
1/2 ÷ 3See a unit fraction split into smaller equal parts.1/6
2/3 ÷ 1/2Measure how many half-size groups fit into two thirds.1 1/3
3 ÷ 2/5Rewrite a whole number as a fraction over 1.7 1/2
1 1/2 ÷ 2/3Convert a mixed number before dividing.2 1/4
Check yourself: Did you rewrite each whole number as a fraction over 1?
Check yourself: Is the answer reasonable when the divisor is smaller or larger than 1?
Common mistakes
Avoid the mistakes that change the value
- Flipping the first fraction instead of the second fraction.
- Forgetting to rewrite a whole number as a fraction over 1.
- Trying to divide numerators and denominators separately.
- Leaving a mixed number unconverted during the calculation.
- Skipping the final simplification or mixed-number form.
Common questions
Dividing Fractions FAQ
The second fraction is the divisor. Dividing by a fraction is equivalent to multiplying by the number that makes that fraction equal one, which is its reciprocal.