Amount we have
9/4 = 9/4
1234
Dividing fractions
How to Divide Mixed Fractions
Mixed-number division is ordinary fraction division plus one opening move: every mixed number converts to an improper fraction before anything flips. Then keep-change-flip runs exactly as always, and the quotient regroups back into a mixed number at the end.
- convert first, flip second
- improper fractions before the flip
- keep-change-flip
- regroup the quotient
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
9/4 ÷ 3/2
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 3/2 fit inside 9/4?
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
3/2 = 6/4
1234
Step 2 — Count groups of 6/4
The blue amount has 9 equal pieces. Each green group needs 6 pieces.
Whole 1
Whole 2
Whole 3
Next, mark 6/4 as one complete group.
1 full group
3/4 left = 1/2 of one more 6/4 group
You measured1 1/2groups.
9/4 ÷ 3/2 = 1 + 1/2 = 1 1/2
Check with the rule
2 1/4 ÷ 1 1/2=9/4 ÷ 3/2=9/4 × 2/3=18/12=3/2
The calculation steps
- 1.Rewrite: 2 1/4 ÷ 1 1/2 becomes 9/4 ÷ 3/2.
- 2.Keep 9/4.
- 3.Flip the divisor: 3/2 becomes 2/3.
- 4.Change division to multiplication: 9/4 × 2/3.
- 5.Simplify before multiplying: 3/2 × 1/1.
- 6.Multiply across: 18/12.
- 7.Simplify the result: 3/2.
- 8.Write the mixed number: 1 1/2.
Quick answer
Convert, flip the divisor, multiply, regroup
In 2 1/4 ÷ 1 1/2, both mixed numbers become improper fractions first: 9/4 and 3/2. Keep 9/4, change ÷ to ×, and flip 3/2 to 2/3. The product 18/12 simplifies to 3/2 and regroups to 1 1/2.
The conversion is not optional. Reciprocals are defined for single fractions, and a mixed number is two quantities written together — 1 1/2 has no single top and bottom to swap until it becomes 3/2.
The method
Four steps: convert, flip, multiply, regroup
Convert every mixed number to an improper fraction
The flip rule needs one numerator and one denominator per number: 1 1/2 becomes 3/2 and 2 1/4 becomes 9/4 before anything is flipped.
Keep the first fraction, flip the divisor
Keep the dividend exactly as it is, change ÷ to ×, and replace the divisor with its reciprocal: 9/4 ÷ 2/3 becomes 9/4 × 3/2.
Multiply across and simplify
Multiply the numerators, multiply the denominators, and cancel common factors — before or after multiplying, whichever keeps the numbers small.
Regroup the answer into a mixed number
A quotient such as 18/12 is unfinished twice over: simplify to 3/2, then regroup to 1 1/2. Mixed-number division normally ends in mixed-number form.
Worked example
Mixed ÷ fraction: 1 3/4 ÷ 1/2
1 3/4 ÷ 1/2 = 7/4 × 2/1 = 14/4 = 7/2 = 3 1/2
The mixed number converts to 7/4 first; the divisor 1/2 was already a fraction. Flipping gives 2/1, the product is 14/4, and the regroup lands on 3 1/2 — one and three quarters holds three and a half halves.
Worked example
Mixed ÷ mixed: 2 1/4 ÷ 1 1/2
2 1/4 ÷ 1 1/2 = 9/4 × 2/3 = 18/12 = 3/2 = 1 1/2
Both numbers convert: 9/4 and 3/2. The flip turns 3/2 into 2/3, and cross-cancelling the 2s and the 3s before multiplying would reach 3/2 immediately. The quotient regroups to 1 1/2.
Worked example
Both mixed, larger numbers: 3 1/3 ÷ 2 2/9
3 1/3 ÷ 2 2/9 = 10/3 × 9/20 = 90/60 = 3/2 = 1 1/2
Conversions first: 10/3 and 20/9. Cross-cancelling before multiplying — 10 with 20, 9 with 3 — leaves 1 × 3 over 3 × 2 = 3/2. Cancelling early is what keeps bigger mixed-number divisions manageable.
Worked example
Mixed ÷ whole: 1 1/2 ÷ 3
1 1/2 ÷ 3 = 3/2 × 1/3 = 3/6 = 1/2
The whole number 3 rewrites as 3/1 and flips to 1/3. The quotient 1/2 answers the sharing question: half of one and a half is one half, shared three ways.
Why the conversion comes before the flip
Dividing by a number means multiplying by its reciprocal — the number that multiplies it to exactly 1. For 3/2, that reciprocal is 2/3, because 3/2 × 2/3 = 6/6 = 1. But a mixed number like 1 1/2 does not have one top and one bottom to swap; its wholes and parts live in different units. Only after the multiply-add conversion merges them into 3/2 does the “flip” have a defined target.
This is also why there is no column shortcut for mixed-number division. In addition and subtraction the wholes and parts can be worked separately (with regrouping), because those operations respect the two units. Division scales the whole amount at once, and scaling needs one number, not two — hence convert first, always.
Review the mixed-to-improper conversionCross-cancelling keeps bigger divisions manageable
In 3 1/3 ÷ 2 2/9, the conversions produce 10/3 ÷ 20/9. Flipping gives 10/3 × 9/20. Multiplying first would churn out 90/60 — correct, but heavy. Cancelling before multiplying is lighter: 10 and 20 share a factor of 10, and 9 and 3 share a factor of 3, leaving 1 × 3 over 3 × 2 = 3/2 = 1 1/2. Same answer, smaller numbers, fewer places to slip.
Cancel only diagonally, between a numerator and the other fraction’s denominator — never within one fraction’s own row, and never across the plus or minus of an unconverted mixed number. In division the diagonal is always available because the expression is one product after the flip.
Common mistakes when dividing mixed fractions
- Flipping before converting the mixed number: Flipping 1 1/2 into 2 1/1 is not a thing — reciprocals are defined for single fractions. Convert 1 1/2 to 3/2 first; only then does the flip produce 2/3.
- Flipping the first fraction: Only the divisor turns over. In 9/4 ÷ 3/2, the 9/4 stays put while 3/2 becomes 2/3. Flipping both turns the quotient into its own reciprocal and quietly changes the problem.
- Dividing the whole parts and fraction parts separately: Mixed-number division has no column shortcut like addition does. The wholes and parts interact through the improper conversion — 2 1/4 is 9/4, not "2 of something plus 1/4 of something" under a division sign.
- Leaving the quotient improper and unsimplified: 18/12 is correct in value but unfinished: simplify to 3/2 and regroup to 1 1/2. Division of mixed numbers is expected to end in mixed-number (or whole) form.
Practice routine
Convert first, predict the size, then flip
For each problem, convert both numbers and estimate before flipping: dividing by something less than 1 makes the answer bigger, dividing by something greater than 1 makes it smaller. Then run keep-change-flip and compare.
TryWhat to noticeAnswer
1 3/4 ÷ 1/2Convert the mixed number, flip only the divisor.3 1/2
2 1/4 ÷ 1 1/2Both numbers convert before the flip.1 1/2
3 1/3 ÷ 2 2/9Cross-cancel early to keep the product small.1 1/2
1 1/2 ÷ 3A whole divisor flips from 3/1 to 1/3.1/2
2 2/5 ÷ 1 1/5Matching denominators after conversion cancel cleanly.2
Keep learning
Related fraction topics
Common questions
Dividing Mixed Fractions FAQ
Convert every mixed number to an improper fraction, keep the first fraction, flip the divisor, and multiply across. Then simplify and regroup the quotient into a mixed number. For example, 2 1/4 ÷ 1 1/2 = 9/4 × 2/3 = 18/12 = 3/2 = 1 1/2.