Amount we have
3/4 = 6/8
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Dividing fractions
How to Find the Quotient of Fractions
The quotient is the answer to a division — how many groups of the second fraction fit inside the first. Keep the first fraction, flip the second, multiply across, and simplify: that is the whole method.
- quotient means the answer to division
- keep change flip
- how many fit
- simplify 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
3/4 ÷ 1/8
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 1/8 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 8 equal parts.
One group to measure with
1/8 = 1/8
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Step 2 — Count groups of 1/8
The blue amount has 6 equal pieces. Each green group needs 1 pieces.
Next, mark 1/8 as one complete group.
6 full groups
No pieces are left over.
You measured6/1groups.
3/4 ÷ 1/8 = 6 = 6/1
Check with the rule
3/4 ÷ 1/8=3/4 × 8/1=24/4=6/1
The calculation steps
- 1.Keep 3/4.
- 2.Flip the divisor: 1/8 becomes 8/1.
- 3.Change division to multiplication: 3/4 × 8/1.
- 4.Simplify before multiplying: 3/1 × 2/1.
- 5.Multiply across: 24/4.
- 6.Simplify the result: 6/1.
Quick answer
Keep, change, flip — then simplify
The quotient of 3/4 ÷ 1/8 is 6: keep 3/4, change ÷ to ×, flip 1/8 to 8/1, and multiply — 3/4 × 8/1 = 24/4 = 6. Six eighth-sized pieces fit inside three quarters, which is what the quotient counts.
A quotient may be a whole number (6), a proper fraction (1/2 ÷ 3/4 = 2/3), or an improper fraction to regroup (5/6 ÷ 1/2 = 1 2/3). All three are ordinary quotients — the counting question decides the shape of the answer.
The method
Four steps: frame, flip, multiply, finish
Read the division as "how many fit"
The quotient of 3/4 ÷ 1/8 answers: how many eighth-sized pieces fit inside three quarters? Framing the question first makes the answer’s size predictable.
Keep the first fraction, flip the second
Keep the dividend exactly as written, change ÷ to ×, and replace the divisor with its reciprocal: 3/4 ÷ 1/8 becomes 3/4 × 8/1.
Multiply across and simplify
Multiply the numerators and the denominators, then reduce: 3/4 × 8/1 = 24/4 = 6. Cancel common factors before multiplying when it keeps the numbers small.
Regroup an improper quotient
If the quotient tops one whole, finish in mixed-number form: 5/6 ÷ 1/2 = 10/6 = 5/3 = 1 2/3.
Worked example
A whole-number quotient: 3/4 ÷ 1/8
3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6
Six eighth-pieces fit inside three quarters — the counting picture and the flip rule agree. The quotient 24/4 simplifies to the whole number 6.
Worked example
A fraction quotient: 1/2 ÷ 3/4
1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3
Three quarters does not fit inside one half even once, so the quotient must be less than 1. The flip gives 2/3 — two thirds of a full three-quarter group.
Worked example
Same fraction divided by itself: 7/8 ÷ 7/8
7/8 ÷ 7/8 = 7/8 × 8/7 = 56/56 = 1
Any number divided by itself is 1, and the flip rule shows why: a fraction times its own reciprocal always makes 1. The numerators and denominators cancel completely.
Worked example
Mixed numbers in the quotient: 1 1/2 ÷ 3/4
1 1/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2
The mixed number converts to 3/2 before the flip. Two quarters fit inside one and a half, so the quotient is the whole number 2 — no fraction part remains.
Why the quotient can be larger than both fractions
Students expect the answer to a fraction problem to come out smaller, but a quotient is a count of groups, not a leftover amount. Asking how many eighths fit in three quarters is like asking how many small cups fill a large pitcher: the answer can be far larger than either number in the question. Dividing by anything less than 1 always grows the value; dividing by anything greater than 1 always shrinks it.
That size expectation doubles as an answer check before any re-computation. The quotient of 1/2 ÷ 3/4 must be less than 1 (three quarters does not fit inside one half even once), and it is: 2/3. The quotient of 9/10 ÷ 3/5 must exceed 1, and it does: 1 1/2. A quotient that disagrees with the size prediction points at a flipped fraction or a lost reciprocal long before the arithmetic is rechecked.
Review why flipping produces the reciprocalCommon mistakes when finding quotients
- Dividing across instead of flipping: Dividing numerator by numerator and denominator by denominator happens to work only when the fractions share their numerators and denominators in matching ways — it is not the rule. Keep-change-flip is the general method: 3/4 ÷ 1/8 runs through 3/4 × 8/1, not 3/1 ÷ 4/8.
- Flipping the first fraction: The dividend stays put; only the divisor turns over. In 5/6 ÷ 1/2, flipping the 5/6 as well yields 6/5 × 1/2 = 3/5 instead of the correct 5/3.
- Judging the answer without a size check: Dividing by a number less than 1 must grow the amount, and dividing by a number greater than 1 must shrink it. A quotient that violates this — 1/2 ÷ 3/4 coming out larger than 1, for instance — announces itself before any re-checking of steps.
Practice routine
Predict the size before you flip
Say whether each quotient should be more or less than 1 — and why — before computing. Then run keep-change-flip and compare.
TryWhat to noticeAnswer
5/6 ÷ 1/2Dividing by a half doubles the amount.1 2/3
2/3 ÷ 4Rewrite the whole number as 4/1 and flip.1/6
5/6 ÷ 5/12Common numerators and denominators cancel cleanly.2
1 1/2 ÷ 3/4Convert the mixed number before the flip.2
9/10 ÷ 3/5Cross-cancel before multiplying.1 1/2
Keep learning
Related fraction topics
Common questions
Finding the Quotient of Fractions FAQ
The quotient is the answer to a division problem. The quotient of 3/4 ÷ 1/2 is 3/2, found by keeping the first fraction, flipping the second into its reciprocal, and multiplying: 3/4 × 2/1 = 6/4 = 3/2. The quotient tells how many groups of the divisor fit inside the dividend.