To divide fractions, keep the first fraction, change the division sign to multiplication, and flip the second fraction upside down (use its reciprocal) — then multiply across. So 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2. Teachers call this "keep, change, flip".
The fraction being divided stays exactly as it is. Only the second fraction — the divisor — gets flipped, so keep track of which is which.
Swap the division sign for multiplication and replace the second fraction with its reciprocal (swap its top and bottom): ÷ 1/4 becomes × 4/1. Dividing by a number and multiplying by its reciprocal are the same operation.
Top times top, bottom times bottom, then reduce: 1/2 × 4/1 = 4/2 = 2. Cross-cancel before multiplying if you want smaller numbers.
Division asks "how many of the second fit in the first?". 1/2 ÷ 1/4 = 2 makes sense because two quarters fit in a half. If your answer fails that check, you probably flipped the wrong fraction.
Fraction ÷ fraction
1/2 ÷ 1/4
Answer: 2
Answer stays a fraction
3/5 ÷ 2/3
Answer: 9/10
Whole number ÷ fraction
4 ÷ 2/3
Answer: 6
Only the divisor — the fraction after the ÷ sign — gets flipped. Flipping the first fraction, or both, gives the reciprocal of the right answer. "Keep, change, flip" is in that order for a reason.
1/2 ÷ 4/1 is not the same as 1/2 ÷ 1/4. The flip only works together with switching ÷ to ×. Do both or neither.
Dividing by a proper fraction makes the answer bigger: 4 ÷ 2/3 = 6. You're asking how many small pieces fit inside, and small pieces fit many times. An answer larger than what you started with is often correct.
A memory aid for dividing fractions: keep the first fraction, change the division sign to multiplication, flip the second fraction (use its reciprocal), then multiply across. 3/5 ÷ 2/3 = 3/5 × 3/2 = 9/10.
Dividing by a number and multiplying by its reciprocal do the same thing — dividing by 2 is multiplying by 1/2, and dividing by 1/4 is multiplying by 4, because you're asking how many quarters fit. The rule is that relationship applied to every fraction.
The fraction turned upside down: the reciprocal of 2/3 is 3/2, and the reciprocal of a whole number like 5 (= 5/1) is 1/5. A number times its reciprocal always equals 1.
Write the whole number over 1, then keep-change-flip: 3/4 ÷ 2 = 3/4 × 1/2 = 3/8. Sharing three quarters between two people gives three eighths each.
Convert to improper fractions first, then keep-change-flip. For 2 1/2 ÷ 1 1/4: 5/2 ÷ 5/4 = 5/2 × 4/5 = 20/10 = 2.
Division by a fraction less than 1 asks how many small pieces fit into the amount — and small pieces fit more than once per whole. 4 ÷ 2/3 = 6 because each whole holds one-and-a-half two-thirds.
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