What is dividing fractions?

Why it matters

Dividing fractions completes the four fraction operations and shows up in practical situations: splitting a recipe into smaller portions, figuring out how many quarter-mile laps fit in a two-mile run, and eventually in every ratio and rate problem in algebra. It also connects back to the idea that fractions and division are the same thing, which is a key insight for middle school math.

Worked example

Divide: 3/4 ÷ 1/2.

1. 1

   Keep the first fraction exactly as it is: 3/4.

   This is the "keep" step. Do not change the first fraction at all.

2. 2

   Change the operation from division (÷) to multiplication (×). This is the "change" step.

3. 3

   Flip the second fraction to get its reciprocal: 1/2 becomes 2/1. This is the "flip" step.

   The reciprocal is just the fraction turned upside down — numerator and denominator swap. 1/2 flipped is 2/1, which equals 2.

4. 4

   Now multiply straight across: 3/4 × 2/1. Numerators: 3 × 2 = 6. Denominators: 4 × 1 = 4. Result: 6/4.

   Once you have done keep-change-flip, everything becomes a multiplication problem — and multiplying fractions is just straight across.

5. 5

   Simplify 6/4. GCF of 6 and 4 is 2. Divide top and bottom by 2: 6 ÷ 2 = 3, 4 ÷ 2 = 2. So 6/4 = 3/2.

   3/2 can also be written as the mixed number 1 and 1/2.

6. 6

   Check: multiply the answer by the divisor and it should equal the dividend. 3/2 × 1/2 = 3/4. ✓

   If dividing was correct, multiplying back should undo it.

Common mistakes

• •Flipping the FIRST fraction instead of the second. Keep, change, flip means flip the number you are dividing BY — the one after the ÷ sign.
• •Forgetting to flip at all — rewriting ÷ as × but keeping the second fraction the same. That gives 3/4 × 1/2 = 3/8, which is the wrong answer.
• •Applying keep-change-flip to addition or subtraction. The method only works for division. For adding and subtracting fractions, you still need a common denominator.
• •Leaving the answer as an improper fraction when the context calls for a mixed number, or vice versa. Check what form the problem or test expects.

How Briveli teaches dividing fractions

Briveli introduces dividing fractions in Grade 6 starting with whole-number divisors (so students see the pattern), then moves to dividing by a unit fraction, then any fraction using keep-change-flip, always connecting the procedure back to multiplication so students understand why it works.