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Keep Change Flip — Definition, Formula & Examples

Keep Change Flip is a memory trick for dividing fractions. You keep the first fraction the same, change the division sign to multiplication, and flip the second fraction upside down.

Keep Change Flip is a mnemonic encoding the procedure for dividing by a fraction: retain the dividend, replace the division operation with multiplication, and replace the divisor with its reciprocal (multiplicative inverse).

Key Formula

ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
Where:
  • ab\frac{a}{b} = The first fraction (the dividend) — keep it
  • ÷\div = The division sign — change it to multiplication
  • cd\frac{c}{d} = The second fraction (the divisor) — flip it to become its reciprocal \frac{d}{c}

How It Works

When you see a problem like ab÷cd\frac{a}{b} \div \frac{c}{d}, follow three steps. Keep the first fraction exactly as it is. Change the division sign to a multiplication sign. Flip the second fraction so the numerator and denominator swap places. Then multiply straight across: numerators together and denominators together. Simplify your answer if possible.

Worked Example

Problem: Divide: 3/4 ÷ 2/5
Keep: Keep the first fraction as it is.
34\frac{3}{4}
Change: Change the division sign to multiplication.
34×\frac{3}{4} \times
Flip: Flip the second fraction (swap its numerator and denominator).
34×52\frac{3}{4} \times \frac{5}{2}
Multiply: Multiply numerators together and denominators together.
3×54×2=158\frac{3 \times 5}{4 \times 2} = \frac{15}{8}
Answer: 158\frac{15}{8}, which equals 1781\frac{7}{8}.

Why It Matters

Keep Change Flip turns every fraction division problem into a multiplication problem, which most students find easier to solve. You will use this skill constantly when working with ratios, proportions, and unit rates in upper elementary and middle-school math.

Common Mistakes

Mistake: Flipping the first fraction instead of the second.
Correction: Only flip the fraction that comes after the division sign (the divisor). The first fraction stays exactly the same — that is the "keep" step.

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