Dividing Fractions
Divide by multiplying by the reciprocal (flip and multiply).
Formula
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Example
1/2 ÷ 1/4 = 2
How it works
To divide by a fraction, you multiply by its reciprocal because division asks "how many of this amount fit into that amount?" Flipping the second fraction turns the division problem into an equivalent multiplication problem that is easier to calculate. For example, dividing by 1/4 is the same as multiplying by 4, since four quarters make one whole.
When to use it
Use this when a problem asks how many fractional parts are in another fraction, such as finding how many 3/5-cup servings fit into 2 cups. It also appears in ratio, measurement, and word problems involving scaling up or splitting amounts.
Worked example, step by step
3/4 ÷ 2/3 = 3/4 × 3/2 = (3 × 3) / (4 × 2) = 9/8 = 1 1/8
Common mistakes to avoid
- Flipping the first fraction instead of the second one
- Multiplying numerators and denominators without changing division to multiplication first
- Forgetting to simplify the final fraction or convert an improper fraction to a mixed number when needed
Did You Know?
"Keep, change, flip" works because dividing by a number is the same as multiplying by its reciprocal.
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