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Chapter 9 · Questions · page 46 of 68

How do you divide fractions?

Short answerKeep the first fraction, change division to multiplication, and flip the second fraction. Then multiply straight across.

levelPre-algebra
standard6.NS.A.1
practiceFraction operations

Dividing by a number is the same as multiplying by its reciprocal. Dividing by 4/5 means asking how many 4/5 fit, and multiplying by 5/4 answers it. People call it keep, change, flip.

How to use it

  1. Keep the first fraction as it is.
  2. Change ÷ to ×.
  3. Flip the second fraction upside down.
  4. Multiply tops and bottoms, then simplify.

Example

23÷45=23×54=1012=56\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4} = \frac{10}{12} = \frac{5}{6}
3÷14=3×4=123 \div \frac{1}{4} = 3 \times 4 = 12
12÷3=12×13=16\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{1}{6}

Where it goes wrong

  • Flipping the first fraction instead of the second.
  • Flipping and then dividing anyway. After the flip, it is multiplication.

Related

Dividing fractionsMultiplying fractions
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