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Dividing by a Fraction

Dividing by a fraction might seem difficult at first, but it''s probably easier than you think. Like many other math problems, there''s a simple trick that makes this a total breeze.

Using reciprocals to divide by fractions

To divide by a fraction, all you need to do is flip the fraction upside down then multiply by the new fraction instead of divide. We call this the reciprocal of the fraction. For example, the reciprocal of:

2/7
is
7/2.

Easy, right?

Let''s use reciprocals to divide by fractions.

4 ÷ 2/7 = 4*7/2

4*7/2 = (4*7)/2 = 28/2

28/2 = 14

Here''s a trickier example:

3/4 ÷ 7/8 = 3/4*8/7

3/4*8/7 = (3*8)/(4*7)

(3*8)/(4*7)= 24/28

24/28 = 6/7

If you''re dividing one fraction by another, don''t make the mistake of turning both fractions into reciprocals.

Only the divisor (the second fraction) gets flipped upside down into its reciprocal.

We also need to remember to simplify the end result, which is when we make the numbers as small as possible. For example, the simplified version of:
50/100
is
1/2
If you don''t simplify, you might not get full marks.

Topics related to the Dividing by a Fraction

Simplifying Expressions

Operations with Fractions

Dividing Fractions

Flashcards covering the Dividing by a Fraction

Common Core: 6th Grade Math Flashcards

Practice tests covering the Dividing by a Fraction

MAP 6th Grade Math Practice Tests