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Dividing Fractions

Turn the the second fraction upside down, then just multiply.

There are 3 Simple Steps to Divide Fractions:

Step 1. Turn the second fraction (the one you want to divide by) upside-down (this is now a reciprocal).
Step 2. Multiply the first fraction by the reciprocal of the second.

Step 3. Simplify the fraction (if needed)

Example 1

1 ÷ 1
2 4

Step 1. Turn the second fraction upside-down (the reciprocal):

1 4
4 1

Step 2. Multiply the first fraction by the reciprocal of the second:

1 × 4 = 1 × 4 = 4
2 1 2 × 1 2

Step 3. Simplify the fraction:

4 = 2
2

(If you are unsure of the last step see the equivalent fractions page)

Example 2

1 ÷ 1
8 4

Step 1. Turn the second fraction upside-down (the reciprocal):

1 4
4 1

Step 2. Multiply the first fraction by the reciprocal of the second:

1 × 4 = 1 × 4 = 4
8 1 8 × 1 8

Step 3. Simplify the fraction:

4 = 1
8 2

Why Turn the Fraction Upside Down?

Simply because division is the "inverse" or opposite of multiplying.

  • Multiplying by 5 makes something 5 times bigger.
  • Dividing by 5 makes something 5 times smaller.

A fraction has both multiply and divide in it ... you multiply by the top number and divide by the bottom number.

Example: 3/4

That means to cut into 4 pieces, and then take 3 of those.

So you divide by 4 then multiply by 3.

So 100 × 3/4 is 100 divided by 4 (=25) then multiplied by 3 (=75).

NOW if you have to DIVIDE by a fraction, you are asked to do the opposite of multiply ... so

  • multiply becomes divide, and
  • divide becomes multiply,

SO 3/4 becomes 4/3

Example: 75 / (3/4) is also 75 × (4/3), which is 75 divided by 3 (=25) then multiplied by 4 (=100)

Note: 100 × (3/4) = 75, and if we then DIVIDE 75 by (3/4), which is the same as multipling 75 by (4/3), you get back to 100 again.