Step 1. Turn the second fraction upsidedown (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:
(If you are unsure of the last step see the equivalent fractions page)
Example 2
Step 1. Turn the second fraction upsidedown (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:
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.