Here’s another: if you want to add 1/3 plus 1/7, you add 3 and 7 to get 10 for the numerator, then you
multiply 3 and 7 to get 21 for the denominator.
Test yourself
Try these for yourself. Do them all in your head.
a) ¼ + 1/3 =
b) 1/5 + ¼ =
c) 1/3 + 1/5 =
d) ¼ + 1/7 =
How did you go? The answers are:
a) 7/12
b) 9/20
c) 8/15
d) 11/28
You should have had no trouble with those.Subtracting fractions
A similar method is used for subtraction. You multiply the numerator of the first fraction by the
denominator of the second fraction. You then multiply the denominator of the first fraction by the
numerator of the second, and subtract the answer. You find the denominator of the answer in the usual
way; by multiplying the denominators together.
Here’s an example:
What we did was multiply 2 × 4 = 8, and then subtract 3 × 1 = 3, to get 5. Five is the numerator of
our answer. We multiplied 3 × 4 = 12 to get the denominator. You could do that entirely in your head.
Test yourself
Try these for yourself. Try them without writing anything down except the answers.
a) ½ − 1/7 =
b) 1/3 − 1/5 =
c) 1/5 −1/7 =
d) ½ −1/3 =
The answers are:
a) 5/14
b) 2/15
c) 2/35
d) 1/6
If you made any mistakes, read the section through again.
Try some for yourself and explain this method to your closest friend. Tell your friend not to tell the
rest of your class.
A shortcut
Just as with addition, there is an easy shortcut when you subtract fractions when both numerators are 1.
The only thing to remember is to subtract backwards.