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How do you add, subtract, multiply and divide
fractions?
Worked examples: Adding, subtracting, multiplying and dividing fractions
Adding fractions
You can add fractions if the denominators (bottom number of the fraction) are the same.
You simply add the numerators (top number of the fraction).
1+3=4
5 5 5
If the fractions have different denominators, determine the lowest common denominator
(LCD) so that you can express each fraction in equivalent form. The lowest common
denominator is the lowest number that the denominator of each individual fraction will divide
into. Multiply both numerator and denominator of each fraction by the same number.
3/5 + 2/3 The lowest common denominator of 5 and 3 is 15.
Multiply 3/5 by 3/3 and multiply 2/3 by 5/5. This will create two equivalent fractions with the
same denominator.
3 + 2 = 9 + 10 = 19
5 3 15 15 15
(Note LCD is 15.)
Convert to mixed number and the answer is 14/15.
Mixed numbers need to be converted to improper fractions before using this addition
technique.
Subtracting fractions
Subtracting fractions is very similar to adding in that all fractions in your calculation need to
have the same denominator. You may need to determine the lowest common denominator
(LCD) as you did with addition.
Subtract 1/3 from 3/4.
3–1 = 9–4= 5
4 3 12 12 12
(Note LCD is 12.)
Multiplying fractions
Multiplication of fractions is carried out by multiplying all the numerators together and all the
denominators together.
Multiply 2/5 by 3/7.
2x3=2x3= 6
5 7 5 x 7 35
Activity sheet: How to add, subtract, multiply and divide fractions
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Sometimes the answer to a multiplication calculation can be simplified by dividing both
numerator and denominator by the same number. This process is called cancelling,
because you strike out the original numbers to create the new fraction.
25 = 5
30 = 6
(divide numerator by 5.)
(divide denominator by 5.)
Dividing fractions
To divide by a fraction, invert it and multiply.
Divide 23/4 by 5/8.
23/4 ÷ 5/8 = 11 ÷ 5 = 11 x 8 = 88 = 22 = 42/5
4 8 4 5 20 5
Fractions problems
1. An old drawing shows that you have to cut 3 tabs of 5/16in, 9/16 in and 11/16in. What is the total
length of tab to be cut (in inches)?
2. A drawing from overseas requires you to cut 4¾in from a piece of pipe which is 6½in long. How long
will the pipe be after cutting off this piece?
3. Divide 7½ by ¾ .
4. Add 6¾ to 4½ and subtract 11/16 from this.
5. How many pieces 1¾ inches long can you get from a piece of wire 15¾ inches long?
Check your responses with the answers below.
Answers
(1) 1 9
16
(2) 1¾
(3) 10
(4) 99
16
(5) 9 pieces
Activity sheet: How to add, subtract, multiply and divide fractions
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