Adding and Subtracting Fractions

By Graeme Henchel

8

3

http://hench-maths.wikispaces.com

Adding Fractions with common denominators

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4

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3

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7

Adding Fractions with different denominators

Problem:

You can’t add fractions with different denominators without getting them ready first. They will be ready to add when they have common denominators

Solution: Turn fractions into equivalent fractions with a

common denominator that is find the Lowest Common Multiple (LCM) of the two denominators

Finding the Lowest Common Denominator

• The lowest common multiple of two numbers is the lowest number in BOTH lists of multiples

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1

2

1

Multiples of 2 are 2, 4, 6, 8, 10……

Multiples of 3 are 3, 6, 9, 12, ………

What is the lowest common multiple?

Finding the Lowest Common Denominator

• The lowest common multiple of two numbers is the lowest number they will BOTH divide into

3

1

2

1

2 divides into 2, 4, 6, 8…..3 divides into 3, 6, 9….

What is the lowest number 2 and 3 both divide into?

+The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths

6

5

6

2

6

3

2

2

3

1

3

3

2

1

You can’t add fractions with different denominators

Special form of 1

3

1

2

1

10

9

10

4

10

5

5

2

2

1

Lowest common denominator is 10 so make all fractions tenths

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3

1

Turn both fractions into twelfths

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7

12

3

12

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3

2

7

3

What is the lowest number BOTH 3 and 7 divide into?

Hmmmmm??????It is 21. So that is my common denominator

21

?

21

?

What special form of 1 will

change 7 to 21. Hmmmm?

It is 3/3So I multiply 3/7 by 3/3

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3

What special form of 1 will

change 3 to 21. Hmmmm?

It is 7/7So I multiply 2/3 by 7/7

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Now 3x3=9 and 2x7=14Now I know the new

numerators

21

14

21

9

Finally the fractions are READY to add. I just have to add the

numerators 9+14=23

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23

Adding Mixed Numbers

• Separate the fraction and the whole number sections, add them separately and recombine at the end

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2

13

15

6

57

7 65

2 2

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