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FOUR RULES FOR FRACTIONS
4
5
numerator
denominator
The language of fractions
5
3improper fraction
2
3
4mixed number
To simplify a fraction you divide the numerator and denominator by a common factor.
6
8
3
4
This can be shown on a diagram:
=
2
2
=
Examples
1 Simplify
6
9
6
9=
3
3
2
3
2 Simplify
14
35
14
35=
7
7
2
5
3 Simplify
36
42
36
42=
6
6
6
7
4 Change to a mixed number.
5
4
5
4=
1
1
4
note: 4 quarters make one whole one
5 Change to a mixed number.
8
3
8
3=
2
2
3
note: 3 thirds make one whole one
Adding and subtracting fractions
To add or subtract fractions a common denominator is needed first.
Example
1 Calculate
1
5
2
3
first write both fractions with a common denominator of 15
So
1
5
2
3
3
15
10
15
1
5
3
15 and
2
3
10
15
13
15
2 Calculate
first write both fractions with a common denominator of 14
So
4
7
1
2
8
14
7
14
4
7
8
14 and
1
2
7
14
1
14
4
7
1
2
3 Calculate
first write both fractions with a common denominator of 20
So 2
2
51
1
42
8
201
5
20
2
5
8
20 and
1
4
5
20
3
13
20
2
2
51
1
4
Multiplying and dividing fractions
Example
1 Calculate
1
5
2
3
multiply the numerators, multiply the denominators
1
5
2
3
12
5 3
2
15
2 Calculate 1
3
42
1
5
multiply the numerators, multiply the denominators.
7 11
4 5
77
20
first change to improper fractions
1
3
4
7
4 and 2
1
5
11
5
1
3
42
1
5
7
4
11
5
change to a mixed number
3
17
20
3 Calculate
5
8
3
5
multiply the numerators, multiply the denominators.
5 5
8 3
25
24
dividing by is the same as multiplying by
5
8
3
5
5
8
5
3
change to a mixed number
1
1
24
3
5
5
3
4 Calculate 1
1
22
3
4
multiply the numerators, multiply the denominators.
3 4
2 11
12
22
dividing by is the same as multiplying by 1
1
22
3
4
3
2
11
4
simplify
6
11
11
4
4
11
first change to improper fractions
1
1
2
3
2 and 2
3
4
11
4
3
2
4
11
