Page 77 - MAT KS3 Y8 Cambridge CheckPoint

7.4 Adding and subtracting fractions

7.4 Adding and subtracting fractions

You already know that you can only add or subtract fractions when the denominators are the same.
If the denominators are different, you must write the fractions as equivalent fractions with a common
denominator, then add or subtract the numerators.

Worked example 7.4a

Work out 2 + 1 6 .
3

4
2
1
2 + 1 = 4 + The denominators are not the same so change the into .
3 6 6 6 3 6 Remember that the
4 + 1 = 5 The denominators are now the same so add the numerators. LCM of 3 and 6 is 6.
6 6 6

In an improper fraction the numerator is bigger than 3 14 53
,
the denominator. 2 3 and 34 are improper fractions.
A mixed number contains a whole-number part and a
fractional part. 3
1
1 , 2 and 14 11 are mixed numbers.
When you add mixed numbers, follow these steps. 2 4 12
c Add the whole-number parts.
d Add the fractional parts and cancel this answer to its simplest form.
If this answer is an improper fraction, write it as a mixed number.
e Add your answers to steps c and d.
When you subtract mixed numbers, follow these steps.
c Change both mixed numbers into improper fractions.
d Subtract the improper fractions and cancel this answer to its simplest form.
e If the answer is an improper fraction, change it back to a mixed number.

Worked example 7.4b
1
Work these out. a 2 1 + 3 5 b 3 − 1 3
4 6 2 5
a c 2 + 3 = 5 Add the whole-number parts.
1
d + 5 = 3 + 10 = 13 Add the fractional parts using a common denominator of 12.
4 6 12 12 12
13 = 1 1 Check that this fraction is in its simplest form and write as a mixed number.
12 12
e 51+ 1 = 6 1 Add the two parts together to get the final answer.
12 12
7
b c 3 1 = and 1 3 = 8 Change both the mixed numbers into improper fractions.
2 2 5 5
7
d − 8 = 35 − 16 = 19 Subtract the fractions using a common denominator of 10.
2 5 10 10 10
19
e = 1 9 The answer is an improper fraction so change it back to a mixed number.
10 10
7 Fractions 75