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7.2 Adding and subtracting fractions

7.2 Adding and subtracting fractions

Before you can add or subtract fractions, make sure they have the same denominator.
If the denominators are different, you must #nd equivalent fractions with a common denominator,

then add or subtract the numerators. It makes the calculation simpler if you use the lowest common
denominator.
You can also add and subtract mixed numbers. Remember to write your answer in

Here is a method for adding mixed numbers. !ere are its simplest form.
other methods, as well.
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.
Here is a method for subtracting mixed numbers.
c Change both mixed numbers into improper fractions. You can use this method for
d Subtract the improper fractions and cancel this answer to its addition, too. Try it out.
simplest form.
e If the answer is an improper fraction, change it back to a mixed number.

Worked example 7.2
5
1
a Work these out. i 4 + 3 ii 1 1 + 2 iii 6 − 2 4
9
4
7
3
4
6
b Read what Dakarai says. Use a counter-example to show that he is wrong.
If I add together two different fractions,
my answer will always be greater than 1.
4 3 16 21
a i 7 + 4 = 28 + 28 Rewrite each fraction with the lowest common denominator before adding.
= 37 = 1 9 The answer is an improper fraction, so change to a mixed number.
28 28
ii c 1 + 2 = 3 Add the whole-number parts.
3
5
1
d + 6 = 12 + 10 = 13 Add the fractional parts, using the lowest common denominator of 12.
4
12
12
13 1 The answer is an improper fraction, so change it to a mixed number.
12 = 1 12
e 3 1+ 1 = 4 1 Add the two parts together to get the fi nal answer.
12 12
1
iii c 6 3 = 19 and 2 4 = 22 Change both the mixed numbers into improper fractions.
9
3
9
19 22 57 22 35
d 3 − 9 = 9 − 9 = 9 Subtract the fractions, using the lowest common denominator of 9.
35 8
e 9 = 3 The answer is an improper fraction so change it back to a mixed number.
9
b 1 + 1 = 3 + 1 = 4 You only need one example (a counter-example), to show that he is wrong.
2 6 6 6 6
4 = 2 and 2 < 1, so the statement is not true.
6 3 3
66 7 Fractions