Page 197 - Math Smart - 7

Example 10

O Work out the following. Express your answers in the simplest form.

a) 2^+1^ b) 8-l§
6
^ 3 ^ '
Solution
a; ^3+«6-3 + 6 Write each mixed number as an improper fraction

_ 14^ n
The LCM of 3 and 6 is 6
- 6 6
- 25 Add the two fractions by adding the numerators
6
Write as a mixed number

b) 8-l| = f-| Write each number as an improper fraction

3 8x3 5
The LCM of 1 and 3 is 3
1x3 3
_ 24
You have two fractions with the same denominator
~ 3
_ IS Subtract the two fractions by subtracting their numerators
~ 3
= 6i Write as a mixed number

Example 11

Find the sum of 21 and 31.

Solution
■y2 . :,2 _,-2 . 2 Add the whole numbers
25 +33 -55 + 3
= 5-^ + ^ Convert the proper fractions to like fractions
^ 15 ^ 15
Add the proper fractions

= 5 + 1^ Convert the improper fraction to a mixed number
= 6i Simplify

Example 12

Subtract 1 ^ from 3 ^ .

Solution

-2^ -
2
3^ 2 7 -•^14 " 7 Subtract the whole numbers
-2^ - 4 Convert the proper fractions to like fractions
-4 14
14
-4 14 Simplify
_ 2 —