Page 74 - Cambridge+Checkpoint+Mathematics+Coursebook+9

7.5 Working with fractions mentally

4 Work out these divisions mentally. Use jottings to help if you need to.
4
2
3
1
1
a 1 ÷ b 1 ÷ c 2 ÷ d 3 ÷ e 4 ÷ f 7 ÷ 7
6 3 12 4 7 5 8 5 5 9 8 12
4
3
4
6
g 2 ÷ h 6 ÷ i 3 ÷ j 8 ÷ k 5 ÷ 10 l 5 ÷ 15
3 5 7 5 4 7 9 5 6 13 6 16
Work out the answers to questions 5 to 8
mentally. Use jottings to help if you need to.
1
1
5 In a UK hockey squad, of the players are English, of the players are Scottish
3 4
and the rest are Welsh.
What fraction of the squad are Welsh?
2
1
6 In a packet of biscuits, are chocolate, are shortbread and the rest are coconut.
5 6
What fraction of the biscuits in the packet are coconut?
3
7 In a cinema of the people watching the fi lm are children.
5
3 of the children are girls.
4

a What fraction of the people watching the film are girls?
b What fraction of the people watching the film are boys?

4
8 At a cricket match of the supporters are supporting the home team.
9
3
The rest are supporting the away team. of the away team supporters
5
are male.
a What fraction of all the supporters are male and supporting the
away team?
b What fraction of all the supporters are female and supporting the
away team?

Summary

You should now know that: You should be able to:
+ You simplify a fraction into its simplest form, or + Write a fraction in its simplest form by cancelling
lowest terms, by dividing the numerator and the common factors.
denominator by the highest common factor (HCF). + Add, subtract, multiply and divide fractions,
+ You can only add or subtract fractions when interpreting division as a multiplicative inverse,
the denominators are the same. If they are and cancel common factors before multiplying
different, write them as equivalent fractions with and dividing.
a common denominator, then add or subtract the + Work with fractions mentally, using jottings where
numerators. appropriate.
+ When you multiply fractions you should cancel + Solve word problems mentally.
common factors before multiplying.
+ When you divide by a fraction you turn this
fraction upside down and multiply instead. This is
called ‘invert and multiply’.

7 Fractions 73