Page 293 - Math Smart - 7

Molly used 4 glasses of blended lemon to prepare the lemonade. How many glasses of
water did she use?

Solution
To find the number of glasses of water, we use the ratio 1 : 3.
1 ;3 = 4:? 1 : 3 and 4 :12 are
equivalent ratios.
1 : 3 j
X 4 X 4
c;;j[
So, Molly used 12 glasses of water to prepare the lemonade.

Simplifying ratios

Example 2

long bought 4 bookshelves and 6 chairs for his new apartment.
a) What is the ratio of the number of chairs to the number of bookshelves?
b) Express the number of bookshelves as a fraction of the number of chairs.

Solution
bookshelves 1
\ k
To simplify a fraction or
chairs
1 1 1
ratio, find the highest
1 1 1
common factor (HCF) of
a) Number of chairs: Number of bookshelves
both numbers in the ratio.
= 6:4 Divide each number by their HCF, 2 Then divide each number
= 3:2 Simplify by the HCF.
The ratio of the number of chairs to the number of bookshelves is 3 : 2.
A ratio Is In its simplest
Number of bookshelves _ 4
b)
Number of chairs 6 form when 1 is the only
_2
whole number that
3
divides exactly into each
of
the
chairs.
of
number
The number of bookshelves is |
part.
Example 3
The ingredients used to make some shortbread biscuits are as follows:
• 360 g flour • 120 g sugar • 240 g butter

Work out the following, giving your answers in simplest form.
a) What is the ratio of the amount of sugar used to the amount of flour used?
b) What is the ratio of the amount of flour used to the amount of butter used?

Solution
a) The recipe needs 120 g sugar and 240 g of flour.
It is important that you
The ratio of the amount of sugar used to the amount of flour used is 120 : 240
write the numbers in the
The highest common factor of 120 and 240 is 120.
correct order.
120:240 The ratio of the amount
•r 1201 ^120 of sugar used to the
amount of flour used is
1 : 2, not 2 : 1.
So, the simplified ratio is 1 : 2.