Number And Algebra - Chapter 7 Applying Ratios And Rates - Nelson Think Math Page 14
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32N E L S O N T H I N K M A T H S
8
A u s t r a l i a n C u r r i c u l u m
for the
Example
12
Determine whether the following pairs of ratios are equivalent.
1
1
5
7
a
15 : 45 and 12 : 36
b
:
and
:
3
2
3
10
Solution
a
Write the first ratio.
15 : 45
Cancel 15 : 45 to simplest form.
¼ 15 4 15 : 45 4 15 ¼ 1 : 3
Write the second ratio.
12 : 36
Cancel 12 : 36 to simplest form.
¼ 12 4 12 : 36 4 12 ¼ 1 : 3
Compare the simplest forms and write the
The ratios are equivalent because they
answer.
are both equivalent to 1 : 3.
1
1
b
Write the first ratio.
:
3
2
1
1
Multiply both by 6 to make whole numbers.
3 6 :
3 6
¼
3
2
This ratio is in simplest form.
¼ 2 : 3
5
7
Write the second ratio.
:
8
10
5
7
Multiply both by 40 and cancel to make
5
4
¼
:
3 40
340
8
10
6
1
1
whole numbers.
This ratio is in simplest form.
¼ 25 : 28
Compare the simplest forms and write the
The ratios are not equivalent because
answer.
their simplest forms are different.
Example
13
Use cross-multiplication to determine whether the following pairs of ratios are equivalent.
a
6 : 8 and 9 : 15
b
91 : 52 and 49 : 28
Solution
6
9
a
Write the ratios in fraction form.
and
8
15
6
9
—
—
Cross-multiply.
8
15
6 3 15 ¼ 90 and 8 3 9 ¼ 72
Compare the cross-products and write
The cross-products are different, so the
the answer.
ratios are not equivalent.
91
49
b
Write the ratios in fraction form.
and
52
28
91
49
—
—
Cross-multiply.
52
28
91 3 28 ¼ 2548 and 52 3 49 ¼ 2548
Compare the cross-products and write
The cross-products are equal, so the ratios
the answer.
are equivalent.
251
9780170214148
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