Making Equivalent Fractions Worksheet
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1STRAND: Measurement
TOPIC:
Ratio & rates
Ratios involving fractions
To express two fractions as a ratio in simplest form, follow the steps below:
1. convert mixed number(s) into improper fraction(s)
2. change both fractions to the equivalent fractions with the same denominator
3. omit denominators and write numerators as a ratio
4. simplify the ratio by dividing both numbers by the highest common factor.
WORKED
Example
Express each of the following as a ratio in its simplest form.
2
11
2
3
4
1
----- -
----- -
-- -
-- -
-- -
-- -
a
b
c
:
2
: 1
1
: 1
13
13
5
5
7
3
Solution
2
11
a
Both
----- -
and
----- -
are proper fractions with the same denominator, so omit the denominators and write the
13
13
numerators as a ratio.
The ratio is 2 : 11
2
3
12
8
=
b
2
-- -
: 1
-- -
----- -
:
-- -
(Change mixed numbers into improper fractions.)
5
5
5
5
Since denominators are the same, write the numerators as a ratio and simplify.
The ratio is 12 : 8
or
3 : 2
(Divide both numbers by 4 — the HCF of 12 and 8.)
4
1
11
4
=
c
1
-- -
: 1
-- -
----- -
:
-- -
(Change the mixed numbers into improper fractions.)
7
3
7
3
33
28
=
----- -
----- -
:
(Change both fractions to the lowest common denominator.)
21
21
Since the denominators are the same, write the numerators as a ratio.
The ratio is
33 : 28
Try these
Express each of the following as a ratio in its simplest form.
2
3
1
1
2
5
3
7
1
2
3
4
-- -
:
-- -
1
-- -
:
-- -
4
-- -
: 2
-- -
2
----- -
: 3
----- -
5
5
2
2
9
9
11
11
3
1
3
3
2
2
5
4
5
6
7
8
6
-- -
: 2
-- -
1
-- -
: 2
-- -
5
-- -
: 7
-- -
2
-- -
: 3
-- -
4
3
7
5
3
9
9
9
5
3
3
1
2
1
5
7
9
10
11
12
1
----- -
: 6
-- -
7
-- -
: 11
-- -
3
----- -
: 4
-- -
9
-- -
: 2
----- -
12
8
4
9
11
3
6
15
15
3
3
1
2
1
1
1
13
14
15
16
----- -
-- -
----- -
----- -
-- -
-- -
-- -
----- -
1
: 1
1
:
3
: 4
12
: 1
16
8
17
51
7
8
3
13
John Wiley & Sons Australia, Ltd 2001
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