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Ratio & Proportion Examples 1-6

Singapore Mathematics Primary 6 Ratio and Proportion word problems
by

Ivy Tan

on 17 September 2014

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Transcript of Ratio & Proportion Examples 1-6

Ratio and Proportion
Ratio and Proportions
Example 1
2/9 spectators at a football match are children. The ratio of the number of men to the number of women is 7:3. There are 800 more adults than children. How many more men than women are there at the football match?
Example 2
Ratio and Proportion
What is the difference between ratio and proportion?
In a wardrobe, there are 81 shirts and coats. The ratio of shirts to coats is 7 : 2. Each shirt costs $56. Each coat costs 2 3/4 times as much as a shirt. Find the total cost of coats.
Example 4
Example 5
Example 6
Example 6
Example 6
2 units
7 units
Difference in units between adults and children
7 - 2 = 5 units
5 units
800 adults
1 unit
800 ÷ 5 = 160
Total number of adults
7 units
7 units
160 X 7 = 1120
There were 1120 adults at the football match
Ratio of Men to Women is 7: 3
Difference in parts between men and women
7 - 3 = 4 parts
Total number of parts representing men and women
7 + 3 = 10 parts
10 parts represent the total number of adults at the football match
10 parts
1120 adults
1 part
1120 ÷ 10 = 112
4 parts
112 X 4 = 448 men
There were 448 more men than women in the football match
2/9 spectators at a football match are children. The ratio of the number of men to the number of women is 7:3. There are 800 more adults than children. How many more men than women are there at the football match?
The commander-trainee ratio in a police academy is 7 : 330. The number of female police trainees is 3/8 the number of male trainees. There are 7, 200 male trainees. How many commanders are there in the police academy?
Total number of male and female trainees = 7200 + 2700
= 9900
The commander-trainee ratio is 7 : 330
7
330
=>
Total number of commanders
Total number trainees
=
7 X
?
330 X
?
330 X ? = 9900
? =
9900
330
= 30
=
7 X
30
Working
330 X
30
=
210
9900
There are 210 commanders in the police academy
Number of female trainees =
3
8
X
7200
= 2700
1 : 2
Ratio
1
2
Proportion
1
2
or 50%
2
5
or 40%
2 : 5
7 units
5 parts
7+ 2 = 9 units
9 units

81
(shirts + coats)
1 unit
81
÷
9
2 units
= 18 coats
= 9
9 X 2
Total cost of coats = (2 3/4 X 56) X 18
= $2, 772
Total number of units in the ratio 7 : 2
= 154 X 18
Example 3
Ron, Wayne and Victor raised a sum of money for their school building fund. Ron raised 3/8 of the sum. The remaining was raised by Wayne and Victor in the ratio 14 : 11. Ron raised $324 more than Victor. How much money did they raise altogether?
3/8
Ron
Wayne & Victor
14 : 11
Wayne : Victor
Total units (Wayne and Victor)
14 + 11 =
25
units
5 parts
25
units
1 part
25
÷ 5 = 5 units
3 parts (Ron)
5 X 3 =
15
units
Total number of units from Ron, Wayne and Victor
15
+
25
= 40 units
Difference (in units) between the contribution of Ron and Victor
15 - 11 = 3 units
3 units
$324
1 unit
$324 ÷ 3 = $81
40 units
$81 X 40 = $3240
Ron, Wayne and Victor raised $3, 240 altogehter
Example 4
Example 5
At the beginning of a party, there were 84 girls. The ratio of girls to boys was 3 : 2. Halfway through the party, more boys joined the party. As a result, the ratio of boys to girls became 7 : 3. How many boys joined the party?
Before
After
At the beginning of a party, there were 84 girls. The ratio of girls to boys was 3 : 2. Halfway through the party, more boys joined the party. As a result, the ratio of boys to girls became 7 : 3. How many boys joined the party?
Difference in units between boys:
7 - 2 = 5 units
3 units
84 girls
1 unit
84 ÷ 3 = 28
5 units
28 X 5 = 140 boys
140 boys joined the party.
At the beginning of a party, there were 84 girls. The ratio of girls to boys was 3 : 2. Halfway through the party, more boys joined the party. As a result, the ratio of boys to girls became 4 : 2. How many boys joined the party?
Before
After
At the beginning of a party, there were 84 girls. The ratio of girls to boys was 3 : 2. Halfway through the party, more

boys joined. As a result, the ratio of boys to girls became 4 : 2. How many boys joined the party?
Before
After
2 : 3
B : G
4 : 2
B : G
If only they were equal......
2
X 2
: 3
X 2
4
X 3
: 2
X 3
4 :
6
12 :
6
B : G
B : G
6 units
84 girls
1 unit
84 ÷ 6 = 14
12 - 4 = 8 units
8 units
14 X 8 = 112 boys
112 boys joined the party
Difference in units between boys:
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