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Ratio and Proportion Examples 7-10

Singapore Mathematics curriculum. Primary 6. Ratio and Proportion word problems.
by

Ivy Tan

on 17 September 2014

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Transcript of Ratio and Proportion Examples 7-10

Ruben had a total of 56 apples and oranges. The ratio of the number of apples to oranges was 5 : 3. Later, he bought 34 more apples and oranges. After that the ratio of apples to oranges became 3 : 2. How many more apples did he buy?
Example 7
(cc) photo by theaucitron on Flickr
Example 8
Before
After
Apples : Oranges
Apples : Oranges
5 : 3
3 : 2
5
X 2
: 3
X 2
3
X 3
: 2
X 3
10 :
6
9 :
6
Total number of units
10 + 6 = 16 units
16 units
56 apples & oranges
1 unit
56 ÷ 16 = 3.5
10 units
3.5 X 10 =
35 apples
6 units
3.5 X 6 = 21 oranges
Before
After
Total number of units
9 + 6 = 15 units
15 units
56 + 34 = 90 apples & oranges
1 unit
90 ÷ 15 = 6
9 units
6 X 9 =
54 apples
Additional apples bought = 54 - 35
= 19 apples
Ruben bought 19 more apples.
There is an equal number of passes and failures in an exam. The ratio of boys to girls who passed is 5 : 3. The ratio of boys to girls who failed is 1 : 7. Find the ratio of boys who failed to boys who passed.
Pass
Fail
B : G
B : G
5 : 3
1 : 7
B
G
B
G
Total number of boys who failed
Total number of boys who passed
=
1
5
X 1
X 1
2
6
1
3
=
1 X 1
5 X 3
=
1
15
The ratio of the total number of boys who failed
to the total number of boys who passed is 1 : 15

Example 8
Example 9
If Tom gives May $12, he will have the same amount of money as May. If May gives Tom $12, the amount of money she has will be 1/7 that of Tom's. How much money does each of them have?
Tom
May
$12
$12
$12
$12
$12
If May gives Tom $12, she has 1/7 of what Tom has:
$12
Tom's $48
6
1 whole
Tom has $56 - $12 = $44
6
7
7
$48
= $56
Working
48
X
7
6
= 8 X 7
48
÷ 6
X
7
6
÷ 6
1
= 56
Amount of money May has = $44 - $24
Tom
$24
May
Tom has $44 and May has $20
= $20
Example 10
Joe bought some guppies, swordtails and goldfishes for $52.50. The ratio of the amount of money he spent on guppies, swordtails and goldfishes was 1 : 2 : 4. Each guppy cost 25 cents. The ratio of the number of swordtails to the number of guppies he bought was 2 : 3.
a.) Find the cost of a swordtail
b.) If each goldfish cost $1.25 more than a swordtail, how many goldfishes did he buy?
Example 10
Example 10
guppies : swordtails : goldfishes
1 : 2 : 4
1 + 2 + 4 = 7 units
7 units
$52.50
(guppies) 1 unit
52.50 ÷ 7 = $7.50
(swordtails) 2 units
(goldfishes) 4 units
7.50 X 2 = $15
7.50 X 4 = $30
1 guppy costs $0.25
Number of guppies bought = 7.50 ÷ 0.25
= 30 guppies
swordtails : guppies
2 : 3
3 units
30 guppies
1 unit
30 ÷ 3 = 10
2 units
10 X 2 = 20 swordtails
20 swordtails
$15
1 swordtail
15 ÷ 20 = $0.75
Each swordtail cost $0.75
Cost of each goldfish = $(1.25 + 0.75)
= $2
Total number of goldfishes he bought =
30 ÷ 2
= 15 goldfishes
Joe bought 15 goldfishes
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