1. Ratio
Objective: Use a multiplier to find an unknown value in a ratio that is proportional similar to a ratio given in its lowest terms
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2. A ratio is a way of comparing things from their numerical values.
On the Titanic, for example, there were, approximately 325 first, 300 second and 700 third class passengers. We could use a ratio to show a comparison as a ratio in this way…
First : Second : Third
325 : 300 : 700
65 : 60 : 140
13 : 12 : 28
We usually write a ratio in its lowest terms
The colons are used instead of the word ‘to’
Divide all by 25
Divide all by 5

3. Write these ratios in their lowest terms1.
12 : 60 2.
45 : 150 3.
12 : 36 : 72 4.
9 : 81 : 270 5.
15 : 100 : 225 6.
18 : 54 : 144 7.
21 : 84 : 133 8.
24 : 108 : 228
Write these ratios in their lowest terms

4. Write these ratios in their lowest terms1.
12 : 60
 1 : 5 2.
45 : 150
 3 : 10 3.
12 : 36 : 72
 1 : 3 : 6 4.
9 : 81 : 270
 1 : 9 : 30 5.
15 : 100 : 225
 3 : 20 : 45 6.
18 : 54 : 144
 1 : 3 : 8 7.
21 : 84 : 133
 3 : 12 : 19 8.
24 : 108 : 228
 2 : 9 : 19
Write these ratios in their lowest terms

5. Finding unknown values in a ratio that is proportionally similar to a ratio given in its lowest terms

6. We can also do the reverse and multiply all the numbers in a ratio
We can also do the reverse and multiply all the numbers in a ratio. Here, for example, we start with…
…and then multiply each number by 4
1 : 3 : 5
x 4
x 4
x 4
We can use this fact to solve ratio problems like… 4 : 12 : 20
This is the same ratio increased by the multiplier 4

7. Cement : Sand : Pebbles 1 : 3 : 6 14 : 42 : 84
Concrete is made from cement, sand and pebbles in the ratio 1 : 3 : 6. How much cement and sand will be required to mix with 84 kg of pebbles?
Cement : Sand : Pebbles
Find the multiplier that increases 6 to 84
84 ÷ 6 = 14
1 : : 6
x 14
x 14
x 14
Check
14 : : 84
Now, use the same multiplier to find the unknown values

8. A cleaning fluid contains three chemical – X, Y and Z - in the ratio 3 : 5 : 12. What amounts of chemicals X and Z will be needed to mix with 32 litres of chemical Y?
Multiply 3 and 5 by 6.4 to find the missing numbers
Find the multiplier from 5 to 12
X : Y : Z
3 : 5 : 12
x 6.4
x 6.4
x 6.4
32 ÷ 5 = 6.4
Want these two numbers
19.2 : 32 : 76.8
Check that it works

9. Find the missing numbers for these ratios:1. 4.
1 : 3 : 7
4 : 5 : 7
4 : 12 : 28
17 : : 29.75 2. 5.
5 : 6 : 11
3 : 7 : 13
40 : 48 : 88
10.5 : 24.5 : 45.5 3. 6.
4 : 5 : 7
7 : 11 : 15
12 : 15 : 21
17.5 : 27.5 : 37.5

10. Here are two questions that are similar to ones that have been on exam papers….

11. T. Glue : Handle : Screws 2 : 12 : 27 450 : 2700 : 6075
A firm makes flat pack furniture and each pack contains tubes of glue, handles and screws in the ratio 2 : 12 : 27. How many tubes of glue and screws will be required for 2700 handles?
T. Glue : Handle : Screws
Find the multiplier that increases 12 to 2700
Check
2 : : 27
x 225
x 225
x 225
450 : :
Now, use the same multiplier to find the unknown values
2700 ÷ 12 = 225

12. Find the multiplier from 7 to 94.5
A paint contains three chemical – A, B and C - in the ratio 5 : 7 : 17. What amounts of chemicals A and B will be needed to mix with litres of chemical B?
94.5 ÷ 7 = 13.5
Find the multiplier from 7 to 94.5
A : B : C
5 : 7 : 17
Check that it works
x 13.5
x 13.5
x 13.5
Multiply 5 and 17 by 13.5
67.5 : :