Lesson 10, Topic 2
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# Find Missing Values in Ratio

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To find the unknown term in a ratio:

1. Write the ratio as a fraction
2. Cross multiply to find the unknown value

### Example 1

Find the missing numbers in the following:

a. 12 : x = 20 : 35
b. 4 : 9 = x : 99

Solution

a. 12 : x = 20 : 35

$$\frac{12}{x} = \frac{20}{35}\; \; \; \; \; \scriptsize \; (cross \; multiply) \\ \scriptsize 20x\: = \: 12 \: \times \:35 \\ \scriptsize x = \normalsize \frac{12 \; \times \; 35}{20} \\ \scriptsize x = 21$$

b. 4 : 9 = x : 99

$$\frac{4}{9} = \frac{x}{99}\; \; \; \; \; \scriptsize \; (cross \; multiply) \\ \scriptsize 9x = 4 \: \times \: 99 \\ \scriptsize x = \normalsize \frac{4 \: \times \: 99}{9} \\ \scriptsize x = \normalsize \frac{4 \: \times \: 11}{1} \\ \scriptsize x = 44$$

### Example 2

Find the missing numbers in the following equivalent ratio:

a. $$\scriptsize 12 : \square = 20 : 35$$
b. $$\scriptsize 4 : 9 = \square : 99$$
c. $$\scriptsize 3 : 4 =21 : \square$$

Solution

a. $$\scriptsize 12 : \square = 20 : 35$$

$$\frac{12}{\square} = \frac{20}{35} \\ \frac{12}{\square} = \frac{4}{7}\scriptsize \; \; \; \; \; (cross \: multiply) \\ \scriptsize 4 \: \times \: \square = 12 \: \times \: 7 \\ \scriptsize \square = \normalsize \frac{12 \: \times \: 7}{4} \\ \scriptsize \square = \normalsize \frac{84}{4} \\ \scriptsize \square = 21$$

Answer: $$\scriptsize 12 : 21 = 20 : 35$$

b. $$\scriptsize 4 : 9 = \square : 99$$

$$\frac{4}{9} = \frac{\square}{99} \; \; \; \; \; \scriptsize \; (cross \; multiply) \\ \scriptsize 9 \: \times \: \square = 99 \: \times \: 4 \\ \scriptsize \square = \normalsize \frac{99 \: \times \: 4}{9} \\ \scriptsize \square = 11 \: \times \: 4 \\ \scriptsize \square = 44$$

Answer: $$\scriptsize 4 : 9 = 44 : 99$$

c. $$\scriptsize 3 : 4 = 21 : \square$$

$$\frac{3}{4} = \frac{21}{\square} \; \; \; \; \; \scriptsize \; (cross \: multiply) \\ \scriptsize 3\: \times \: \square = 21 \: \times \: 4 \\ \scriptsize \square = \normalsize \frac{21 \: \times \: 4}{3} \\ \scriptsize \square =7 \: \times \: 4 \\ \scriptsize \square = 28$$

Answer: $$\scriptsize 3 : 4 = 21 : 28$$

### Example 4

In a car park, there are 30 white cars and 20 blue cars.

a. What is the ratio of the white car to the blue car?
b. What is the ratio of the blue car to the white car?

Solution

a. Number of white cars =  30

Number of blue cars    =  20

Ratio of white cars to blue cars  =

White car   :   blue car

30 : 20   =  3 : 2

b. Ratio of blue car to white car =

Number of blue cars:   Number of white cars =  20 : 30

= 2 : 3

Evaluation Question:

1.Â Â Â  In a certain class of 80 pupils, 50 are boys. What is the ratio ofÂ

a.Â Â Â  girls to boys

b.Â Â Â  boys to girls

2.Â Â Â  In a certain supermarket, a tin of milk costs â‚¦70 and a tin of chocolate costs â‚¦210.Â  What is the ratio of the cost of tin of milk to the cost of tin of chocolate?

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