Ratio and Proportion Worksheet available here makes it easy for you to grasp the related concepts. Questions covered in the Worksheet on Ratio and Proportion includes Simplifying Ratios, Arranging Ratios in Ascending or Descending Order, Expressing Ratio in Simplest Form, etc. Practice as many times as possible using the Ratio and Proportion Worksheets and test your preparation standard. To make it convenient for you we have provided detailed solutions for all the Problems provided.

1. Express each of the following Ratios in Simplest Form?

a) 2.4 m to 20 cm

b) 4 hours to half day

c) 10 liters to 7 liters

d)144 to 108

## Solution:

a) 2.4 m to 20 cm

We know 1m = 100 cm

2.4 m = 240 cm

express it in the form of Ratio

= 240: 20

Divide the ratios with their GCF to obtain the simplest form

GCF(240, 20) = 20

Dividing with GCF we obtain the simplified ratio as 12:1

Therefore, 2.4 m to 20 cm expressed in simplest form is 12:1

b) 4 hours to half day

We know half-day has 12 hours

Expressing 4 hours to half-day we have the ratio as 4:12

Divide the ratio with their GCF(4, 12) i.e. 4

= 1:3

4 hours to half-day expressed in simplest form is 1:3

c) 10 liters to 7 liters

= 10:7

Given Ratio is in its simplest form since their GCF is 1 and it can’t be simplified further.

d) 144 to 108

= 144:108

To obtain the simplified form of the given ratio Divide it with their GCF

GCF(144, 108) = 36

= 4:3

2. Simplify the following ratios

(a) 1/3: 1/5: 1/8

(b) 5.4: 6.3

## Solution:

(a) 1/3: 1/5: 1/8

Find the LCM of the Denominators

LCM(3, 5, 8) = 120

Express the given ratios with a common denominator

= 40/120: 24/120: 15/120

= 40: 24: 15

Therefore, 1/3: 1/5: 1/8 in simplest form is 40:24:15

(b) 5.4: 6.3

Convert the decimals to integers firstly.

Multiply with 10 i.e. 5.4*10 = 54

6.3*10 = 63

Expressing the integers in terms of ratio we have 54:63

GCF(54, 63) =9

Divide the ratio with GCF to get the simplified form

= 6: 7

Therefore, 5.4:6.3 in simplified form is 6:7

3. Determine whether the following Ratios form a Proportion or not

a) 4:5 and 8:10

b) 6:7 and 5:3

## Solution:

a) 4:5 and 8:10

4:5 = 4/5

8:10 = 8/10

= 4/5

Since both the ratios are in the same proportion they are said to be in proportion

Therefore, 4:5 and 8:10 are equal.

b)6:7 and 5:3

6:7 = 6/7

5:3 = 5/3

Since both proportions aren’t equal they are not in proportion.

4. Compare Ratio 5: 10 and 3: 6

## Solution:

5:10 = 5/10

3:6 = 3/6

LCM of 10, 6 is 30

Expressing given ratios as Equivalent Ratios we have

5/10 = 5*3/10*3 = 15/30

3/6 = 3*5/6*5 = 15/30

Since both the ratio are having same fractions they are equal.

5. Find the Mean Proportional between 9 and 16?

## Solution:

Let the Mean Proportional be x

x^{2}= 9*16

x^{2} = 144

x = 12

6. If 10, x, x, 10 are in proportion, then find the value of x?

## Solution:

Product of Means= Product of Extremes

x*x = 10*10

x^{2} = 100

x= 10

7. From the total strength of the class, if the no of boys in the class is 10 and no of girls in the class is 20, then find the ratio between girls and boys?

## Solution:

Given Strength of Boys = 10

Strength of Girls = 20

The ratio of Girls and Boys = 20:10

Simplifying the ratio we get 2:1

8. Suppose 2 numbers are in the ratio 4:3. If the sum of two numbers is 70. Find the numbers?

## Solution:

Given Ratio of Two Numbers is 4:3

As per the given data

4x+3x = 70

7x = 70

x = 10

Numbers are 4x, 3x

4x = 4*10 = 40

3x = 3*10 = 30