[Maths Class Notes] on Fractions and Decimals Pdf for Exam

Addition and Subtraction of Fractions and Decimals

An important part of fractions and decimals questions is also represented by the sample decimal problems given in the article involving adding or subtracting decimal. One of the ways to add or subtract decimal numbers is by converting them into fractions. Let us consider the following decimal word problems as an example:

1. Add 34.45 and 52.31

34.45 + 52.31

= [(frac{3445}{100})] + [(frac{5231}{100})]

= [frac{(3445+ 5231)}{100}]

= [frac{(8676)}{100}]

= 86.76

2. Subtract 54.42 from 75. 21

75.21 – 54.42

= (7521/100) – (5421/100)

= (7521 – 5421)/ 100

= (2100)/ 100

= 21

In both these cases, you shall see that the decimal places remain the same as the original numbers. If the sum involves carrying over a number while adding or borrowing while subtracting then the calculation is done by using the rules of simple addition and subtraction. However, do note that the same does not hold true for multiplication and division involving decimals. To understand how it works, please refer to the fraction word problems with answers given below.

Solved Examples – Word Problems Involving Decimals 

Example 1: Manish decided to buy 18 mobile phones for his shop at Rs 6742.75 a piece. What is the total amount of money he spends on buying the phones?

Solution: Given,

Cost of a single piece of mobile phone = Rs 6742.75

Total number of mobile phones he bought = 18

Therefore, total amount of money he spent in buying the phones = 6742.75 x 18 = Rs 1,21,369.5 

Ans: Rs 1,21,369.5

Example 2: Two numbers when multiplied allows the resultant product to be 3458.65 if the first number is 139.426, then what is the second number?

Solution: Given,

Let the first number be a, a = 139.426

Let the second number be b

Product of the two numbers = 3458.65 

Hence, a x b = 3456.65

b = 3456.65 ÷ 139.426

b = [frac{(345665 div 139426)}{100000}]

b = 25

Ans: 25

Example 3: After having bought a new car, Sudeshna decided to take a long drive to Mahabaleshwar, when she started her journey the meter reading on her car showed 25.22 km travelled. If she drove 165.34 km to reach Mahabaleshwar and drove 72.57 km more to visit a friend’s house, What should be the final meter reading on her car?

Solution: Given,

Car meter reading at the start of the journey = 25.22 km

Distance travelled to reach Mahabaleshwar = 165.34 km

Distance travelled to reach friend’s house = 72.57 km

Therefore, distance travelled in total = 165.34 + 72.57 = 237.91

However, the initial reading of the car was 25.22 km

Final meter reading of the car = 237.91 – 25.22 = 212.69 km

Ans: 212.69 km

Example 4: A tank contains 75.57 litres of water. If Ramu uses 27.34 litres of water to wash his car, then how much water is left in the tank?

Solution: Given,

The capacity of the tank = 75.57 litres

Amount of water used by Ramu to wash the car = 27.34 litres

Therefore, the amount of water left in the tank afterwards = 75.57 – 27.34 = 48.23 litres

Ans: 48.23 litres

Example 5: If the radius of a circle is 7.5 cm, what will be the diameter and area of the circle? (π=3.14)

Solution: Given,

Radius of the circle = 7.5 cm

Diameter = 7.5 x 2 = 15

ℼ = 3.14

Area of the circle, a = ℼ x r x r

a = 3.14 x 7.5 x 7.5

a = 176.625 sq. cm

Ans: Area – 176.625 sq. cm