Fractions and Decimals

Fractions are a representation of numbers, which are a part of a whole. Decimals in an alternative way of expressing fractions.

For instance, if you cut up an apple pie into 8 pieces and distribute 3 pieces among your friends, then the amount of pie you would have left is 5/8. Here 8 represents the total number of pieces that you had of the apple pie, and 5 represents the number of pieces you have left.

Now, in mathematical terms, these parts of a fraction have specific names. The upper part of the fraction, meaning the 'part of a whole' is referred to as the numerator, while the lower part meaning the 'whole' is known as the denominator. 

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In fraction problems, these fractions can be referred to in decimal places. For instance 27/100 can also be written as 0.27. These different types of representations form an important part of fraction and decimal word problems.

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

FAQ (Frequently Asked Questions)

1. How Does the Place Value of 0 After the Decimal Point Affect the Overall Value of the Number?

Answer: The value of zero does not apply after the decimal in the same way as it does in the case of whole numbers. Let us try to understand this using a few examples. Consider the numbers 3.408, 3.40 and 3.048. 

In the case of 3.408, the '0' serves a similar function as in a whole number. Thus the ‘0.408’ part is greater than ‘0.4’ by a small amount. 

If 0 is placed at the end of a decimal value as is the case with ‘3.40’, then essentially it has no extra significance. Thus ‘3.4’, ‘3.40’ and ‘3.400’ all essentially mean the same thing. 

If 0 is placed just after the decimal point, then the entire value of the number would be less than ‘0.1’ of the number before the decimal. For example ‘4.1’ is greater than ‘4.09’.

Thus if the numbers 3.408, 3.40 and 3.048 are arranged in ascending order, then the result would be 3.048 < 3.40 < 3.408.

2. How does Multiplication Work when Multiplying two Numbers, Both of Which have Decimal Places?

Answer: Multiplication is essentially compounding two numbers to find out the resultant. So, for instance, if you received two candies per day for two days, then the resultant would be 2 x 2 = 4. In the case of decimal numbers, the product of the two numbers and its subsequent decimal point in the result would be based upon how many decimal places the two multiplying numbers have. So if ‘2.22’ and ‘3.33’ is multiplied, then the result would be 7.3926. You will see that the two multiplying numbers each have two places in decimal and thus, as a result, the product would be four places in decimal.