What Are Fractions and Decimals Definition Conversion Methods and Solved Examples
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
FAQs on Fractions and Decimals Explained for Students
1. What is a fraction in Maths?
A fraction is a number that represents a part of a whole and is written in the form a/b, where a is the numerator and b ≠ 0 is the denominator. The numerator shows how many parts are taken, and the denominator shows the total equal parts. For example, in 3/4:
- 3 is the numerator (parts taken).
- 4 is the denominator (total equal parts).
2. What is a decimal number?
A decimal is a number written using a decimal point to represent parts of a whole based on powers of 10. Decimals are another way to express fractions with denominators like 10, 100, or 1000. For example:
- 0.5 means five tenths (5/10).
- 0.75 means seventy-five hundredths (75/100).
3. How do you convert a fraction to a decimal?
To convert a fraction to a decimal, divide the numerator by the denominator. Use the formula Decimal = Numerator ÷ Denominator. For example:
- Convert 3/4 → 3 ÷ 4 = 0.75.
- Convert 1/2 → 1 ÷ 2 = 0.5.
4. How do you convert a decimal to a fraction?
To convert a decimal to a fraction, write the decimal over the correct power of 10 and simplify. Steps:
- Write the decimal as a fraction over 10, 100, or 1000.
- Simplify the fraction.
5. What is the difference between fractions and decimals?
The main difference between fractions and decimals is that fractions are written as a ratio (a/b) while decimals are written using a decimal point. Key differences:
- Fraction example: 2/5
- Decimal form: 0.4
- Fractions show division explicitly.
- Decimals are based on powers of 10.
6. How do you add fractions with different denominators?
To add fractions with different denominators, find a common denominator, then add the numerators. Steps:
- Find the least common denominator (LCD).
- Rewrite each fraction with the LCD.
- Add the numerators.
- Simplify the result.
7. How do you multiply fractions?
To multiply fractions, multiply the numerators together and the denominators together using the formula (a/b) × (c/d) = (ac)/(bd). Example:
- 2/3 × 4/5 = (2×4)/(3×5) = 8/15.
8. How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal of the second fraction using (a/b) ÷ (c/d) = (a/b) × (d/c). Steps:
- Keep the first fraction.
- Flip the second fraction (reciprocal).
- Multiply.
9. What is a terminating and repeating decimal?
A terminating decimal ends after a finite number of digits, while a repeating decimal has digits that repeat forever. Examples:
- Terminating: 0.25, 0.8
- Repeating: 0.333..., 0.727272...
10. How do you compare fractions and decimals?
To compare fractions and decimals, convert them to the same form or use a common denominator. Methods:
- Convert fractions to decimals (e.g., 3/5 = 0.6).
- Convert decimals to fractions.
- Use cross-multiplication for fractions.
