Subtracting fractions questions given here cover all types of fractions including like, unlike and mixed. These involve both numerical and word problems of subtracting fractions. Practising various questions on subtracting fractions will enhance your understanding of performing various arithmetic operations on fractions. Let’s learn how to subtract fractions using the solved problems given below.
What is the Subtraction of Fractions?
In mathematics, the subtraction of fractions involves finding the difference between two or more fractions with the same denominators or different denominators. The subtraction of fractions involves the following cases.
- Subtracting fractions from whole numbers
- Subtracting fractions with the same denominator
- Subtracting fractions with different denominators
- Subtracting mixed fractions
Also, check: Subtracting fractions
Subtracting Fractions Questions and Answers
1. Subtract: 3 – (4/13)
Solution:
3 – (4/13)
Here, 3 is a whole number and 4/13 is a fraction.
3 – (4/13)
= (39 – 4)/13
= 35/13
Therefore, 3 – (4/13) = 35/13
2. Evaluate the following:
(i) (9/14) – (5/14)
(ii) (7/10) – (3/10)
Solution:
(i) (9/14) – (5/14)
Here, the denominators are the same, i.e., they are like fractions.
Thus, (9/14) – (5/14) = (9 – 5)/14
= 4/14
On further simplification, we have;
(9/14) – (5/14) = 4/14 = 2/7
(ii) (7/10) – (3/10)
= (7 – 3)/10
= 4/10
Thus, (7/10) – (3/10) = 4/10 = ⅖
3. Compute the following.
(i) (10/12) – (⅓)
(ii) (⅔) – (5/20)
Solution:
(i) (10/12) – (⅓)
= (⅚) – (⅓)
By taking the LCM of denominators, we have;
= (5 – 2)/6
= 3/6
= ½
Therefore, (10/12) – (⅓) = ½
(ii) (⅔) – (5/20)
= (⅔) – (¼)
By taking the LCM of denominators, we have;
= (8 – 3)/12
= 5/12
Therefore, (⅔) – (5/20) = 5/12
4. Find the value of
Solution:
Here, both terms are mixed fractions.
Let’s convert the mixed fractions into improper fractions.
Therefore,
5. Subtract 5 from 11 â…—.
Solution:
11 ⅗ – 5
Here, 11 â…— is a mixed fraction.
11 ⅗ = (11 × 5 + 3)/5 = 58/5
Now, 11 ⅗ – 5
= (58/5) – 5
= (58 – 25)/5
= 33/5
Therefore, 11 ⅗ – 5 = 33/5.
6. Find the value of (23/4) – (5/3).
Solution:
(23/4) – (5/3)
By taking the LCM of denominators, we get;
= (23 × 3 – 5 × 4)/12
= (69 – 20)/12
= 49/12
= 4 1/12
Thus, (23/4) – (5/3) – 4 1/12.
7. Evaluate:
Solution:
8. A father leaves his money to his four children. The first received 1/3, the second received 1/6, and the third received 2/5. How much did the remaining child receive (assume that the total money is one whole)?
Solution:
Given,
Total money = 1
The amount received by the first child = 1/3
The amount received by the second child = 1/6
The amount received by the third child = 2/5
The amount received by the last child = 1 – (1/3) – (1/6) – (2/5)
= (30 – 10 – 5 – 12)/30 {since the LCM of 3, 6, and 5 is 30}
= (30 – 27)/30
= 3/30
= 1/10
Thus, the remaining child will receive 1/10th of the father’s money.
9. Vinu worked for 14/3 hours on Friday and his friend Shan worked for 25/6 hours. How many more hours than Shan did Vinu work?
Solution:
Number of hours worked by Vinu = 14/3
Number of hours worked by Shan = 25/6
Difference = 14/3 – 25/6
= (28 – 25)/6
= 3/6
= ½
Thus, Vinu worked ½ hour, i.e., half an hour more than Shan.
10. Arnav bought some sweets that weighed 4 2/3 kg. If he gave 3 1/6 kg to his friends, what is the amount of sweets he has left?
Solution:
Given,
Sweets bought by Arnav = 4 2/3 kg
Sweets given to his friends = 3 1/6 kg
Sweets left with Arnav = 4 2/3 – 3 1/6
= 14/3 – 19/6
= (28 – 19)/6
= 9/6
= 3/2
= 1 1/2
Therefore, Arnav is left with 1 1/2 kg of sweets.
Practice Questions on Subtracting Fractions
- Calculate the following:
(i) (9/11) – (½)
(ii) (11/12) – (⅚) - Subtract 6 ⅘ from 7.
- A jar contains 1 2/5 litres of mango juice. Kevin pours 4/15 litres of the juice into a glass. How much mango juice is left in the jar?
- David cleaned about 3/5 of the school lawn on Saturday. He cleaned another 1/4th of the lawn on Sunday. How much of the lawn is left to clean?
- Subtract: 3 7/12 – 1 2/6
Comments