Solved Questions on Operations on Fractions
1. Solve the following:
i. (2/3) + (3/4)
ii. (3/4) - (1/2)
iii. (2/3) x (4/5)
iv. (2/3) ÷ (1/2)
a) i.17/12, ii. 1/4, iii. 8/15, iv. 4/3
b) i. 7/2, ii. 1/4, iii. 8/15, iv. 4/3
c) i. 17/12, ii. 2/8, iii. 9/15, iv. 3/4
d) i. 17/12, ii. 1/8, iii. 7/15, iv. 4/3
Answer: a) i.17/12, ii. 1/4, iii. 8/15, iv. 4/3
Explanation: i. (2/3) + (3/4)
LCM of (3, 4) is 12
= (2 x 4 + 3 x 3) / 12
= (8 + 9)/12
= 17/12
ii. (3/4) - (1/2)
LCM of (4, 2) is 4
= (3 x 1 - 1 x 2) / 4
= (3 - 2) / 4
= 1/4
iii. (2/3) x (4/5)
= (2 x 4) / (3 x 5)
= 8/15
iv. (2/3) ÷ (1/2)
= 2/3 x 2/1(Reciprocal of 1/2)
= (2 x 2) / (3 x 1)
= 4/3
2. Compare the fractions: 2/5 __ 3/5
a) >
b) <
c) =
d) ≤
Answer: b) <
Explanation: Denominators are the same. So, compare the numerator, 2 is less than 3.
So, the answer is 2/5 < 3/5
3. Rachel took 1/2 hour to paint a table and 1/3 hour to paint a chair. How much time did she take in total?
a) 1/2
b) 3/4
c) 5/6
d) 7/3
Answer: c) 5/6
Explanation: Time taken to paint a table = 1/2 hour
Time taken to paint a chair = 1/3 hour
Total time taken = 1/2 hour + 1/3 hour
1/2 + 1/3
L.C.M. of 2, 3 is 6.
= (1 x 3 + 1 x 2) / 6 = (3 + 2) / 6
= 5/6 hours
4. One-half of the students in a school are girls, and 3/5 of these girls are studying in lower classes. What fraction of girls are studying in lower classes?
a) 3/10
b) 2/5
c) 1/7
d) 1/4
Answer: a) 3/10
Explanation: Fraction of girls studying in school = 1/2
Fraction of girls studying in lower classes = 3/5 of 1/2
= 3/5 × 1/2
= (3 × 1) / (5 × 2)
= 3/10
Therefore, 3/10 of girls study in lower classes.
5. A herd of cows gives 4 litres of milk each day. But each cow gives one-third of the total milk each day. They give 24 litres of milk in six days. How many cows are there in the herd?
a) 1
b) 2
c) 3
d) 4
Answer: c) 3
Explanation: A herd of cows gives 4 litres of milk each day.
Each cow gives one-third of the total milk each day = 1/3 of 4
So, each cow gives 4/3 of milk each day.
Total number of cows = 4 ÷ 4/3 = 4 × 3/4 = 3
Therefore, there are 3 cows in the herd.
Practice Questions on Operations on Fractions
1. Simplify the following: 5/8 - 2/3
a) 1/24
b) -1/24
c) 3/2
d) 2/3
Answer: b) -1/24
2. Sarah has 3/4 of pizza left. She wants to share it equally with her two friends. What fraction of the original pizza will each person get?
a) 3/8
b) 2/3
c) 3/4
d) 5/2
Answer: a) 3/8
3. A recipe calls for 3/8 cups of sugar, but you only have 1/4 cup of sugar. How much more sugar do you need?
a) 1/2
b) 1/4
c) 1/8
d) 3/4
Answer: c) 1/8
4. Maddy reads three-fifth of 75 pages of his lesson. How many more pages does he need to complete the lesson?
a) 10
b) 20
c) 30
d) 40
Answer: c) 30
5. Ellen planned to interview some applicants for a position in her office. If she scheduled 1/4 of an hour to meet each of them, how much time did she schedule for all 6 applicants?
a) 1/2 hour
b) 1/4 hour
c) 2/5 hour
d) 3/2 hour
Answer: d) 3/2 hour
6. Tom decides to go on a vacation. He can go on leave for 2/3 of a month. Assuming a month is 30 days, how many days of vacation can he have?
a) 10
b) 20
c) 30
d) 40
Answer: b) 20
7. Maria spent 1/3 of the money her grandparents gave her on an adventure book. She also spent 1/9 of the money on a bag of candy. What fraction of the payment has Maria spent?
a) 1/9
b) 3/9
c) 4/9
d) 5/9
Answer: c) 4/9
8. Jill had 3 full pans of brownies. Each pan made 8 brownies. She gave 3/8 of the brownies to her friends. How many brownies did Jill give away?
a) 10
b) 9
c) 8
d) 7
Answer: b) 9
9. Which of the following option is incorrect?
a) 2/7 > 3/7
b) 8/7 > 2/9
c) 6/7 > 2/3
d) 2/3 > 1/3
Answer: a) 2/7 > 3/7
10. At a party, out of 280 ice creams prepared, the children ate 4/7 of them. Find the number of ice creams eaten by the children.
a) 50
b) 120
c) 145
d) 160
Answer: d) 160
