# Selina Concise Solutions for Chapter 3 Fractions (including Problems) Class 7 ICSE Mathematics

**Exercise 3 (A)**

**1. Classify, each fraction given below, as decimal or vulgar fraction, proper or improper fraction and mixed fraction :**

**(i) 3/5 (ii) 11/10(iii) 13/20(iv) 13/7(vi) 19/10**

^{3 }(viii) 23/500

**Answer **

(i) Vulgar and Proper

(ii) Decimal and Improper

(iii) Decimal and Proper

(iv) Vulgar and Improper

(v) Mixed

(vi) Decimal

(vii) Mixed and Decimal

(viii) Vulgar and Proper Ans.

**2. Express the following improper fractions as mixed fractions : **

**(i) 18/5**

**(ii) 7/4**

**(iii) 25/6**

**(iv) 38/5**

**(v) 22/5**

**Answer **

**3. Express the following mixed fractions as Improper fractions : **

**Answer**

**4. Reduce the given fractions to lowest terms **

**(i) 8/18(ii) 27/36(iii) 18/42(iv) 35/75(v) 18/45**

**Answer **

**5. State: true of false (i) 30/40 and 12/16 are equivalent fractions.(ii) 10/25 and 25/10 are equivalent fractions.(iii) 35/49, 20/28, 45/63 and 100/140 arc equivalent **

**Answer **

**6. Distinguish each of the following fractions, given below, as a simple fraction or a complex fraction : **

**(i) 0/8**

**(ii) -3/-8**

(iii) 5/-7

(iii) 5/-7

**Answer**

**Exercise 3 (B)**

**1.**

**For each pair, given below, state whether it forms like fractions or unlike fractions**

**(i) 5/8 and 7/8**

(ii) 8/15 and 8/21

(iii) 4/9 and 9/4

(ii) 8/15 and 8/21

(iii) 4/9 and 9/4

**Answer**

**2. Convert given fraction into fractions into fractions with equal denominators :**

(i) 5/6 and 7/9

(ii) 2/3, 5/6 and 7/12

(iii) 4/5, 17/20, 23/40 and 11/16

(i) 5/6 and 7/9

(ii) 2/3, 5/6 and 7/12

(iii) 4/5, 17/20, 23/40 and 11/16

**Answer**

**3. Convert given fractions into fractions with equal numerators :**

(i) 8/9 and 12/17

(ii) 6/13, 15/23 and 12/17

(iii) 15/19 , 25/28 , 9/11 and 45/47

(i) 8/9 and 12/17

(ii) 6/13, 15/23 and 12/17

(iii) 15/19 , 25/28 , 9/11 and 45/47

**Answer**

**4. Put the given fractions in ascending order by making denominators equal :**

**(i) 1/3, 2/5, 3/4 and 1/6**

(ii) 5/6, 7/8, 11/12 and 3/10

(iii) 5/7, 3/8, 9/14 and 20/21

(ii) 5/6, 7/8, 11/12 and 3/10

(iii) 5/7, 3/8, 9/14 and 20/21

**Answer**

**5. Arrange the given fractions in descending order by making numerators equal :**

**(i) 5/6, 4/15, 8/9 and i/3**

(ii) 3/7, 4/9, 5/7 and 8/11

(iii) 1/10, 6/11, 8/11 and 3/5

(ii) 3/7, 4/9, 5/7 and 8/11

(iii) 1/10, 6/11, 8/11 and 3/5

**Answer**

**6. Find the greater fraction :**

**(i) 3/5 and 11/15**

(ii) 4/5 and 3/10

(iii) 6/7 and 5/9

(iv)3/8 and 4/9

(v) -2/7 and -3/10

(ii) 4/5 and 3/10

(iii) 6/7 and 5/9

(iv)3/8 and 4/9

(v) -2/7 and -3/10

**Answer**

**7. Insert one fraction between : (i) 3/7 and 4/9**

(ii) 2 and 8/3

(iii) 9/17 and 6/13

(ii) 2 and 8/3

(iii) 9/17 and 6/13

**Answer**

**8. Insert three fractions between**

**(i) 2/5 and 4/9**

(ii) 1/2 and 5/7

(iii) 3/8 and 6/11

(iv) 11/12 and 2/3

(v) 4/7 and 3/4

(ii) 1/2 and 5/7

(iii) 3/8 and 6/11

(iv) 11/12 and 2/3

(v) 4/7 and 3/4

**Answer**

**Answer**

**Exercise 3 (C)**

**1. Reduce to a single fraction :**

**Answer**

**2. Simplify :**

**(vii) 2 ÷ 1/3**

(viii) 3

(viii) 3

**÷**

**2/5**

(ix) 1

(ix) 1

**÷**

**3/5**

(x) 1/3

(x) 1/3

**÷**

**1/4**

(xi) -5/8

(xi) -5/8

**÷**

**3/4**

**Answer**

**3. Subtract :**

(i) 2 from 2/3

(ii) 1/8 from 5/8

(iii) -2/5 from 2/5

(iv) -3/7 from 3/7

(v) 0 from -4/5

(vi) 2/9 from 4/5

(viii) -4/7 from -6/11

(i) 2 from 2/3

(ii) 1/8 from 5/8

(iii) -2/5 from 2/5

(iv) -3/7 from 3/7

(v) 0 from -4/5

(vi) 2/9 from 4/5

(viii) -4/7 from -6/11

**Answer**

**4. Find the value of**

(i) 1/2 of 10 kg

(ii) 3/5 of 1 hour

(i) 1/2 of 10 kg

(ii) 3/5 of 1 hour

**(vi) 5/11 of 4/5 of 22 kg.**

**Answer**

**5. Simplify and reduce to a simple fraction :**

**(x) 4/5**

**÷**

**7/15 of 8/9**

(xi) 4/5

(xi) 4/5

**÷**

**7/15 × 8/9**

(xii) 4/5 of 7/15

(xii) 4/5 of 7/15

**÷**

**8/9**

(xiii)1/2 of 3/4 × 1/2 + 2/3

(xiii)1/2 of 3/4 × 1/2 + 2/3

**Answer**

**Answer**

**7. Which is greater, 3/5 or 7/10 and by how much ?**

**Answer**

3 × 10 = 30 and 7×5 = 35

Since, 3 × 10 (i.e., 30) is smaller than 7 × 5 (i.e.,)

**Answer**

**Answer**

**Answer**

**Answer**

**12. A motor cycle runs km consuming 1 litre of petrol. How much distance will it run consuming liter of petrol ?**

**Answer**

=km = 125/4 km

∴ Distance covered inlitre of petrol

= 125/4 × 8/5

= 1000/20 = 50 km

**Answer**

= 117/5 × 50/3

= 39 × 10 = 390 m

^{2}

**Answer**

**15. Out of 24 kg of wheat, 5/6 th of wheat is consumed. Find, how much wheat is still left ?**

**Answer**

Wheat consumed = 5/6 th of 24 kg

= 5/6 × 24 = 20 kg

∴ Remaining wheat = 24 - 20 kg = 4 kg

**16. A rod of length metre is divided into five equal parts. Find the length of each part so obtained.**

**Answer**

**(i) A + B**

(ii) BA

(ii) BA

**Answer**

**Answer**

**Answer**

**Answer**

**3. 1/4(1/4 + 1/3) - 2/5**

**Answer**

**Answer**

**7. (1/2 + 2/3)**

**÷**

**(3/4 - 2/9)**

**Answer**

**Answer**

**Exercise 3 (E)**

**1. A line AB is of length 6 cm. Another line CD is of length 15 cm. What fraction is :**

**(i) The length of AB to that of CD ?**

**(ii) 1/2 the length of AB to that of 1/3 of CD ?**

**(iii) 1/5 of CD to that of AB ?**

**Answer**

and length of line CD = 15 cm

**2. Subtract 2/7 - 5/21 from the sum of 3/4, 5/7 and 7/12**

**Answer**

**3. From a sack of potatoes weighing 120 kg, a merchant sells portions weighing 6 kg**

**(i) How many kg did he sell ?**

(ii) How many kg are still left in the sack ?

(ii) How many kg are still left in the sack ?

**Answer**

(i) Quantity of potatoes he sold

**4. If a boy works for six consecutive days for 8 hours,hours and 7 hours respectively. How much money will he earn at the rate of Rs. 36 per hour ?**

**Answer**

**5. A student bought of yellow ribbon, of red ribbon and of blue ribbon for decorating a room. How many metres of ribbon did he buy ?**

**Answer**

**6. In a business, Ram and Deepak invest 3/5 and 2/5 of the total investment. If Rs. 40,000 is the total investment, calculate the amount invested by each ?**

**Answer**

Ram's investment = 3/5 or Rs. 40, 000

= Rs. 3/5 × 40,000

= Rs. 3 × 8000 = Rs. 24, 000

Deepak's investment = 2/5 of Rs. 40,000

= Rs. 2/5 × 40,000

= Rs. 2 × 8000 = Rs. 16, 000

**7. Geeta had 30 problems for home work. she worked out 2/5 of them. How many problems were still left to be worked out by her ?**

**Answer**

No. of problems worked out = 2/3 of 30

= 2/3 ×30 = 20

No. of problems left out = 30 - 20 = 10

**8. A picture was marked at Rs. 90. It was sold at 3/4 of its marked price. What was the sale price ?**

**Answer**

Sale price = 3/4 of Rs. 90

= 3/4 × 90

= Rs. 270/4 = 67.50

**9. Mani had sent fifteen parcels of oranges. What was the total weight of the parcels, if each weighed 21/2 kg ?**

**Answer**

Weight of each parcel = 21/2 kg

Total weight = 15 of 21/2 kg = 21/2 × 15 kg

= 315/2 = 157.5 kg

**Answer**

**11. The heights of two vertical poles, above the earth's surface, are 57/4 m and 67/3 respectively. How much higher is the second pole as compared with the height of the first pole ?**

**Answer**

∴ Second pole is higher than the first pole

= 67/3 - 57/4

= (268 - 171)/ 12 = 97/12 m

**12. Vijay weighed . He gained during the first week, during the second week, but lost 5/16 kg during the 16 third week. What was his weight after the third week ?**

Answer

Answer

Gained in first week =

Gained in the second week =

Lost in the third week = 5/16 kg

∴Weight of Vijay after third week

**13. A man spends 2/5 of his salary on food and 3/10 on house rent, electricity, etc. What fraction of his salary is still left with him ?**

**Answer**

Amount spent on food = 2/5 or Re. 1 = Re. 2/5

and amount spent house rent = 3/10 or Re. 1

= Re. 3/10

**14. A man spends 2/5 of his salary on food and 3/10 of the remaining on house rent, electricity, etc. What fraction of his salary is still left with him ?**

**Answer**

Amount spent on food = 2/5 of Re. 1

Remaining amount = 1 - 2/5

= (5-2)/5 = Rs. 3/5

Amount spent on house rent etc.

= 3/10 of 3/5 = Rs. 9/50

Remaining amount left

= 3/5 - 9/50

= Rs (30- 9)/50 = Rs. 21/50

∴ Fraction of amount left = 21/50

**15. Shyam bought a refrigerator for Rs. 5000. He paid 1/10 of the price in cash and the rest in 12 equal monthly instalments. How much had he o pay each month ?**

**Answer**

Amount paid in cash = 1/10 or Rs. 5000

= 1/10 × 5000 = Rs. 500

Balance amount = Rs. 5000 - Rs. 500

= Rs. 4500

No. of equally instalments = 12

∴ Amount of each instalment

= Rs. 4500

**÷**12 = Rs. 4500 × 1/12

= Rs. 375 Ans.

**16. A lamp post has half of its length in mud, and 1/3 of its length in water.**

(i) What fraction of its length is above the water ?

(ii) If m of the lamp post is above the water, find the whole length of the lamp post.

(i) What fraction of its length is above the water ?

(ii) If m of the lamp post is above the water, find the whole length of the lamp post.

**Answer**

then length of post in mud = 1/2 m

and length of post in water = 1/3 m

∴ Length of post above the water

**17. I spent 3/5 of my savings and still have Rs. 2,000 left. What were my savings ?**

**Answer**

∴ part left = 1 - 3/5 = (5 -3)/5 = 2/5 of savings

But he left = Rs. 2000

∴ 2/5 of savings = Rs. 2000

∴ Total savings = Rs. 2000 × 5/2

= Rs. 5000 Ans.

**18. In a school, 4/5 of the children are boys. If the number of girls is 200, find the number of boys.**

**Answer**

= (5-4)/5 = 1/5 of total children.

But no. of girls = 200

∴ 1/5 of total children = 200

Hence total number of children = 200 × 5/1 = 1000

∴ No. of boys = 4/5 of 1000 = 4/5 × 1000 = 800 Ans.

**19. If 4/5 of an estate is worth Rs. 42, 000, find the worth of whole estate. Also, find the value of 3/7 of it.**

**Answer**

∴ Total value of estate = Rs. 42000 × 5/4

= Rs. 10500 × 5= 52500 Ans.

and value of 3/7 of it = 3/7 of its value

= 3/7 of Rs. 52500 = 3/7 × 52500

= 3 × 7500 = Rs. 22500

**20. After going 3/4 of my journey, I find that I have covered 16 km. How much journey is still left ?**

**Answer**

**21. When Krishna travelled 25 km, he found that 3/5 of his journey was still left. What was the length of the whole journey.**

**Answer**

∴ Journey travelled by him = 1 - 3/5

∴ 2/5 of total journey = 25 km

∴ Total journey = 25 km × 5/2 = 125/2 km

**22. From a piece of land, one - third is bought by Rajesh and one - third of remaining is bought by Manoj. If 600 m**

^{2}land is still left unsold, find the total area of the piece of land.**Answer**

**23 . A boy spent 3/5 of his money on buying 1 cloth and 1/4 of the remaining of buying shoes. If initially he has 2400 ; How much did he spend on shoes ?**

**Answer**

Money spent on buying clothes

= 3/5 or ₹ 2400

= 3/5 × 2400 = 3 × 480 = ₹ 1440

Remaining money = ₹ 2400 - ₹ 1440 = ₹ 960

Now, boy spent 1/4 of the remaining money on buying shoes.

∴ Money spent on buying shoes = ₹ 960 × 1/4 = ₹240

**24. A boy spent 3/5 of his money on buying cloth and 1/4 of his money on buying shoes.**

**Answer**

Money spent on buying clothes

= 3/5 of ₹ 2400

= 3/5 × 2400 = ₹1440

Remaining money = ₹ 2400 - ₹ 1440 = ₹ 960

Now, boy spent 1/4 of the remaining money on buying shoes.

Money spent on buying shoes = ₹ 960 × 1/4 = ₹ 240