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**Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 3 Fractions (Including Problems)**

Question 1.

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

Solution:

Question 2.

Express the following improper fractions as mixed fractions :

Solution:

Question 3.

Express the following mixed fractions as improper fractions :

Solution:

Question 4.

Reduce the given fractions to lowest terms

Solution:

Question 5.

State : true or false

Solution:

Question 6.

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

Solution:

Question 1.

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

Solution:

Question 2.

Convert given fractions into fractions with equal denominators :

Solution:

Question 3.

Convert given fractions into fractions with equal numerators :

Solution:

Question 4.

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

Solution:

Question 5.

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

Solution:

Question 6.

Find the greater fraction :

Solution:

Question 7.

Insert one fraction between :

Solution:

Question 8.

Insert three fractions between

Solution:

Question 9.

Insert two fractions between

Solution:

Question 1.

Reduce to a single fraction :

Solution:

Question 2.

Simplify :

Solution:

Question 3.

Subtract :

Solution:

Question 4.

Find the value of

Solution:

Question 5.

Simplify and reduce to a simple fraction :

Solution:

Question 6.

A bought 3 \(\frac { 3 }{ 4 }\) kg of wheat and 2 \(\frac { 1 }{ 2 }\) kg of rice. Find the total weight of wheat and rice bought.

Solution:

Question 7.

Which is greater,\(\frac { 3 }{ 5 }\) or \(\frac { 7 }{ 10 }\) and by how much?

Solution:

Question 8.

What number should be added to 8 \(\frac { 2 }{ 3 }\) to 12 \(\frac { 5 }{ 6 }\)

Solution:

Question 9.

What should be subtracted from 8\(\frac { 3 }{ 4 }\) to get 2 \(\frac { 2 }{ 3 }\)

Solution:

Question 10.

A field is 16 \(\frac { 1 }{ 2 }\) m long and 12 \(\frac { 2 }{ 5 }\) m wide. Find the perimeter of the field.

Solution:

Question 11.

Sugar costs ₹37 \(\frac { 1 }{ 2 }\)per kg. Find the cost of 8\(\frac { 3 }{ 4 }\) kg sugar.

Solution:

Question 12.

A motor cycle runs 31\(\frac { 1 }{ 4 }\) km consuming 1 litre of petrol. How much distance will it run consuming 1\(\frac { 3 }{ 5 }\) liter of petrol?

Solution:

Question 13.

A rectangular park has length = 23 \(\frac { 2 }{ 3 }\) m and breadth = 16 \(\frac { 2 }{ 3 }\) m. Find the area of the park.

Solution:

Question 14.

Each of 40 identical boxes weighs 4 \(\frac { 4 }{ 5 }\) kg Find the total weight of all the boxes.

Solution:

Question 15.

Out of 24 kg of wheat, \(\frac { 5 }{ 6 }\) th of wheat is consumed. Find, how much wheat is still left?

Solution:

Question 16.

A rod of length 2 \(\frac { 2 }{ 5 }\) metre is divided into five equal parts. Find the length of each part so obtained.

Solution:

Question 17.

IfA = 3\(\frac { 3 }{ 8 }\) and B = 6\(\frac { 5 }{ 8 }\) find :

(i) A+B

(ii) B A

Solution:

Question 18.

Cost of 3 \(\frac { 5 }{ 7 }\) litres of oil is ₹83 \(\frac { 1 }{ 2 }\). Find the

cost of one litre oil.

Solution:

Question 19.

The product of two numbers is 20 \(\frac { 5 }{ 7 }\). If one of these numbers is 6 \(\frac { 2 }{ 3 }\), find the other.

Solution:

Question 20.

By what number should 5 \(\frac { 5 }{ 6 }\) be multiplied 1 to get 3\(\frac { 1 }{ 3 }\) ?

Solution:

Question 1.

Simplify

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

Question 10.

Solution:

Question 11.

Solution:

Question 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) \(\frac { 1 }{ 2 }\) the length of AB to that of \(\frac { 1 }{ 3 }\) of CD ?

(iii) \(\frac { 1 }{ 5 }\) of CD to that of AB ?

Solution:

Question 2.

Subtract \(\frac { 2 }{ 7 }\) – \(\frac { 5 }{ 21 }\) from the sum of \(\frac { 3 }{ 4 }\) , \(\frac { 5 }{ 7 }\) and \(\frac { 7 }{ 12 }\)

Solution:

Question 3.

From a sack of potatoes weighing 120 kg, a merchant sells portions weighing 6 kg, 5\(\frac { 1 }{ 4 }\) kg, 9\(\frac { 1 }{ 2 }\) kg and 9\(\frac { 3 }{ 4 }\) kg respectively.

(i) How many kg did he sell ?

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

Solution:

Question 4.

If a boy works for six consecutive days for 8 hours, 7\(\frac { 1 }{ 2 }\) hours, 8\(\frac { 1 }{ 4 }\) hours, 6 \(\frac { 1 }{ 4 }\)4 3hours, 6\(\frac { 3 }{ 4 }\) hours and 7 hours respectively. How much money will he earn at the rate of Rs. 36 per hour ?

Solution:

Question 5.

A student bought 4 \(\frac { 1 }{ 3 }\) m of yellow ribbon, 6 \(\frac { 1 }{ 6 }\) m of red ribbon and 3\(\frac { 2 }{ 9 }\) m of blue ribbon for decorating a room. How many metres of ribbon did he buy ?

Solution:

Question 6.

In a business, Ram and Deepak invest \(\frac { 3 }{ 5 }\) and \(\frac { 2 }{ 5 }\) of the total investment. IfRs. 40,000 is the total investment, calculate the amount invested by each ?

Solution:

Question 7.

Geeta had 30 problems for home work. She worked out \(\frac { 2 }{ 5 }\) of them. How many problems were still left to be worked out by her ?

Solution:

Question 8.

A picture was marked at Rs. 90. It was sold at \(\frac { 3 }{ 4 }\) of its marked price. What was the sale price ?

Solution:

Question 9.

Mani had sent fifteen parcels of oranges. What was the total weight of the parcels, if each weighed 10\(\frac { 1 }{ 2 }\) kg ?Solution:

Question 10.

A rope is 25\(\frac { 1 }{ 2 }\) m long. How many pieces , 1 \(\frac { 1 }{ 2 }\) each of length can be cut out from it?Solution:

Question 11.

The heights of two vertical poles, above the earth’s surface, are 14 \(\frac { 1 }{ 4 }\) m and 22 \(\frac { 1 }{ 3 }\) respectively. How much higher is the second pole as compared with the height of the first pole ?

Solution:

Question 12.

Vijay weighed 65\(\frac { 1 }{ 2 }\) kg. He gained 1\(\frac { 2 }{ 5 }\) kg during the first week, 1 \(\frac { 1 }{ 4 }\) kg during the second week, but lost \(\frac { 5 }{ 16 }\) kg during the 16 third week. What was his weight after the third week ?

Solution:

Question 13.

A man spends \(\frac { 2 }{ 5 }\) of his salary on food and \(\frac { 3 }{ 10 }\) on house rent, electricity, etc. What fraction of his salary is still left with him ?

Solution:

Question 14.

A man spends \(\frac { 2 }{ 5 }\) of his salary on food and \(\frac { 3 }{ 10 }\) of the remaining on house rent, electricity, etc. What fraction of his salary is still left with him ?

Solution:

Question 15.

Shyam bought a refrigerator for Rs. 5000. He paid \(\frac { 1 }{ 10 }\) of the price in cash and the rest in 12 equal monthly instalments. How much had he to pay each month ?

Solution:

Question 16.

A lamp post has half of its length in mud, and \(\frac { 1 }{ 3 }\) of its length in water.

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

(ii) If 3\(\frac { 1 }{ 3 }\) m of the lamp post is above the water, find the whole length of the lamp post.

Solution:

Question 17.

I spent \(\frac { 3 }{ 5 }\) of my savings and still have Rs. 2,000 left. What were my savings ?

Solution:

Question 18.

In a school, \(\frac { 4 }{ 5 }\) of the children are boys. If the number of girls is 200, find the number of boys.

Solution:

Question 19.

If \(\frac { 4 }{ 5 }\) of an estate is worth Rs. 42,000, find the worth of whole estate. Also, find the value of \(\frac { 3 }{ 7 }\) of it.

Solution:

Question 20.

After going \(\frac { 3 }{ 4 }\) of my journey, I find that I have covered 16 km. How much Journey is still left ?

Solution:

Question 21.

When Krishna travelled 25 km, he found that \(\frac { 3 }{ 5 }\) of his journey was still left. What was the length of the whole journey.

Solution:

Question 22.

From a piece of land, one-third is bought by Rajesh and one-third of remaining is bought by Manoj. If 600 m² land is still left unsold, find the total area of the piece of land.

Solution:

Question 23.

A boy spent \(\frac { 3 }{ 5 }\) of his money on buying 1 cloth and \(\frac { 1 }{ 4 }\) of the remaining on buying shoes. If initially he has ?2,400; how much did he spend on shoes?

Solution:

Question 24.

A boy spent \(\frac { 3 }{ 5 }\) of his money on buying cloth and \(\frac { 1 }{ 4 }\) of his money on buying shoes. If initially he has ?2,400; how much did he spend on shoes?

Solution:

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