Selina solutions for Concise Mathematics [English] Class 7 ICSE chapter 3 - Fractions (Including Problems) [Latest edition]

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

`3/5`

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

`11/10`

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

`13/20`

Classify, the fraction is given below, as decimal or vulgar fraction, proper or improper fraction and mixed fraction: `18/7`

Classify, the fraction is given below, as decimal or vulgar fraction, proper or improper fraction and mixed fraction: `3 2/9`

Classify, the fraction is given below, as a decimal or vulgar fraction, proper or improper fraction and mixed fraction: `19/10^3`

Classify, the fraction is given below, as a decimal or vulgar fraction, proper or improper fraction and mixed fraction: `2 7/10`

Classify, the fraction is given below, as a decimal or vulgar fraction, proper or improper fraction and mixed fraction: `23/500`

Express the following improper fraction as a mixed fraction: `18/5`

Express the following improper fraction as a mixed fraction: `7/4`

Express the following improper fraction as a mixed fraction: `25/6`

Express the following improper fraction as a mixed fraction: `38/5`

Express the following improper fraction as a mixed fraction: `22/5`

Express the following mixed fractions as improper fractions: `2 4/9`

Express the following mixed fractions as improper fractions: `7 5/13`

Express the following mixed fractions as improper fractions: `3 1/4`

Express the following mixed fractions as improper fractions: `2 5/48`

Express the following mixed fractions as improper fractions: `12 7/11`

Reduce the given fraction to lowest term `8/18`

Reduce the given fraction to lowest term `27/36`

Reduce the given fraction to lowest term `18/42`

Reduce the given fraction to lowest term `35/75`

Reduce the given fraction to lowest term `18/45`

State the true or false of the given statement:

`30/40` and `12/16` are equivalent fractions.

State the true or false of the given statement:

`10/25` and `25/10` are equivalent fractions.

State the true or false of the given statement:

`35/49, 20/28, 45/63` and `100/140` are equivalent fractions.

Distinguish of the following fraction, given below, as a simple fraction or a complex fraction: `0/8`

Distinguish of the following fraction, given below, as a simple fraction or a complex fraction: `(-3)/-8`

Distinguish of the following fraction, given below, as a simple fraction or a complex fraction: `(5)/-7`

Distinguish of the following fraction, given below, as a simple fraction or a complex fraction: `(3 3/5)/18`

Distinguish of the following fraction, given below, as a simple fraction or a complex fraction: `(-6)/(2 2/5)`

Distinguish of the following fraction, given below, as a simple fraction or a complex fraction: `(3 1/3)/(7 2/7)`

Distinguish of the following fraction, given below, as a simple fraction or a complex fraction: `(-5 2/9)/5`

Distinguish of the following fraction, given below, as a simple fraction or a complex fraction: `(-8)/0`

For the pair, given below, state whether it forms like fraction or unlike fraction: 

`5/8  "and"  7/8`

For the pair, given below, state whether it forms like fraction or unlike fraction: 

`8/15  "and"  8/21`

For the pair, given below, state whether it forms like fraction or unlike fraction: 

`4/9  "and"  9/4`

Convert given fraction into a fraction with equal denominator: 

`5/6  "and"  7/9`

Convert given fraction into a fraction with equal denominator: 

`2/3, 5/6  "and"  7/12`

Convert given fraction into a fraction with equal denominator: 

`4/5, 17/20, 23/40  "and"  11/16`

Convert given fraction into a fraction with equal numerators: 

`8/9  "and"  12/17`

Convert given fraction into a fraction with equal numerators: 

`6/13, 15/23  "and"  12/17`

Convert given fraction into a fraction with equal numerators: 

`15/19, 25/28, 9/11  "and"  45/47`

Put the given fraction in ascending order by making denominator equal:

`1/3, 2/5, 3/4  "and"  1/6`

Put the given fraction in ascending order by making denominator equal:

`5/6, 7/8, 11/12  "and" 3/10`

Put the given fraction in ascending order by making denominator equal:

`5/7, 3/8, 9/14  "and" 20/21`

Arrange the given fraction in descending order by making numerator equal:

`5/6, 4/15, 8/9  "and"  1/3`

Arrange the given fraction in descending order by making numerator equal:

`3/7, 4/9, 5/7 and 8/11`

Arrange the given fraction in descending order by making numerator equal:

`1/10, 6/11, 8/11  "and"  3/5`

Find the greater fraction: 

`3/5  "and"  11/15`

Find the greater fraction: 

`4/5  "and"  3/10`

Find the greater fraction: 

`6/7  "and"  5/9`

Find the greater fraction: 

`3/8  "and"  4/9`

Find the greater fraction: 

`(-2)/7  "and"  (-3)/10`

Insert one fraction between: 

`3/7  "and"  4/9` 

Insert one fraction between: 

`2  "and"  8/3` 

Insert one fraction between: 

`9/17  "and"  6/13` 

Insert three fractions between

`2/5  "and"  4/9`

Insert three fractions between

`1/2  "and"  5/7`

Insert three fractions between

`3/8  "and"  6/11`

Insert three fractions between

`11/12  "and"  2/3`

Insert three fractions between

`4/7  "and"  3/4`

Insert two fractions between 1 and `3/11`

Insert two fractions between `5/9  "and"  1/4`

Insert two fractions between `5/6  "and"  1 1/5`

Reduce to a single fraction:

`1/2 + 2/3`

Reduce to a single fraction:

`3/5 - 1/10`

Reduce to a single fraction:

`2/3 - 1/6`

Reduce to a single fraction:

`1 1/3 + 2 1/4`

Reduce to a single fraction:

`1/4 + 5/6 - 1/12`

Reduce to a single fraction:

`2/3 - 3/5 + 3 - 1/5`

Reduce to a single fraction:

`2/3 - 1/5 + 1/10`

Reduce to a single fraction:

`2 1/2 + 2 1/3 - 1 1/4`

Reduce to a single fraction:

`2 5/8 - 2 1/6 + 4 3/4`

Simplify: `3/4 xx 6` 

Simplify: `2/3 xx 15` 

Simplify: `3/4 xx 1/2` 

Simplify: `9/12 xx 4/7`

Simplify: `45 xx 2 1/3`

Simplify: `36 xx 3 1/4`

Simplify: `2 div 1/3`

Simplify: `3 div 2/5`

Simplify: `1 div 3/5`

Simplify: `1/3 div 1/4`

Simplify: `- 5/8 div 3/4`

Simplify: `3 3/7 div 1 1/14`

Simplify: `3 3/4 xx 1 1/5 xx 20/21`

Subtract: `2  "from"  2/3`

Subtract: `1/8  "from"  5/8`

Subtract: `-2/5  "from"  2/5`

Subtract: `-3/7  "from"  3/7`

Subtract: `0  "from"  -4/5`

Subtract: `2/9  "from"  4/5`

Subtract: `-4/7  "from"  -6/11`

Find the value of `1/2  "of"  10  "kg"`

Find the value of `3/5  "of"  1  "hour"`

Find the value of `4/7  "of"  2 1/3  "kg"`

Find the value of `3 1/2` times of 2 meters 

Find the value of `1/2  "of"  2 2/3` 

Find the value of `5/11  "of"  4/5  "of"  22  "kg"` 

Simplify and reduce to a simple fraction:

`3/(3 3/4)`

Simplify and reduce to a simple fraction:

`(3/5)/7`

Simplify and reduce to a simple fraction:

`3/(5/7)`

Simplify and reduce to a simple fraction:

`(2 1/5)/(1 1/10)`

Simplify and reduce to a simple fraction:

`2/5  "of"  6/11 xx 1 1/4`

Simplify and reduce to a simple fraction:

`2 1/4 div 1/7 xx 1/3`

Simplify and reduce to a simple fraction:

`1/3 xx 4 2/3 div 3 1/2 xx 1/2`

Simplify and reduce to a simple fraction:

`2/3 xx 1 1/4 div 3/7  "of"  2 5/8`

Simplify and reduce to a simple fraction:

`0 div 8/11`

Simplify and reduce to a simple fraction:

`4/5 div 7/15  "of"  8/9`

Simplify and reduce to a simple fraction:

`4/5 div 7/15 xx 8/9`

Simplify and reduce to a simple fraction:

`4/5  "of"  7/15 div 8/9`

Simplify and reduce to a simple fraction:

`1/2  "of"  3/4 xx 1/2 div 2/3`

A bought `3 3/4` kg of wheat and `2 1/2` kg of rice. Find the total weight of wheat and rice bought.

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

What number should be added to `8 2/3` to `12 5/6`.

What should be subtracted from `8 3/4` to get `2 2/3`?

A field is `16 1/2` m long and `12 2/5` m wide. Find the perimeter of the field.

Sugar costs ₹ `37 1/2` per kg. Find the cost of `8 3/4` kg sugar.

A motorcycle runs `31 1/4` km consuming 1 liter of petrol. How much distance will it run consuming `1 3/5` liter of petrol?

A rectangular park has length = `23 2/3` m and breadth = `16 2/3` m. Find the area?

Each of 40 identical boxes weighs `4 4/5` kg Find the total weight of all the boxes.

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

A rod of length `2 2/5` meter is divided into five equal parts. Find the length of each part so obtained.

If A = `3 3/8` and B = `6 5/8` find:

(i) A ÷ B

(ii) B ÷ A

Cost of `3 5/7` litres of oil is ₹ `83 1/2`. Find the cost of one-litre oil.

The product of two numbers is `20 5/7`. If one of these numbers is `6 2/3`, find the other.

By what number should `5 5/6` be multiplied 1 to get `3 1/3`?

Simplify: `6 + {4/3 + (3/4 - 1/3)}`

Simplify: `8 - {3/2 + (3/5 - 1/2)}`

Simplify: `1/4 (1/4 + 1/3) - 2/5`

Simplify: `2 3/4 - [3 1/8 div {5 - (4 2/3 - 11/12)}]`

Simplify: `12 1/2 - [8 1/2 + {9 - (5 - bar(3 - 2))}]`

Simplify: `1 1/5 ÷ {2 1/3 - (5 + bar(2 - 3))} - 3 1/2`

Simplify: `(1/2 + 2/3) div (3/4 - 2/9)`

Simplify: `6/5  "of"  (3 1/3 - 2 1/2) + (2 5/21 - 2)`

Simplify: `10 1/8  "of"  4/5  div  35/36  "of"  20/49`

Simplify: `5 3/4 - 3/7 xx 15 3/4 + 2 2/35 div 1 11/25`

Simplify: `3/4  "of"  7 3/7 - 5 3/5 div 3 4/15`

A line AB is of length 6 cm. Another line CD is of length 15 cm. What fraction is: The length of AB to that of CD?

A line AB is of length 6 cm. Another line CD is of length 15 cm. What fraction is: `1/2` the length of AB to that of `1/3` of CD?

A line AB is of length 6 cm. Another line CD is of length 15 cm. What fraction is: `1/5` of CD to that of AB?

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

From a sack of potatoes weighing 120 kg, a merchant sells portions weighing 6 kg, `5 1/4` kg, `9 1/2` kg, and `9 3/4` kg respectively.

(i) How many kg did he sell?
(ii) How many kg is still left in the sack?

If a boy works for six consecutive days for 8 hours, `7 1/2` hours, `8 1/4` hours, `6 1/4` hours + `6 3/4` hrs and 7 hours respectively. How much money will he earn at the rate of Rs. 36 per hour?

A student bought `4 1/3` m of yellow ribbon, 6 1/6 m of red ribbon and `3 2/9` m of blue ribbon for decorating a room. How many meters of ribbon did he buy?

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.

Geeta had 30 problems for homework. She worked out `2/5` of them. How many problems were still left to be worked out by her?

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

Mani had sent fifteen parcels of oranges. What was the total weight of the parcels, if each weighed `10 1/2` kg?

A rope is `25 1/2` m long. How many pieces, `1 1/2` each of length can be cut out from it?

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

Vijay weighed `65 1/2` kg. He gained `1 2/5` kg during the first week, `1 1/4` kg during the second week, but lost `5/16` kg during the 16 third week. What was his weight after the third week?

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?

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?

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 to pay each month?

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 `3 1/3` m of the lamp post is above the water, find the whole length of the lamp post.

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

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

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

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

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

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.

A boy spent `3/5` of his money on buying cloth and `1/4` of the remaining on buying shoes. If initially, he has ₹2,400; how much did he spend on shoes?