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

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

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**POINTS TO REMEMBER**

**Fraction.**A rational number in form of — where a and b are integers is called a fraction.

‘a’ is called the numerator and Lb’ is called the denominator of the fraction.**Classification of Fractions :**

**Decimal fraction :**A fraction whose denominator is 10 or multiple of 10.

**Vulgur fraction :**A fraction whose denominator is oilier than 10 or multiple of 10.

**Proper fraction :**A fraction whose denominator is greater than its numerator.

**Improper fraction :**A fraction whose denominator less than its numerator.

**Mixed fraction :**A fraction which consists of an integer and a proper fraction.

**Note**. If the numerator of a fraction is equal to its denominator, then the fraction is equal to unity i.e. 1.**Equivalent Fractions**

Fractions having the same value are called the equivalent fractions.**Simple and Complex Fractions**

A fraction whose numerator and denominator both are integers, is called a simple fraction.

A fraction whose numerator or denominator or both are not integers, is called a complex fraction.**Like and Unlike Fractions**

Fractions having the same denominators are called like fractions.

The fractions with different denominators are called unlike fractions.**Converting unlike fractions into like fractions**Find the LCM of the denominators of all the give- fractions.

For each given fraction, multiply its denominator by a suitable numbers so that the product obtained is equal to the LCM in (i).

Multiply the numerator also by the same number.**To insert a fraction between two given fractions .**

Add the numerators as well as denominators of the given fractions. Then simplify if required.**Addition and Subtraction of fractions**- For like fractions, add or subtract (as required) their numerators, keeping the denominator same.

For unlike fractions, first change all the fractions into like fractions and then add or subtract as above given in (i). **Multiplication**

To multiply two or more fractions, multiply their numerators as well as their denominators.**Division**

To divide on fraction or integer by some other fractions or integer, multiply the first by the reciprocal of the second as given above in multiplication.**Using ‘BODMAS’**

The word ‘BODMAS’ is the abbreviation formed by taking the initial letters of six operations i.e. ‘Bracket’, ;OF, ‘Division’, ‘Multiplication’, ‘Addition’ and ‘Subtraction’. So, according to the rule of ‘BODMAS’, working must be done in the order corresponding to the letters in the word ‘BODMAS’.**Brackets and their removal**

Brackets are four kinds i.e., bar bracket , circular brackets ( ), curly brackets { } and square brackets [ ] and these can be removed in this order i.e. firstly bar, then circular, then curly and lastly square brackets keeping in considerations of the sign given before them.

### Fractions Exercise 3A – Selina Concise Mathematics Class 7 ICSE Solutions

**Question 1.**

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

**Solution:
**

**(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.

**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:**

### Fractions Exercise 3B – Selina Concise Mathematics Class 7 ICSE Solutions

**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:**

### Fractions Exercise 3C – Selina Concise Mathematics Class 7 ICSE Solutions

**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:**

### Fractions Exercise 3D – Selina Concise Mathematics Class 7 ICSE Solutions

**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:**

**EXERCISE 3 (E)**

**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:**