Examples (Revised) - Chapter 2 - Fractions & Decimals - Ncert Solutions class 7 - Maths

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Chapter 2: Fractions & Decimals - NCERT Solutions for Class 7 Maths

Example 1

In a class of 40 students $\frac{1}{5}$ of the total number of studetns like to study English, $\frac{2}{5}$ of the total number like to study Mathematics and the remaining students like to study Science.
(i) How many students like to study English?
(ii) How many students like to study Mathematics?
(iii) What fraction of the total number of students like to study Science?

Solution

Total number of students in the class $=40$.
(i) Of these $\frac{1}{5}$ of the total number of students like to study English.

Example 2

Sushant reads $\frac{1}{3}$ part of a book in 1 hour. How much part of the book will he read in $2 \frac{1}{5}$ hours?

Solution

The part of the book read by Sushant in 1 hour $=\frac{1}{3}$.
So, the part of the book read by him in $2 \frac{1}{5}$ hours $=2 \frac{1}{5} \times \frac{1}{3}$
$
=\frac{11}{5} \times \frac{1}{3}=\frac{11 \times 1}{5 \times 3}=\frac{11}{15}
$

Let us now find $\frac{1}{2} \times \frac{5}{3}$. We know that $\frac{5}{3}=\frac{1}{3} \times 5$.
So, $\frac{1}{2} \times \frac{5}{3}=\frac{1}{2} \times \frac{1}{3} \times 5=\frac{1}{6} \quad 5=\frac{5}{6}$

Also, $\frac{5}{6}=\frac{1 \times 5}{2 \times 3}$. Thus, $\frac{1}{2} \times \frac{5}{3}=\frac{1 \times 5}{2 \times 3}=\frac{5}{6}$.
This is also shown by the figures drawn below. Each of these five equal shapes (Fig 2.10) are parts of five similar circles. Take one such shape. To obtain this shape we first divide a circle in three equal parts. Further divide each of these three parts in two equal parts. One part out of it is the shape we considered. What will it represent?
It will represent $\frac{1}{2} \times \frac{1}{3}=\frac{1}{6}$. The total of such parts would be $5 \times \frac{1}{6}=\frac{5}{6}$.

Similarly $\quad \frac{3}{5} \times \frac{1}{7}=\quad \frac{3 \times 1}{5 \times 7}=\frac{3}{35}$.
We can thus find $\frac{2}{3} \times \frac{7}{5}$ as $\frac{2}{3} \times \frac{7}{5}=\frac{2 \times 7}{3 \times 5}=\frac{14}{15}$.

$\text { So, we find that we multiply two fractions as } \frac{\text { Product of Numerators }}{\text { Product of Denominators }} \text {. }$

Example 3

The side of an equilateral triangle is $3.5 \mathrm{~cm}$. Find its perimeter.
Solution All the sides of an equilateral triangle are equal.

So, length of each side $=3.5 \mathrm{~cm}$
Thus, perimeter $=3 \times 3.5 \mathrm{~cm}=10.5 \mathrm{~cm}$
Example 4

The length of a rectangle is $7.1 \mathrm{~cm}$ and its breadth is $2.5 \mathrm{~cm}$.
What is the area of the rectangle?

Solution

Length of the rectangle $=7.1 \mathrm{~cm}$
Breadth of the rectangle $=2.5 \mathrm{~cm}$
Therefore, area of the rectangle $=7.1 \times 2.5 \mathrm{~cm}^2=17.75 \mathrm{~cm}^2$

Example 5

Find the average of 4.2,3.8 and 7.6.
Solution

 The average of $4.2,3.8$ and 7.6 is $\frac{4.2+3.8+7.6}{3}=\quad=5.2$.

Example 6

Each side of a regular polygon is $2.5 \mathrm{~cm}$ in length. The perimeter of the polygon is $12.5 \mathrm{~cm}$. How many sides does the polygon have?

Solution

The perimeter of a regular polygon is the sum of the lengths of all its equal sides $=12.5 \mathrm{~cm}$.

Length of each side $=2.5 \mathrm{~cm}$. Thus, the number of sides $=\frac{12.5}{2.5}=\frac{125}{25}=5$
The polygon has 5 sides.
Example 7

A car covers a distance of $89.1 \mathrm{~km}$ in 2.2 hours. What is the average distance covered by it in 1 hour?

Solution

Distance covered by the car $=89.1 \mathrm{~km}$.
Time required to cover this distance $=2.2$ hours.
So distance covered by it in 1 hour $=\frac{89.1}{2.2}=\frac{891}{22}=40.5 \mathrm{~km}$.