Solution of NCERT Exercise 2.2

Solution of NCERT Exercise 2.2

Question (1) Which of the drawings (a) to (d) show:

(i) `2xx1/5`

(ii) `2xx1/2`

(iii) `3xx2/3`

(iv) `3xx1/4`

Solution:

(i) Given, `2xx1/5`

Answer Figure

Explanation : In given figure (d) each circle has five parts among which one part is shaded. This means shaded portion in each of the circle represents `1/5` part. Thus, shaded portion both circles represents `2xx1/5`.

(ii) Given, `2xx1/2`

Answer figure

Explanation : In the given figure (b) each of the box is divided into two parts. In which half portion is shaded. Thus, both of the boxes together becomes `2xx1/2`

(iii) Given, `3xx2/3`

Answer figure

Explanation : Each of the circle in given figure (a) has three equal parts. And in which two parts out of three parts are shaded in each circle. This means `2/3` parts are shaded. Since, there are three circles, thus all of the three circles together represent `3xx2/3`.

(iv) Given, `3xx1/4`

Answer figure

Explanation : Each of the boxes are divided into four equal parts. And one part out of four parts in each box is shaded, this means `1/4` part is shaded. Since, there are three boxes thus all of them together represent `3xx1/4`.

Question (2) Some pictures (a) to (c) are given below. Tell which of them show:

(i) `3xx1/5=3/5`

(ii) `2xx1/3=2/3`

(iii) `3xx3/4=2 1/4`

Solution :

(i) Given, `3xx1/5=3/5`

Answer figure

Explanation :

In the given figure (c), there are three boxes in left side. And each box is divided into five parts out of which one part has been shaded.

Shaded portion each box in right side denotes `1/5`. Thus, all the three boxes together in right side denotes `3xx1/5`.

And in the right part there is one box, which is divided into five equal parts out of which three parts has been shaded. This denotes `3/5` part

Thus, all boxes together denotes `3xx1/5 = 3/5`

(ii) Given `2xx1/3=2/3`

Answer figure

Explanation :

In the left hand side there are two circles. In which each circle is divided into three equal parts and one part has been shaded.

Thus, shaded portion in circles in left side denotes `2xx1/3`

In the right hand side there is one circle which is divided into three equal parts out of three parts two parts has been shaded.

Thus, shaded portion in the circle in the left hand side denotes `2/3`

Thus, whole figure denotes `2xx1/3=2/3`

(iii) Given, `3xx3/4=2 1/4`

Answer figure

Explanation :

There are three triangles in each side and each has been divided into four equal parts.

In the left hand side, three portions out of four parts of each triangle have been shaded. Thus, shaded portion in each triangle denote `3/4` part.

Thus, total shaded portions in triangles in left hand side denote `3xx3/4`

And, in right hand side all of the three parts of two triangles are shaded and one part in one triangle is shaded.

Thus, shaded portions of two triangle denote 2 and 1 shaded part out of four parts in one triangle denote `1/4`. In total shaded portions in the triangles in right hand side denote `2 1/4`

Thus, the figure denotes `3xx3/4 = 2 1/4`.

Question (3) Multiply and reduce to lowest form:

(i) `7xx3/5`

Solution :

Given, `7xx3/5`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=7/1xx3/5`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

Thus, `=(7xx3)/(1xx5)`

`=21/5`

`=4 1/5` Answer

(ii) `4xx1/3`

Solution :

Given, `4xx1/3`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=4/1xx1/3`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

Thus, `=(4xx1)/(1xx3)`

`=4/3`

`=1 1/3` Answer

(iii) `2xx6/7`

Solution :

Given, `2xx6/7`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=2/1xx6/7`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

`=(2xx6)/(1xx7)`

`=12/7`

`=1 5/7` Answer

(iv) `5xx2/9`

Solution :

Given, `5xx2/9`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=5/1xx2/9`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

Thus, `=(5xx2)/(1xx9)`

`=10/9`

`=1 1/9` Answer

(v) `2/3xx4`

Solution :

Given, `2/3xx4`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=2/3xx4/1`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

Thus, `=(2xx4)/(3xx1)`

`=8/3`

`=2 2/3` Answer

(vi) `5/2xx6`

Solution :

Given, `5/2xx6`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=5/2xx6/1`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

Thus, `=(5xx6)/(2xx1)`

`=(cancel30 15)/cancel2`

= 15 Answer

(vii) `11xx4/7`

Solution :

Given, `11xx4/7`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=11/1xx4/7`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

Thus, `=(11xx4)/(1xx7)`

`=44/7`

`=6 2/7` Answer

(viii) `20xx4/5`

Solution :

Given, `20xx4/5`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=(cancel20 4)/1xx4/cancel5`

`= 4/1xx4/1`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

`=(4xx4)/(1xx1)`

`=16/1`

= 16 Answer

(ix) `13xx1/3`

Solution :

Given, `13xx1/3`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=13/1xx1/3`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

Thus, `=(13xx1)/(1xx3)`

`=13/3`

`=4 1/3` Answer

(x) `15xx3/5`

Solution :

Given, `15xx3/5`

We know that denominator is always 1, if there is no denominator for a number.

Thus, `=(cancel15 3)/1xx3/cancel5`

`=3/1xx3/1`

Now, to multiply two or more fractions numerator is multiplied with numerator and denominator is multiplied with denominator.

Thus, `=(3xx3)/(1xx1)`

`=9/1`

= 9 Answer

Back to 7-math-home

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