Solution NCERT Exercise 2.2 part2

Solution NCERT Exercise 2.2 part2

Question (4) Shade: (i) `1/2` of the circles in box (a)

Solution :

Given, Shade `1/2` of the circles in box (a)

There are 12 circles in the given box

Thus, `1/2` of 12

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

`=1/2xx12/1`

`=1/cancel2xx(cancel12 6)/1`

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

`=1/1xx6/1`

`=(1xx6)/(1xx1)`

`=6/1`

= 6

Thus, we have to shade 6 circles out of 12 circles given in the box

Thus, Answer =

Shade (ii) `2/3` of the triangles in box (b)

Solution :

Given, to shade `2/3` of the triangles in box (b)

There are 9 triangles in the given box

Thus, `2/3` of 9

`=2/3xx9`

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

`=2/cancel3xx(cancel9 3)/1`

`=2/1xx3/1`

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

`=(2xx3)/(1xx1)`

`=6/1`

= 6

Thus, we have to shade 6 triangles in the given box

Thus, Answer is

Shade (iii) `3/5` of the squares in box (c)

Solution :

Given, to shade `3/5` of the squares in box (c)

There are 15 squares in the given box

Thus, `3/5` of 15

`=3/5xx15`

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

`=3/cancel5xx(cancel15 3)/1`

`=3/1xx3/1`

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

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

`=9/1`

= 9

Thus, we have shade 9 squares in the given box

Thus, Answer is

Question (5) Find:

(a) `1/2` of (i) 24

Solution :

Given, `1/2` of 24

`=1/2xx24`

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

`=1/cancel2xx(cancel24 12)/1`

`=1/1xx12/1`

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

`=(1xx12)/(1xx1)`

`=12/1`

= 12 Answer

(a) `1/2` of (ii) 46

Solution :

To find `1/2` of 46

`= 1/2xx46`

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

`=1/cancel2xx(cancel46 23)/1`

`=1/1xx23/1`

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

`=(1xx23)/(1xx1)`

`=23/1`

= 23 Answer

(b) `2/3` of (i) 18

Solution :

Given, to find `2/3` of 18

`=2/3xx18`

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

`=2/cancel3xx(cancel18  6)/1`

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

`=(2xx6)/(1xx1)`

`=12/1`

= 12 Answer

(b) `2/3` of (ii) 27

Solution :

Given, to find `2/3` of 27

`=2/3xx27`

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

`=2/cancel3xx(cancel27 9)/1`

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

`=(2xx9)/(1xx1)`

`=18/1`

= 18 Answer

(c) `3/4` of (i) 16

Solution :

Given, to find `3/4` of 16

`=3/4xx16`

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

`=3/cancel4xx(cancel16 4)/1`

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

`=(3xx4)/(1xx1)`

`=12/1`

= 12 Answer

(c) `3/4` of (ii) 36

Solution :

Given, to find `3/4` of 36

`=3/4xx36`

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

`=3/cancel4xx(cancel36 9)/1`

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

`=(3xx9)/(1xx1)`

`=27/1`

= 27 Answer

(d) `4/5` of (i) 20

Solution :

Given, to find `4/5` of 20

`=4/5xx20`

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

`=4/cancel5xx(cancel20 4)/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

(d) `4/5` of (ii) 35

Solution :

Given, to find `4/5` of 35

`=4/5xx35`

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

`=4/cancel5xx(cancel35 7)/1`

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

`=(4xx7)/(1xx1)`

`=28/1`

= 28 Answer

Question (6) Multiply and express as mixed fraction

(a) `3xx5 1/5`

Solution :

Given, `3xx5 1/5`

`=3xx26/5`

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

`=3/1xx26/5`

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

`=(3xx26)/(1xx5)`

`=78/5`

`=15 3/5` Answer

(b) `5xx63/4`

Solution :

Given, `5xx6 3/4`

`=5xx27/4`

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

Thus, `= 5/1xx27/4`

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

`=(5xx27)/(1xx4)`

`=135/4`

`=33 3/4` Answer

(c) `7xx2 1/4`

Solution :

Given, `7xx2 3/4`

`=7xx11/4`

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

`=7/1xx11/4`

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

`=(7xx11)/(1xx4)`

`=77/4`

`=19 1/4` Answer

(d) `4xx6 1/3`

Solution :

Given, `4xx6 1/3`

`=4xx19/3`

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

`=4/1xx19/3`

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

`=(4xx19)/(1xx3)`

`=76/3`

`=25 1/3` Answer

(e) `3 1/4xx6`

Solution :

Given, `3 1/4xx6`

`=13/4xx6`

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

`=13/4xx6/1`

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

`=(13xx6)/(4xx1)`

`=(13xx3xxcancel2)/(2xxcancel2 xx1)`

`=(13xx3)/(2xx1)`

`=39/2`

`=19 1/2` Answer

(f) `3 2/5xx8`

Solution :

Given, `3 2/5xx8`

`=17/5xx8`

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

`=17/5xx8/1`

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

`=(17xx8)/(5xx1)`

`=136/5`

`=27 1/5` Answer

Question (7) Find (a) `1/2` of (i) `2 3/4`

Solution :

Given, to find `1/2` of `2 3/4`

`=1/2 xx11/4`

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

`=(1xx11)/(2xx4)`

`=11/8`

`=1 3/8` Answer

(a) `1/2` of (ii) `4 2/9`

Solution :

Given, to find `1/2` of `4 2/9`

`=1/cancel2xx(cancel38 19)/9`

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

`=(1xx19)/(1xx9)`

`=19/9`

`=2 1/9` Answer

(b) `5/8` of (i) `3 5/6`

Solution :

Given, to find `5/8` of `3 5/6`

`=5/8xx23/6`

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

`=(5xx23)/(8xx6)`

`=115/32`

`=3 19/32` Answer

(b) `5/8` of (ii) `9 2/3`

Solution :

Given, to find `5/8` of `9 2/3`

`=5/8xx29/3`

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

`=(5xx29)/(8xx3)`

`=145/24`

`=6 1/24` Answer

Question (8) Vidya and Pratap went for a picnic. Their mother gave them a water bag that contained 5 litres of water. Vidya consumed `2/5` of the water. Pratap consumed the remaining water.

(i) How much water did Vidya drink?

(ii) What fraction of the total quantity of water did Pratap drink?

Solution :

Given, total water in water bag = 5 litre

Water consumed by vidya `=2/5` of the water

Water consumed by vidya (in litre) = ?

Fraction of water consumed by Pratap = ?

(i) How much water did Vidya drink?

Water drink by vidya `=2/5` of total water

`=2/cancel5xxcancel5` litre

= 2 litre

Thus, water drink by vidya = 2 litre

(ii) What fraction of the total quantity of water did Pratap drink?

Fraction of water consumed by Pratap = total water – fraction of water consumed by Vidya

`=1-2/5`

[here, total water is taken 1 to calculate fraction]

`=(5-2)/5`

`=3/5`

Thus, fraction of water consumed by Pratap `=2/5`

Thus, water consumed by vidya = 2 litre and fraction of water consumed by Pratap `=3/5` Answer

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