Andhra Pradesh SCERT Class 7 Maths Fractions and Decimals Question and Answers Solutions
Andhra Pradesh SCERT 7th Class Maths Solutions Chapter 2 Fractions and Decimals Question and answers. Students who are searching for Andhra Pradesh Class 7 Maths Chapter 2 can find here Solution of this chapter.
Board |
Andhra Pradesh (AP Board) |
Class |
7th |
Subject |
Maths |
Topic |
Solution |
EXERCISE 2.1
1.) Which of the drawings (a) to (d) show:
(i) 2 x 1/5
(ii) 2 x 1/2
(iii) 3 x 2/3
(iv) 3 x 1/4
ANSWER:
Here, we have to match given figure and fraction.
In given figure,
There are 3 parts and each part is divided in 2/3 parts.
The correct match for given figure is 3 x 2/3.
ANSWER:
Here, we have to match given figure and fraction.
In given figure,
There are 2 parts and each part is divided in 2 parts.
The correct match for given figure is 2 x 1/2.
ANSWER:
Here, we have to match given figure and fraction.
In given figure,
There are 3 parts and each part is divided in 4 parts.
The correct match for given figure is 3 x 1/4.
ANSWER:
Here, we have to match given figure and fraction.
In given figure,
There are 2 parts and each part is divided in 5 parts.
The correct match for given figure is 2 x 1/5.
2.) Some pictures (a) to (c) are given below. Tell which of them show:
(i) 3 x 1/5 = 3/5
(ii) 2 x 1/3 = 2/3
(iii) 3 x 3/4 = 2 (1/4)
ANSWER:
Here, we have to match given figure and fraction.
In given figure,
There are 2 parts and each part is divided in 3 parts.
2 x 1/3 = 2/3
ANSWER:
Here, we have to match given figure and fraction.
In given figure,
There are 3 parts and each part is divided in 4 parts.
3 x 3/4 = 2 (1/4)
ANSWER:
Here, we have to match given figure and fraction.
In given figure,
There are 3 parts and each part is divided in 5 parts.
3 x 1/5 = 3/5
3.) Multiply and reduce to lowest form and convert into a mixed fraction:
(i) 7 x 3/5
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
7 x 3/5 = 21/5
Now, we have to convert this into mixed fraction.
21/5 = 4 (1/5)
(ii) 4 x 1/3
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
4 x 1/3 = 4/3
Now, we have to convert this into mixed fraction.
4/3 = 1 (1/3)
(iii) 2 x 6/7
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
2 x 6/7 = 12/7
Now, we have to convert this into mixed fraction.
12/7 = 1 (5/7)
(iv) 5 x 2/9
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
5 x 2/9 = 10/9
Now, we have to convert this into mixed fraction.
10/9 = 1 (1/9)
(v) 2/3 x 4
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
2/3 x 4 = 8/3
Now, we have to convert this into mixed fraction.
8/3 = 2 (2/3)
(vi) 5/2 x 6
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
5/2 x 6 = 30/2 = 15
(vii) 11 x 4/7
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
11 x 4/7 = 44/7
Now, we have to convert this into mixed fraction.
44/7 = 6 (2/7)
(viii) 20 x 4/5
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
20 x 4/5 = 80/5 = 16
(ix) 13 x 1/3
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
13 x 1/3 = 13 / 3
Now, we have to convert this into mixed fraction.
13 / 3 = 4 (1/3)
(x) 15 x 3/5
ANSWER:
Here, we have to multiply given fractions and reduce to lowest form and convert them into a mixed fraction.
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
15 x 3/5 = 45/5 = 9
4.) Shade: (1) 1/2 of the circles in box (a)
(ii) 2/3 of the triangles in box (b)
(iii) 3/5 of the squares in box (c).
ANSWER:
Here, we have to shade 1/2 of the circles in box (a)
There are total 12 circles in box (a).
½ x 12 = 6 circles we have to shade.
Here, we have to shade 2/3 of the triangles in box (b)
There are total 9 circles in box (a).
2/3 x 9 = 6 triangles we have to shade.
Here, we have to shade 3/5 of the squares in box (c).
There are total 15 squares in box (c).
3/5 x 15 = 9 we squares have to shade.
5.) Find:
(a) 1/2 of
(i) 24
ANSWER:
Here we have to find 1/2 of 24.
1/2 x 24 = 24/2 = 12
(ii) 46
ANSWER:
Here we have to find 1/2 of 46.
1/2 x 46. = 46/2 = 23
(b) 2/3 of
(i) 18
ANSWER:
Here we have to find 2/3 of 18.
2/3 x 18. = 36/3 = 12
(ii) 27
ANSWER:
Here we have to find 2/3 of 27
2/3 x 27 = 54/3 = 18
(c) 3/4 of
(i) 16
ANSWER:
Here we have to find 3/4 of 16
3/4 x 16 = 48 / 4 = 12
(ii) 36
ANSWER:
Here we have to find 3/4 of 36.
3/4 x 36 = 108/4 = 27
(d) 4/5 of
(i) 20
ANSWER:
Here we have to find 4/5 of 20
4/5 x 20 = 80/5 = 16
(ii) 35
ANSWER:
Here we have to find 4/5 of 35
4/5 x 35 = 140 /5 = 28
6.) Multiply and express as a mixed fraction:
(a) 3 x 5 (1/5)
ANSWER:
Here, we have to multiply given fraction and express it as a mixed fraction.
We know,
To multiply a mixed fraction to a whole number, we first convert the mixed fraction to an improper fraction and then multiply.
5 (1/5) = 26/5
3 x 26/5
Now,
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
3 x 26/5 = 78/5
78/5 = 15 (3/5)
(b) 5 x 6 (3/4)
ANSWER:
Here, we have to multiply given fraction and express it as a mixed fraction.
We know,
To multiply a mixed fraction to a whole number, we first convert the mixed fraction to an improper fraction and then multiply.
6 (3/4) = 27/4
5 x 27/4
Now,
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
5 x 27/4 = 135/4
135/4 = 33 (3/4)
(c) 7 x 2 (1/4)
ANSWER:
Here, we have to multiply given fraction and express it as a mixed fraction.
We know,
To multiply a mixed fraction to a whole number, we first convert the mixed fraction to an improper fraction and then multiply.
2 (1/4) = 9/4
7 x 9/4
Now,
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
7 x 9/4 = 63/4
63/4 = 15 (3/4)
(d) 4 x 6 (1/3)
ANSWER:
Here, we have to multiply given fraction and express it as a mixed fraction.
We know,
To multiply a mixed fraction to a whole number, we first convert the mixed fraction to an improper fraction and then multiply.
6 (1/3) = 19/3
4 x 19/3
Now,
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
4 x 19/3 = 76/3
76/3= 25 (1/3)
(e) 3 (1/4) x 6
ANSWER:
Here, we have to multiply given fraction and express it as a mixed fraction.
We know,
To multiply a mixed fraction to a whole number, we first convert the mixed fraction to an improper fraction and then multiply.
3 (1/4) = 13/4
6 x 13/4
Now,
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
6 x 13/4 = 78/4
78/4 = 19 (1/2)
(f) 3 (2/5) x 8
ANSWER:
Here, we have to multiply given fraction and express it as a mixed fraction.
We know,
To multiply a mixed fraction to a whole number, we first convert the mixed fraction to an improper fraction and then multiply.
3 (2/5) = 17/5
8 x 17/5
Now,
We know,
To multiply a whole number with a proper or an improper fraction, we have to multiply the whole number with the numerator of the fraction, and taking the denominator same.
8 x 17/5 = 136/5
136/5 = 27 (1/5)
7.) Find: (a) 1/2 of
(i) 2 (3/4)
ANSWER:
We have to find 1/2 of 2 (3/4).
We first convert the mixed fraction to an improper fraction and then multiply.
2 (3/4) = 11/4
1/2 x 11/4 = 11/8 = 1 (3/8)
(ii) 4 (2/9)
ANSWER:
We have to find 1/2 of 4 (2/9).
We first convert the mixed fraction to an improper fraction and then multiply.
4 (2/9) = 38/9
1/2 x 38/9 = 38/18 = 2 (1/9)
(b) 5/8 of
(i) 3 (5/6)
ANSWER:
We have to find 5/8 of 3 (5/6).
We first convert the mixed fraction to an improper fraction and then multiply.
3 (5/6) = 23/6
5/8 x 23/6 = 115/48 = 2 (19/48)
(ii) 9 (2/3)
ANSWER:
We have to find 5/8 of 9 (2/3)
We first convert the mixed fraction to an improper fraction and then multiply.
9 (2/3) = 29/3
5/8 x 29/3 = 145/24 = 6 (1/24)
8.) Vidya and Pratap went for a picnic. Their mother gave them a water bottle 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?
ANSWER:
Given that,
A water bottle that contained 5 litres of water.
Vidya consumed 2/5 of the water. Pratap consumed the remaining water.
We have to find how much water did Vidya drink.
Water did Vidya drink = 2/5 of 5 litres
Water did Vidya drink = 2/5 x 5 litres
Water did Vidya drink = 2 litres
(ii) What fraction of the total quantity of water did Pratap drink?
ANSWER:
Total 5 litre water in water bottle.
Vidya drink 2 litre water.
Water did Pratap drink = 5 litre – 2 litre = 3 litre
Fraction of the total quantity of water did Pratap drink = Water did Pratap drink / Total water
Fraction of the total quantity of water did Pratap drink = 3/5
EXERCISE 2.2
1.) Find:
(1) 1/4 of
(a) 1/4
ANSWER:
Here we have to find 1/4 of 1/4
1/4 x 1/4 = 1
(b) 3/5
ANSWER:
Here we have to find 1/4 of 3/5
1/4 x 3/5 = 3/20
(c) 4/3
ANSWER:
Here we have to find 1/4 of 4/3
1/4 x 4/3 = 4/12 = 1/3
(ii) 1/7 of
(a) 2/9
ANSWER:
Here we have to find 1/7 of 2/9
1/7 x 2/9 = 2/63
(b) 6/5
ANSWER:
Here we have to find 1/7 of 6/5
1/7 x 6/5 = 6/35
(c) 3/10
ANSWER:
Here we have to find 1/7 of 3/10
1/7 x 3/10 = 3/70
2.) Multiply and reduce to lowest form (if possible):
(i) 2/3 x 2 (2/3)
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
2/3 x 2 (2/3)
We first convert the mixed fraction to an improper fraction and then multiply.
2 (2/3) = 8/3
2/3 x 8/3 = 16/9 = 1 (7/9)
(ii) 2/7 x 7/9
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
2/7 x 7/9 = 14/63
14/63 in lowest form = 2/9
(iii) 3/8 x 6/4
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
3/8 x 6/4 = 18/32
18/32 in lowest form = 9/16
(iv) 9/5 x 3/5
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
9/5 x 3/5 = 27/25
27/25 in lowest form = 1 (2/25)
(v) 1/3 x 15/8
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
1/3 x 15/8 = 15/24
15/24 in lowest form = 5/8
(vi) 11/2 x 3/10
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
11/2 x 3/10 = 33 /30
33/30 in lowest form = 11/10
(vii) 4/5 x 12/7
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
4/5 x 12/7 = 48/35
48/35 in lowest form = 1(13/35)
3.) Multiply the following fractions:
(i) 2/5 x 5 (1/4)
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
2/5 x 5 (1/4)
We first convert the mixed fraction to an improper fraction and then multiply.
5 (1/4) = 21/4
2/5 x 21/4
2/5 x 21/4 = 42 / 20
42 / 20 = 21/10
(ii) 6 (2/5) x 7/9
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
6 (2/5) x 7/9
We first convert the mixed fraction to an improper fraction and then multiply.
6 (2/5) = 32/5
32/5 x 7/9
32/5 x 7/9 = 224 /45
224 /45 = 4 (44/45)
(iii) 3/2 x 5 (1/3)
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
3/2 x 5 (1/3)
We first convert the mixed fraction to an improper fraction and then multiply.
5 (1/3) = 16/3
3/2 x 16/3
3/2 x 16/3 = 48/6 = 8
(iv) 5/6 x 2 (3/7)
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
5/6 x 2 (3/7)
We first convert the mixed fraction to an improper fraction and then multiply.
2 (3/7) = 17/7
5/6 x 17/7
5/6 x 17/7 = 85/42
85/42 = 2 (1/42)
(v) 3 (2/5) x 4/7
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
3 (2/5) x 4/7
We first convert the mixed fraction to an improper fraction and then multiply.
3 (2/5) = 17/5
17/5 x 4/7
17/5 x 4/7 = 68/35
68/35 = 1(33/35)
(vi) 2 (3/5) x 3
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
2 (3/5) x 3
We first convert the mixed fraction to an improper fraction and then multiply.
2 (3/5) = 13/5
13/5 x 3 = 39/5
39/5 = 7 (4/5)
(vii) 3 (4/7) x 3/5
ANSWER:
Here we have to multiply given fractions and reduce them to lowest form.
3 (4/7) x 3/5
We first convert the mixed fraction to an improper fraction and then multiply.
3 (4/7) = 25/7
25/7 x 3/5 = 75/35 = 15/7
15/7 = 2 (1/7)
4.) Which is greater:
(i) 2/7 of 3/4 ог 3/5 of 5/8
ANSWER:
We have to find which is greater between 2/7 of 3/4 and 3/5 of 5/8.
We 1st find 2/7 of 3/4
2/7 x 3/4 = 6/28 = 3/14
Now,
We find 3/5 x 5/8.
3/5 x 5/8 = 3/8
3/8 > 3/14
3/5 of 5/8 is greater.
(ii) 1/2 of 6/7 ог 2/3 of 3/7
ANSWER:
We have to find which greater between 1/2 of 6/7 is and 2/3 of 3/7.
We 1st find 1/2 of 6/7
1/2 x 6/7 = 6/14 = 3/7
Now,
We find 2/3 x 3/7.
2/3 x 3/7 = 6/21 = 2/7
3/7 > 2/7
1/2 of 6/7 is greater.
5.) Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is 3/4 m. Find the distance between the first and the last sapling.
ANSWER:
Given that,
Saili plants 4 saplings, in a row, in her garden
The distance between two adjacent saplings is 3/4 m.
We have to find the distance between the first and the last sapling.
We know, when there are 4 saplings the distance between the first and the last sapling is only 3 times of given distance.
The distance between the first and the last sapling = 3 x 3/4
The distance between the first and the last sapling = 9/4 = 2 (1/4)
6.) Lipika reads a book for 1 (3/4) hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
ANSWER:
Given that,
Lipika reads a book for 1 (3/4) hours every day.
She reads the entire book in 6 days
We have to find how many hours in all were required by her to read the book.
We first convert mixed fraction into improper or proper fraction.
1 (3/4) hours = 7/4 hours
She reads the entire book in 6 days
Hours in all were required by her to read the book = 7/4 hours x 6 days
Hours in all were required by her to read the book = 42/4
Hours in all were required by her to read the book = 10 (1/2)
7.) A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2 (3/4) litres of petrol.
ANSWER:
Given that,
A car runs 16 km using 1 litre of petrol
We have to find how much distance will it cover using 2 (3/4) litres of petrol.
We first convert mixed fraction into improper or proper fraction.
2 (3/4) litres = 11/4 litres
Distance will it cover using 2 (3/4) litres of petrol = 11/4 litres x 16 km
Distance will it cover using 2 (3/4) litres of petrol = 44 km.
8.) (a) (i) Provide the number in the box such that 2/3 x Box= 10/30.
ANSWER:
Given,
2/3 x Box = 10/30.
We have to find value of Box.
Box = 10/30 x 3/2
Box = 5/10
(ii) The simplest form of the number obtained in is Box.
ANSWER:
The simplest form of the number obtained in is 5/10 is 1/2
(b) (i) Provide the number in the box, such that 3/5 x Box= 24 / 75 .
ANSWER:
Given,
3/5 x Box = 24 / 75.
We have to find value of Box.
Box = 24 / 75 x 5/3
Box = 8/15
(ii) The simplest form of the number obtained in is Box.
ANSWER:
The simplest form of the number obtained in is Box is 8/15.
EXERCISE 2.3
1.) Find:
(i) 12 / (3/4)
ANSWER:
We have to find 12 / (3/4)
We know,
To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction.
The reciprocal of fraction (3/4) is 4/3.
12 / (3/4) = 12 x 4/3 = 16
(ii) 14 / (5/6)
ANSWER:
We have to find 14 / (5/6)
We know,
To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction. The reciprocal of fraction (5/6) is 6/5.
14 / (5/6) = 14 x 6/5 = 84/5
84/5 = 16 (4/5)
(iii) 8 / (7/3)
ANSWER:
We have to find 8 / (7/3)
We know,
To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction. The reciprocal of fraction (7/3) is 3/7.
8 / (7/3) = 8 x 3/7 = 24/7
(iv) 4 / (8/3)
ANSWER:
We have to find 4 / (8/3)
We know,
To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction. The reciprocal of fraction (8/3) is 3/8.
4 / (8/3) = 4 x 3/8 = 12/8 = 3/2
(v) 3 / (2 1/3)
ANSWER:
We have to find 3 / (2 1/3)
We first convert mixed fraction into improper or proper fraction.
(2 1/3) = 7/3
We know,
To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction. The reciprocal of fraction (7/3) is 3/7.
3 / (2 1/3) = 3 x 3/7 = 9/7
(vi) 5 / (3 4/7)
ANSWER:
We have to find 5 / (3 4/7)
We first convert mixed fraction into improper or proper fraction.
(3 4/7) = 25/7
We know,
To divide a whole number by any fraction, multiply that whole number by the reciprocal of that fraction. The reciprocal of fraction 25/7 is 7/25.
5 / (3 4/7) = 5 x 7/25 = 35/25 = 7/5
2.) Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) 3/7
ANSWER:
We have to find reciprocal of given fraction and classify them into proper fractions, improper fractions and whole numbers.
The reciprocal of 3/7 = 7/3
Here numerator is greater than denominator.
7/3 is improper fraction.
(ii) 5/8
ANSWER:
We have to find reciprocal of given fraction and classify them into proper fractions, improper fractions and whole numbers.
The reciprocal of 5/8 = 8/5
Here numerator is greater than denominator.
8/5 is improper fraction.
(iii) 9/7
ANSWER:
We have to find reciprocal of given fraction and classify them into proper fractions, improper fractions and whole numbers.
The reciprocal of 9/7 = 7/9
Here denominator is greater than numerator.
7/9 is proper fraction.
(iv) 6/5
ANSWER:
We have to find reciprocal of given fraction and classify them into proper fractions, improper fractions and whole numbers.
The reciprocal of 6/5 = 5/6
Here denominator is greater than numerator.
5/6 is proper fraction.
(v) 12/7
ANSWER:
We have to find reciprocal of given fraction and classify them into proper fractions, improper fractions and whole numbers.
The reciprocal of 12/7 = 7/12
Here denominator is greater than numerator.
7/12 is proper fraction.
(vi) 1/8
ANSWER:
We have to find reciprocal of given fraction and classify them into proper fractions, improper fractions and whole numbers.
The reciprocal of 1/8 = 8
8 is a whole number
(vii) 1/11
ANSWER:
We have to find reciprocal of given fraction and classify them into proper fractions, improper fractions and whole numbers.
The reciprocal of 1/11 = 11
11 is a whole number.
- Find:
(i) (7/3) / 2
ANSWER:
We have to find (7/3) / 2
We know,
To divide a fraction by any whole number, multiply that fraction by the reciprocal of that whole number. The reciprocal of whole number 2 is 1/2.
(7/3) / 2 = 7/3 x 1/2 = 7/6
(ii) (4/9) / 5
ANSWER:
We have to find (4/9) / 5
We know,
To divide a fraction by any whole number, multiply that fraction by the reciprocal of that whole number. The reciprocal of whole number 5 is 1/5.
(4/9) / 5 = 4/9 x 1/5 = 4/45
(iii) 6/13 / 7
ANSWER:
We have to find 6/13 / 7
We know,
To divide a fraction by any whole number, multiply that fraction by the reciprocal of that whole number. The reciprocal of whole number 7 is 1/7.
6/13 / 7 = 6/13 x 1/7= 6/91
(iv) 4 (1/3) / 3
ANSWER:
We have to find 4 (1/3) / 3
We first convert mixed fraction into improper or proper fraction.
4 (1/3) = 13/3
We know,
To divide a fraction by any whole number, multiply that fraction by the reciprocal of that whole number. The reciprocal of whole number 3 is 1/3.
4 (1/3) / 3 = 13/3 x 1/3= 13/9
(v) 3 (1/2) / 4
ANSWER:
We have to find 3 (1/2) / 4
We first convert mixed fraction into improper or proper fraction.
3 (1/2) = 7/2
We know,
To divide a fraction by any whole number, multiply that fraction by the reciprocal of that whole number. The reciprocal of whole number 4 is 1/4.
3 (1/2) / 4 = 7/2 x 1/ 4 = 7/8
(vi) 4 (3/7) / 7
ANSWER:
We have to find 4 (3/7) / 7
We first convert mixed fraction into improper or proper fraction.
4 (3/7) = 31/7
We know,
To divide a fraction by any whole number, multiply that fraction by the reciprocal of that whole number. The reciprocal of whole number 7 is 1/7.
4 (3/7) / 7 = 31/7 x 1/ 7 = 31/49
4.) Find:
(i) 2/5 / (1/2)
ANSWER:
We have to find 2/5 / (1/2)
We know,
To divide a Fraction by any fraction, multiply that fraction by the reciprocal of 2nd fraction.
The reciprocal of fraction 1/2 is 2.
2/5 / (1/2) = 2/5 x 2 = 4/5
(ii) 4/9 / (2/3)
ANSWER:
We have to find 4/9 / (2/3)
We know,
To divide a Fraction by any fraction, multiply that fraction by the reciprocal of 2nd fraction.
The reciprocal of fraction 2/3 is 3/2.
4/9 / (2/3) = 4/9 x 3/2 = 12/18 = 2/3
(iii) 3/7 / (8/7)
ANSWER:
We have to find 3/7 / (8/7)
We know,
To divide a Fraction by any fraction, multiply that fraction by the reciprocal of 2nd fraction.
The reciprocal of fraction 8/7 is 7/8.
3/7 / (8/7) = 3/7 x 7/8 = 21/56 = 3/8
(iv) 2 (1/3) / (3/5)
ANSWER:
We have to find 2 (1/3) / (3/5)
We first convert mixed fraction into improper or proper fraction.
2 (1/3) = 7/3
We know,
To divide a Fraction by any fraction, multiply that fraction by the reciprocal of 2nd fraction.
The reciprocal of fraction3/5 is 5/3.
2 (1/3) / (3/5) = 7/3 x 5/3 = 35/9
(v) 3 (1/2) / (8/3)
ANSWER:
We have to find 3 (1/2) / (8/3)
We first convert mixed fraction into improper or proper fraction.
3 (1/2) = 7/2
We know,
To divide a Fraction by any fraction, multiply that fraction by the reciprocal of 2nd fraction.
The reciprocal of fraction 8/3 is 3/8.
3 (1/2) / (8/3) = 7/2 x 3/8 = 21/16
(vi)2/5 / 1 (1/2)
ANSWER:
We have to find 2/5 / 1 (1/2)
We first convert mixed fraction into improper or proper fraction.
1 (1/2) = 3/2
We know,
To divide a Fraction by any fraction, multiply that fraction by the reciprocal of 2nd fraction.
The reciprocal of fraction 3/2 is 2/3.
2/5 / 1 (1/2) = 2/5 x 2/3 = 4/15
(vii) 3 (1/5) / (1 2/3)
ANSWER:
We have to find 3 (1/5) / (1 2/3)
We first convert mixed fraction into improper or proper fraction.
3 (1/5) = 16/5
(1 2/3) = 5/3
We know,
To divide a Fraction by any fraction, multiply that fraction by the reciprocal of 2nd fraction.
The reciprocal of fraction 5/3 is 3/5.
3 (1/5) / (1 2/3) = 16/5 x 3/5 = 48/25
(viii) 2 1/5 / (1 1/5)
ANSWER:
We have to find 2 1/5 / (1 1/5)
We first convert mixed fraction into improper or proper fraction.
2 1/5 = 11/5
(1 1/5)= 6/5
We know,
To divide a Fraction by any fraction, multiply that fraction by the reciprocal of 2nd fraction.
The reciprocal of fraction 6/5 is 5/6.
2 1/5 / (1 1/5) = 11/5 x 5/6 = 55/30 = 11/6
EXERCISE 2.4
1.) Find:
(i) 0.2 x 6
ANSWER:
We have to find 0.2 x 6
We know,
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
0.2 x 6 = 2 x 6 = 12
Now, there are only 1 decimal point. We give decimal point from rightmost digit and moved towards left.
0.2 x 6 = 1.2
(ii) 8 x 4.6
ANSWER:
We have to find 8 x 4.6
We know,
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
8 x 4.6 = 8 x 46 = 368
Now, there are only 1 decimal point. We give decimal point from rightmost digit and moved towards left.
8 x 4.6 = 36.8
(iii) 2.71 x 5
ANSWER:
We have to find 2.71 x 5
We know,
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
2.71 x 5 = 271 x 5 = 1355
Now, there are 2 decimal point. We give decimal point from rightmost digit and moved towards left.
2.71 x 5 = 13.55
(iv) 20.1 x 4
ANSWER:
We have to find 20.1 x 4
We know,
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
20.1 x 4 = 201 x 4 = 804
Now, there are only 1 decimal point. We give decimal point from rightmost digit and moved towards left.
20.1 x 4 = 80.4
(v) 0.05 x 7
ANSWER:
We have to find 0.05 x 7
We know,
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
0.05 x 7 = 5 x 7 = 35
Now, there are 2 decimal point. We give decimal point from rightmost digit and moved towards left.
0.05 x 7 = 0.35
(vi) 211.02 x 4
ANSWER:
We have to find 211.02 x 4
We know,
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
211.02 x 4 = 21102 x 4 = 84408
Now, there are 2 decimal point. We give decimal point from rightmost digit and moved towards left.
211.02 x 4 = 844.08
(vii) 2 x 0.86
ANSWER:
We have to find 2 x 0.86
We know,
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
2 x 0.86 = 2 x 86 = 172
Now, there are 2 decimal point. We give decimal point from rightmost digit and moved towards left.
2 x 0.86 = 1.72
2.) Find the area of rectangle whose length is 5.7cm and breadth is 3 cm.
ANSWER:
We have to find the area of rectangle whose length is 5.7cm and breadth is 3 cm.
We know,
The area of rectangle = Length x Breadth
The area of rectangle = 5.7cm x 3 cm.
The area of rectangle = 17.1 cm2
3.) Find:
(i) 1.3 x 10
ANSWER:
We have to find 1.3 x 10
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
1.3 x 10 = 1.3 here decimal point is shifted to the right by 1 as zeros over one is 1.
1.3 x 10 = 13
(ii) 36.8 x 10
ANSWER:
We have to find 36.8 x 10
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
36.8 x 10 = 36.8 here decimal point is shifted to the right by 1 as zeros over one is 1.
36.8 x 10 = 368
(iii) 153.7 x 10
ANSWER:
We have to find 153.7 x 10
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
153.7 x 10 =153.7 here decimal point is shifted to the right by 1 as zeros over one is 1.
153.7 x 10 =1537
(iv) 168.07 x 10
ANSWER:
We have to find 168.07 x 10
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
168.07 x 10 =168.07 here decimal point is shifted to the right by 1 as zeros over one is 1.
168.07 x 10 =1680.7
(v) 31.1 x 100
ANSWER:
We have to find 31.1 x 100
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
31.1 x 100 =31.1 here decimal point is shifted to the right by 2 as zeros over one is 2.
31.1 x 100 =3110
(vi) 156.1 x 100
ANSWER:
We have to find 156.1 x 100
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
156.1 x 100 = 156.1 here decimal point is shifted to the right by 2 as zeros over one is 2.
156.1 x 100 = 15610
(vii) 3.62 x 100
ANSWER:
We have to find 3.62 x 100
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
3.62 x 100 =3.62 here decimal point is shifted to the right by 2 as zeros over one is 2.
3.62 x 100 =362
(viii) 43.07 x 100
ANSWER:
We have to find 43.07 x 100
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
43.07 x 100 = 43.07 here decimal point is shifted to the right by 2 as zeros over one is 2.
43.07 x 100 = 4307
(ix) 0.5 x 10
ANSWER:
We have to find 0.5 x 10
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
0.5 x 10 = 0.5 here decimal point is shifted to the right by 1 as zeros over one is 1.
0.5 x 10 = 5
(x) 0.08 x 10
ANSWER:
We have to find 0.08 x 10
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
0.08 x 10 = 0.08 here decimal point is shifted to the right by 1 as zeros over one is 1.
0.08 x 10 = 0.8
(xi) 0.9 x 100
ANSWER:
We have to find 0.9 x 100
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
0.9 x 100 = 0.9 here decimal point is shifted to the right by 2 as zeros over one is 2.
0.9 x 100 = 90
(xii) 0.03 x 1000
ANSWER:
We have to find 0.03 x 1000
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
0.03 x 1000 = 0.03 here decimal point is shifted to the right by 3 as zeros over one is 3.
0.03 x 1000 = 30
4.) A two-wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol?
ANSWER:
Given that,
A two-wheeler covers a distance of 55.3 km in one litre of petrol.
We have to find how much distance it will cover in 10 litres of petrol.
Distance cover in 10 litres of petrol = 55.3 km x 10 litres
We know,
when a decimal number is multiplied by 10, 100 or 1000, the digits in the product are same as in the decimal number but the decimal point in the product is shifted to the right by as, many of places as there are zeros over one.
55.3 km x 10 litres = 55.3 here decimal point is shifted to the right by 1 as zeros over one is 1.
55.3 km x 10 litres = 553 km.
Distance cover in 10 litres of petrol = 553 km.
5.) Find:
(i) 2.5 x 0.3
ANSWER:
We have to find 2.5 x 0.3
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
2.5 x 0.3 = 25 x 3 = 75
There are 2 decimal point.
2.5 x 0.3 = 0.75
(ii) 0.1 x 51.7
ANSWER:
We have to find 0.1 x 51.7
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
0.1 x 51.7 = 1 x 517= 517
There are 2 decimal point.
0.1 x 51.7 = 5.17
(iii) 0.2 x 316.8
ANSWER:
We have to find 0.2 x 316.8
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
0.2 x 316.8 = 2 x 3168 = 6336
There are 2 decimal point.
0.2 x 316.8 = 63.36
(iv) 1.3 x 3.1
ANSWER:
We have to find 1.3 x 3.1
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
1.3 x 3.1 = 13 x 31 = 403
There are 2 decimal point.
1.3 x 3.1 = 4.03
(v) 0.5 x 0.05
ANSWER:
We have to find 0.5 x 0.05
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
0.5 x 0.05 = 5 x 5 = 25
There are 3 decimal point.
0.5 x 0.05 = 0.025
(vi) 11.2 x 0.15
ANSWER:
We have to find 11.2 x 0.15
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
11.2 x 0.15 = 112 x 15= 1680
There are 3 decimal point.
11.2 x 0.15 = 1.680
(vii) 1.07 x 0.02
ANSWER:
We have to find 1.07 x 0.02
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
1.07 x 0.02 = 107 x 2 = 214
There are 4 decimal point.
1.07 x 0.02 = 0.0214
(viii) 10.05 x 1.05
ANSWER:
We have to find 10.05 x 1.05
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
10.05 x 1.05 = 1005 x 105 = 105525
There are 4 decimal point.
10.05 x 1.05 = 10.5525
(ix) 101.01 x 0.01
ANSWER:
We have to find 101.01 x 0.01
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
101.01 x 0.01 = 10101 x 1 = 10101
There are 4 decimal point.
101.01 x 0.01 = 1.0101
(x) 100.01 x 1.1
ANSWER:
We have to find 100.01 x 1.1
First we multiplied them as whole numbers ignoring the decimal point. Then, we counted the number of digits starting from the rightmost digit and moved towards left.
100.01 x 1.1 = 10001 x 11 = 110011
There are 3 decimal point.
100.01 x 1.1 = 110.011
EXERCISE 2.5
1.) Find:
(i) 0.4/2
ANSWER:
Here we have to find 0.4/2
0.4/2 = 0.4 x reciprocal of 2
0.4 = 4/10
0.4/2 = 4/10 x 1/2
0.4/2 = 1/10 x 4/2 = 1/10 x 2
0.4/2 = 0.2
(ii) 0.35/5
ANSWER:
Here we have to find 0.35/5
0.35/5= 0.35 x reciprocal of 5
0.35 = 35/100
0.35/5 = 35/100 x 1/5
0.35/5= 1/100 x 35/5 = 1/100 x 7
0.35/5 = 0.07
(iii) 2.48/4
ANSWER:
Here we have to find 2.48/4
2.48/4 = 2.48 x reciprocal of 4
2.48= 248/100
2.48/4 = 248/100 x 1/4
2.48/4 = 1/100 x 248/4 = 1/100 x 62
2.48/4 = 0.62
(iv) 65.4/6
ANSWER:
Here we have to find 65.4/6
65.4/6 =65.4x reciprocal of 6
65.4= 654/10
65.4/6 = 654/10 x 1/6
65.4/6 = 1/10 x 654/6 = 1/10 x 109
65.4/6 = 10.9
(v) 651.2/4
ANSWER:
Here we have to find 651.2/4
651.2/4 =651.2 x reciprocal of 4
651.2 =6512 /10
651.2/4 = 6512/10 x 1/4
651.2/4 = 1/10 x 6512/4 = 1/10 x 1628
651.2/4 = 162.8
(vi) 14.49/7
ANSWER:
Here we have to find 14.49/7
14.49/7= 14.49 x reciprocal of 7
14.49=1449 /100
14.49/7 = 1449/100 x 1/7
14.49/7 = 1/100 x 1449/7 = 1/100 x 207
14.49/7 = 2.07
(vii) 3.96/4
ANSWER:
Here we have to find 3.96/4
3.96/4 = 3.96 x reciprocal of 4
3.96 = 396 /100
3.96/4 = 396/100 x 1/4
3.96/4 = 1/100 x 396/4 = 1/100 x 99
3.96/4 = 0.99
(viii) 0.8/5
ANSWER:
Here we have to find 0.8/5
0.8/5 =0.8x reciprocal of 5
0.8 = 8 /10
0.8/5= 8 /10 x 1/5
0.8/5 = 1/10 x 8/5 = 1/10 x 1.6
0.8/5= 0.16
2.) Find:
(i) 4.8/10
ANSWER:
We have to find 4.8/10
We know,
When we dividing a number by 10, 100 or 1000, the digits of thenumber and the quotient are same but the decimal point in the quotient shifts to theleft by as many places as there are zeros over 1.
4.8/10 = 4.8 here decimal point shifts to the left by 1 as there are zeros over 1 is 1.
4.8/10 = 0.48
(ii) 52.5/10
ANSWER:
We have to find 52.5/10
We know,
When we dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
52.5/10 =52.5 here decimal point shifts to the left by 1 as there are zeros over 1 is 1.
52.5/10 = 5.25
(iii) 0.7/10
ANSWER:
We have to find 0.7/10
We know,
When we dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
0.7/10 = 0.7 here decimal point shifts to the left by 1 as there are zeros over 1 is 1.
0.7/10 = 0.07
(iv) 33.1/10
ANSWER:
We have to find 33.1/10
We know,
When we dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
33.1/10 = 33.1 here decimal point shifts to the left by 1 as there are zeros over 1 is 1.
33.1/10 = 3.31
(v) 272.23/10
ANSWER:
We have to find 272.23/10
We know,
When we dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
272.23/10 =272.23 here decimal point shifts to the left by 1 as there are zeros over 1 is 1.
272.23/10 = 27.223
(vi) 0.56/10
ANSWER:
We have to find 0.56/10
We know,
When we dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
0.56/10=0.56here decimal point shifts to the left by 1 as there are zeros over 1 is 1.
0.56/10= 0.056
(vii) 3.97/10
ANSWER:
We have to find 3.97/10
We know,
When we dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
3.97/10 =3.97 here decimal point shifts to the left by 1 as there are zeros over 1 is 1.
3.97/10 = 0.397
3.) Find:
(i) 2.7/100
ANSWER:
We have to find 2.7/100
We know,
When we dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
2.7/100 =2.7 here decimal point shifts to the left by 2 as there are zeros over 1 is 2.
2.7/100 = 0.027
(ii) 0.3/100
ANSWER:
We have to find 0.3/100
We know,
When we dividing a number by 10, 100 or 1000, the digits of the number and the quotient are same but the decimal point in the quotient shifts to the left by as many places as there are zeros over 1.
0.3/100 = 0.3 here decimal point shifts to the left by 2 as there are zeros over 1 is 2.
0.3/100 = 0.003