PSEB Class 6 Maths Chapter 5 Fractions Questions and Answers Solution
PSEB Punjab Board Class 6 Maths Textbook Solution Chapter 5 Fractions Exercise Questions and Answers. We have also included some Additional questions, so that students can prepare more strongly.
Exercise 5.1
1.) Write the fraction representing the shaded portion:-
ANSWER:
We have to write the fraction representing the shaded portion
There are total 4 parts out of 1 portion is shaded.
Fraction is 1/4.
ANSWER:
We have to write the fraction representing the shaded portion
There are total 8 parts out of 5 portion is shaded.
Fraction is 5/8.
ANSWER:
We have to write the fraction representing the shaded portion
There are total 9 parts out of 4 portion is shaded.
Fraction is 4/9.
ANSWER:
We have to write the fraction representing the shaded portion
There are total 8 parts out of 5 portion is shaded.
Fraction is 5/8.
ANSWER:
We have to write the fraction representing the shaded portion
There are total 12 parts out of 7 portion is shaded.
Fraction is 7/12.
ANSWER:
We have to write the fraction representing the shaded portion
There are total 3 parts out of 3 portion is shaded.
Fraction is 3/3 = 1.
ANSWER:
We have to write the fraction representing the shaded portion
There are total 5 parts out of 2 portion is shaded.
Fraction is 2/5.
ANSWER:
We have to write the fraction representing the shaded portion
There are total 7 parts out of 4 portion is shaded.
Fraction is 4/7.
2.) Colour the part according to the given fraction:-
ANSWER:
We have to colour 5 parts out of 8 parts.
ANSWER:
We have to colour 3 parts out of 4 parts.
ANSWER:
We have to colour 2 parts out of 6 parts.
ANSWER:
We have to colour 7 parts out of 9 parts.
ANSWER:
We have to colour 11 parts out of 16 parts.
3.) Write the fraction for each of the following:-
(i) Three-Fourth
ANSWER:
We have to write the fraction for Three-Fourth
Three-Fourth = 3/4
(ii) Seven-Tenth
ANSWER:
We have to write the fraction for Seven-Tenth
Seven-Tenth = 7/10
(iii) Quarter
ANSWER:
We have to write the fraction for Quarter
Quarter = 1/4
(iv) Five-Eighth
ANSWER:
We have to write the fraction for Five-Eighth
Five-Eighth = 5/8
(v) Three-Twelvth
ANSWER:
We have to write the fraction for Three-Twelvth
Three-Twelvth = 3/12
4.) Write the fraction for the followings:-
(i) Numerator = 5 denominator = 9
ANSWER:
We have to write the fraction having Numerator = 5 denominator = 9
Fraction is 5/9.
(ii) Numerator = 2 denominator = 11
ANSWER:
We have to write the fraction having Numerator = 2 denominator = 11
Fraction is 2/11.
(iii) Numerator = 6 denominator = 7
ANSWER:
We have to write the fraction having Numerator = 6 denominator = 7
Fraction is 6/7.
5.) Write the numerator and the denominator for the followings:-
(i)2/3
ANSWER:
We have to write the numerator and the denominator of given fraction.
Numerator = 2
Denominator = 3
(ii)1/ 4
ANSWER:
We have to write the numerator and the denominator of given fraction.
Numerator = 1
Denominator = 4
(iii) 5/11
ANSWER:
We have to write the numerator and the denominator of given fraction.
Numerator = 5
Denominator = 11
(iv) 9/13
ANSWER:
We have to write the numerator and the denominator of given fraction.
Numerator = 9
Denominator = 13
(v)17/16
ANSWER:
We have to write the numerator and the denominator of given fraction.
Numerator = 17
Denominator = 16
6.) Express:-
(i) 1 day as a fraction of 1 week.
ANSWER:
We know,
1 week = 7 days.
1 day as a fraction of 1 week = 1/7
(ii) 40 seconds as a fraction of 1 minute.
ANSWER:
We know,
1 minute = 60 seconds
40 seconds as a fraction of 1 minute. = 40 / 60 = 2/3
(iii) 15 hours as a fraction of 1 day.
ANSWER:
We know,
1 day = 24 hours
15 hours as a fraction of 1 day. = 15 / 24 = 5/8
(iv) 2 months as a fraction of 1 year.
ANSWER:
We know,
1 year = 12 months
2 months as a fraction of 1 year. = 2 / 12 = 1/6
(v) 45cm as a fraction of 1 meter.
ANSWER:
We know,
1 meter = 100 cm
45cm as a fraction of 1 meter = 45 / 100 = 9/20
7.) Write the numbers from 1 to 25.
There are total 25 numbers from 1 to 25.
(i) What fraction of them are even numbers?
ANSWER:
Out of Total 25 numbers there are 12 even numbers
Fraction of them are even numbers = 12/25
(ii) What fraction of them are prime numbers?
ANSWER:
Out of Total 25 numbers there are 9prime numbers
Fraction of them are prime numbers = 9 /25
(iii) What fraction of them are multiples of 3?
ANSWER:
Out of Total 25 numbers there are 8 multiples of 3
Fraction of them are multiples of 3 = 8 /25
8.) In class 6th, there are 24 boys and 18 girls. What fraction of total students represent boys and girls.
ANSWER:
Given that,
There are 24 boys and 18 girls
We have to find fraction of total students represent boys and girls.
Total students = 24 boys + 18 girls = 42 students
Fraction of total students represent boys = 24 / 42 = 4/7
Fraction of total students represent girls = 18 / 42 = 3/7
9.) A bag contains 6 red balls and 7 blue balls. What fraction of balls represent red and blue colour?
ANSWER:
Given that,
A bag contains 6 red balls and 7 blue balls
We have to find fraction of balls represent red and blue colour.
Totalballs = 6 red balls + 7 blue balls = 13 balls
Fraction of balls represent red balls = 6/13
Fraction of balls represent blue balls = 7/13
10.) Sidharth has a cake. He cuts it into 10 equal parts. He gave 2 parts to Naman, 3 parts to Nidhi, 1 parts to Seema and the remaining four parts he kept for himself. Find
(i) What fraction of cake, he gave to Naman?
ANSWER:
Given that,
He cuts cake into 10 equal parts.
He gave 2 parts to Naman
Fraction of cake, he gave to Naman = 2/10 = 1/5
(ii) What fraction of cake, he gave to Nidhi?
ANSWER:
Given that,
He cuts cake into 10 equal parts.
He gave 3 parts to Nidhi
Fraction of cake, he gave to Nidhi = 3/10
(iii) What fraction of cake, he kept for himself?
ANSWER:
Given that,
He cuts cake into 10 equal parts.
Four parts he kept for himself
Fraction of cake, he kept for himself = 4/10 = 2/5
(iv) Who has more cake than others?
ANSWER: Sidharthhas more cake than others.
11.) In a box, there are 12 apples, 7 oranges and 5 guavas. What fraction of fruits in box represents each?
ANSWER:
Given that,
Here are 12 apples, 7 oranges and 5 guavas.
We have to find what fraction of fruits in box represents each.
Total fruits = 12 apples + 7 oranges + 5 guavas. = 24
Fraction of apples = 12 / 24 = 1/2
Fraction oforanges = 7/24
Fraction of guavas = 5/24
12.) Dishmeet has 20 pens. He gives one-fourth to Balkirat. How many pens Dishmeet and Balkirat have?
ANSWER:
Given that,
Dishmeet has 20 pens. He gives one-fourth to Balkirat.
We have to find how many pens Dishmeet and Balkirat have.
Pens given to Balkirat = ¼ x 20 = 5
Pens Dishmeet have = 20 – 5 = 15 pens
Pens Balkirat have = 5 pens
13.) Represent the following fraction on the number line?
(i) 2/5
ANSWER:
We have to represent 2/5 on the number line.
(ii) 5/7
ANSWER:
We have to represent 5/7 on the number line.
(iii)3/10,5/10,1/10
ANSWER:
We have to represent 3/10,5/10,1/10 on the number line.
14.) Find:-
(i) 3/5 of 20 books
ANSWER:
3/5 of 20 books = 3/5 x 20 = 12 books
(ii) 5/8 of 32 pens
ANSWER:
5/8 of 32 pens = 5/8 x 32 pens = 20 pens
(iii) 1/6 of 36 Copies
ANSWER:
1/6 of 36 Copies = 1/6 x 36 Copies = 6 Copies
(iv) 4/7 of 21 apples
ANSWER:
4/7 of 21 apples = 4/7 x 21 apples = 12 apples
(v) 3/4 of 28 pencils
ANSWER:
3/4 of 28 pencils = 3/4 x 28 pencils = 21 pencils
15.) Balkirat had a box of 36 erasers. He gave 1/2 of them to Rani, 2/9 of them to Yuvraj and keeps the rest.
(i) How many erasers does Rani get?
ANSWER:
Given that,
Balkirat had a box of 36 erasers.
He gave 1/2 of them to Rani.
Erasers does Rani Get = ½ x 36 = 18erasers.
(ii) How many erasers does Yuvraj get?
ANSWER:
Given that,
Balkirat had a box of 36 erasers.
2/9 of them to Yuvraj
Erasers does Yuvraj get = 2/9 x 36 = 8 erasers.
(iii) How many erasers does Harnik keep?
ANSWER:
Given that,
Balkirat had a box of 36 erasers.
Erasers does Harnik keep = 36 – (Erasers does Rani Get + Erasers does Yuvraj get)
Erasers does Harnik keep = 36 – 26
Erasers does Harnik keep = 10 erasers.
16.) State True/False.
ANSWER:
False.
ANSWER:
True.
ANSWER:
True.
ANSWER:
True.
Exercise 5.2
1.) Classify the following as proper and improper fractions:-
5/4, 9/13, 6/11, 3/2, 5/2, 6/6, 7/9, 2/15, 4/17, 7/8
ANSWER:
We have to classify fractions proper and improper fractions.
We know,
In proper fractions, always numerator is less than denominator.
In improper fractions, always denominator is less than numerator.
Proper fractions = 9/13, 6/11, 7/9, 2/15, 4/17, 7/8
Improper fractions = 5/4, 3/2, 5/2, 6/6
2.) Express each of the following as mixed fractions, Also represent with diagrams.
(i)27 /5
ANSWER:
We have to express 27 /5 as mixed fractions
27 /5 = 5 (2/5)
(ii)13/4
ANSWER:
We have to express13/4 as mixed fractions
13/4 = 3 (1/4)
3.) Express each of the following mixed fractions as improper fractions:-
(i)2(1/3)
ANSWER:
We have to write given mixed fractions as improper fractions.
2(1/3) = 2 x 3 + 1 / 3 = 7/3
(ii) 5(2/7)
ANSWER:
We have to write given mixed fractions as improper fractions.
5(2/7) = 5 x 7 + 2 / 7 = 37/7
(iii) 4(3/5)
ANSWER:
We have to write given mixed fractions as improper fractions.
4(3/5) = 4 x 5 + 3 / 5 = 23/5
(iv) 3(3/4)
ANSWER:
We have to write given mixed fractions as improper fractions.
3(3/4) = 3 x 4 + 3/4 = 15/4
(v)9(5/8)
ANSWER:
We have to write given mixed fractions as improper fractions.
9(5/8) = 9 x 8 + 5 / 8 = 77/8
4.) Express the shaded portion as Improper fraction and Mixed fraction:-
ANSWER:
We have to express the shaded portion as Improper fraction and Mixed fraction
Improper fraction = 7/3
Mixed fraction = 2(1/3)
ANSWER:
We have to express the shaded portion as Improper fraction and Mixed fraction
Improper fraction = 13/4
Mixed fraction = 3(1/4)
ANSWER:
We have to express the shaded portion as Improper fraction and Mixed fraction
Improper fraction = 19/5
Mixed fraction = 3(4/5)
ANSWER:
We have to express the shaded portion as Improper fraction and Mixed fraction
Improper fraction = 21/8
Mixed fraction = 2(5/8)
ANSWER:
We have to express the shaded portion as Improper fraction and Mixed fraction
Improper fraction = 25/6
Mixed fraction = 4(1/6)
Exercise 5.3
1.) Write the fraction for the shaded part and check whether these fractions are equivalent or not?
ANSWER:
We have to write the fraction for the shaded part and check whether these fractions are equivalent or not.
= 1/2 = 2/4 = 3/6 = 4/8 = 1/2
All values of fraction is equal hence these fractions are equivalent.
ANSWER:
We have to write the fraction for the shaded part and check whether these fractions are equivalent or not.
2/3 = 4/6 = 6/9 = 10/15
All values of fraction is equal hence these fractions are equivalent.
ANSWER:
We have to write the fraction for the shaded part and check whether these fractions are equivalent or not.
4/12 = 2/6 = 3/9 = 1/3
All values of fraction is equal hence these fractions are equivalent.
2.) Find four equivalent fractions of the followings:-
(i) 1/4
ANSWER:
Here, we have to write four equivalent fractions of 1/4
Four equivalent fractions of 1/4 = 2/8 = 3/12 = 4/16 = 5/20 = 6/24
(ii) 3/5
ANSWER:
Here, we have to write four equivalent fractions of 3/5
Four equivalent fractions of 3/5 = 6/10 = 9/15 = 12/20 = 15/25
(iii) 7/9
ANSWER:
Here, we have to write four equivalent fractions of 7/9
Four equivalent fractions of 7/9 = 14/18 = 21/27 = 28/36 = 35/45
(iv) 5/11
ANSWER:
Here, we have to write four equivalent fractions of 5/11
Four equivalent fractions of 5/11 = 10/22 = 15/33 = 20/44 = 25/55
(v) 2/3
ANSWER:
Here, we have to write four equivalent fractions of 2/3
Four equivalent fractions of 2/3 = 4/6 = 6/9 = 8/12 = 10/15
3.) Write the lowest equivalent fraction (simplest form) of:-
(i) 10/25
ANSWER:
Here, we have to write 10/25 in simplest form.
we divide both by 5
10/25 = 2/5
(ii) 27/54
ANSWER:
Here, we have to write 27/54 in simplest form.
We divide both by 27
27/54 = 1/2
(iii) 48/72
ANSWER:
Here, we have to write 48/72 in simplest form.
We divide both by 24
48/72= 2/3
(iv) 150/60
ANSWER:
Here, we have to write 150/60 in simplest form.
We divide both by 30
150/60 = 5/2
(v) 162/90
ANSWER:
Here, we have to write 162/90 in simplest form.
We divide both by 18
162/90 = 9/5
4.) Are the following fractions equivalent or not?
(i) 5/12, 25/60
ANSWER:
Here, we have to show fractions are equivalent or not.
5/12 we multiply by 5 to both numerator and denominator
5 x 5 /12 x 5 = 25 / 60
5/12, 25/60 are equivalent
(ii) 6/7, 36/42
ANSWER:
Here, we have to show fractions are equivalent or not.
6/7 we multiply by 6 to both numerator and denominator
6 x 6 /7 x 6 = 36/42
6/7, 36/42 are equivalent
(iii) 7/9, 56/72
ANSWER:
Here, we have to show fractions are equivalent or not.
7/9 we multiply by 8 to both numerator and denominator
7 x 8 /9 x 8 = 56/72
7/9, 56/72 are equivalent
5.) Replace in each of the following by the correct number.
(i) 2/7 = 12/Box
ANSWER:
Here, we have to replace box by the correct number.
2/7 we multiply by 6 to both numerator and denominator
2 x 6 /7 x 6 = 12 / 42
Box = 42
(ii) 5/8 = 35/ Box
ANSWER:
Here, we have to replace box by the correct number.
5/8 we multiply by 7 to both numerator and denominator
5 x 7 /8 x 7 = 35 / 56
Box = 56
(iii) 24/36 = 6/ Box
ANSWER:
Here, we have to replace box by the correct number.
24/36 we divide by 4 to both numerator and denominator
(24/4) /(36 / 4) = 6/9
Box = 9
(iv) 30/48 = Box/ 8
ANSWER:
Here, we have to replace box by the correct number.
30/48 we divide by 6 to both numerator and denominator
(30/6) / (48 / 6) = 5/8
Box = 5
(v) 7/4 = 42/Box
ANSWER:
Here, we have to replace box by the correct number.
7/4 we multiply by 6 to both numerator and denominator
7 x 6 /4 x 6 = 42 / 24
Box = 24
6.) Find the equivalent fraction of 3/5 having
(i) Numerator 18
ANSWER:
Here, we have to write equivalent fraction of 3/5 having Numerator 18.
3/5 we multiply by 6 to both numerator and denominator
3 x 6 /5 x 6 = 18/30
(ii) Denominator 20
ANSWER:
Here, we have to write equivalent fraction of 3/5 having Denominator 20
3/5 we multiply by 4 to both numerator and denominator
3 x 4 /5 x 4 = 12/20
(iii) Numerator 24
ANSWER:
Here, we have to write equivalent fraction of 3/5 having Numerator 24.
3/5 we multiply by 8 to both numerator and denominator
3 x 8 /5 x 8 = 24/40
7.) Find the equivalent fraction of 24/40 having
(i) Numerator 6
ANSWER:
Here, we have to write equivalent fraction of 24/40 having Numerator 6
24/40 we divide by 4 to both numerator and denominator
(24/4) / (40 / 4) = 6/10
(ii) Numerator 48
ANSWER:
Here, we have to write equivalent fraction of 24/40 having Numerator 48
24/40 we multiply by 2 to both numerator and denominator
(24 x 2) / (40 x 2) = 48/ 80
(iii) Denominator 20
ANSWER:
Here, we have to write equivalent fraction of 24/40 having Denominator 20
24/40 we divide by 2 to both numerator and denominator
(24/2) / (40 / 2) = 12/20
Exercise 5.4
1.) Find the different set of like fractions:
3/7, 5/11, 2/7, 6/13, 3/11, 1/11, 2/13, 5/13, 6/7, 10/13
ANSWER:
Here, we have to write different set of like fractions.
3/7, 2/7,6/7
3/11, 5/11, 1/11
2/13, 5/13, 6/13, 10/13
2.) Write any three like fractions of:-
(i) 2/5
ANSWER:
Here, we have to write any three like fractions of 2/5
We know,
Fractions with same denominator is called like fractions.
Like fractions of 2/5 = 1/5, 4/5, 7/5
(ii) 1/4
ANSWER:
Here, we have to write any three like fractions of 1/4
We know,
Fractions with same denominator is called like fractions.
Like fractions of 1/4 = 2/4, 5/4, 7/4
(iii) 11/6
ANSWER:
Here, we have to write any three like fractions of 11/6
We know,
Fractions with same denominator is called like fractions.
Like fractions of 11/6 = 1/6, 3/6, 5/6
3.) Encircle unit fractions:-
6/11, 2/3, 1/8, 15/7, 1/9, 1/7, 3/3
ANSWER:
Here, we have to encircle unit fractions.
6/11, 2/3, 1/8, 15/7, 1/9, 1/7, 3/3
4.) Fill in the boxes with >, < or =
(i) 4/7 Box 6/7
ANSWER:
When denominator is same then numerator of those fraction is larger that fraction is larger.
4/7 < 6/7
(ii) 4/5Box 3/5
ANSWER:
When denominator is same then numerator of those fraction is larger that fraction is larger.
4/5 > 3/5
(iii) 7/8Box 0/8
ANSWER:
When denominator is same then numerator of those fraction is larger that fraction is larger.
7/8 > 0/8
(iv) 5/13Box 7/13
ANSWER:
When denominator is same then numerator of those fraction is larger that fraction is larger.
5/13 < 7/13
5.) Compare using >, < or =
(i) 5/7 Box 5/9
ANSWER:
When Numerator is same, then denominator of those fraction is smaller that fraction is larger.
5/7 > 5/9
(ii) 1/3 Box 1/2
ANSWER:
When Numerator is same, then denominator of those fraction is smaller that fraction is larger.
1/3 < 1/2
(iii) 6/11 Box 6/13
ANSWER:
When Numerator is same, then denominator of those fraction is smaller that fraction is larger.
6/11 > 6/13
(iv) 11/12 Box 11/ 17
ANSWER:
When Numerator is same, then denominator of those fraction is smaller that fraction is larger.
11/12 > 11/ 17
(v) 7/13 Box 7/10
ANSWER:
When Numerator is same, then denominator of those fraction is smaller that fraction is larger.
7/13 < 7/10
6.) Compare using>, <or=
(i) 5/6 Box 2/5
ANSWER:
When numerator and denominator none of them are same, we have to do cross multiplication.
5/6 2/5
5 x 5 6 x 5
25 < 30
5/6 < 2/5
(ii) 3/4 Box 1/3
ANSWER:
When numerator and denominator none of them are same, we have to do cross multiplication.
3/4 1/3
3 x 3 > 4 x 1
9 > 4
3/4 > 1/3
(iii) 3/7 Box 5/9
ANSWER:
When numerator and denominator none of them are same, we have to do cross multiplication.
3/7 5/9
3 x 9 7 x 5
27 < 35
3/7 < 5/9
(iv) 7/10 Box 4/5
ANSWER:
When numerator and denominator none of them are same, we have to do cross multiplication.
7/10 4/5
7 x 5 10 x 4
35 < 40
7/10 < 4/5
(v) 7/7 Box1
ANSWER:
When numerator and denominator none of them are same, we have to do cross multiplication.
We know,
7/7 = 1
1 = 1
7/7 = 1
7.) Arrange the following fractions in ascending order:-
(i) 7/10, 3/10, 5/10
ANSWER:
We have to arrange given fractions in ascending order.
Ascending order of fractions are 3/10, 5/10, 7/10
(ii) 6/7, 1/7, 4/7
ANSWER:
We have to arrange given fractions in ascending order.
Ascending order of fractions are 1/7, 4/7,6/7
(iii) 5/8 7/8, 1/8, 3/8
ANSWER:
We have to arrange given fractions in ascending order.
Ascending order of fractions are 1/8, 3/8,5/8, 7/8
(iv) 5/7, 5/9, 5/3
ANSWER:
We have to arrange given fractions in ascending order.
Ascending order of fractions are 5/9,5/7, 5/3
(v) 3/11, 3/7, 3/13
ANSWER:
We have to arrange given fractions in ascending order.
Ascending order of fractions are 3/13,3/11, 3/7
(vi) 1/4, 1/6, 5/12
ANSWER:
We have to arrange given fractions in ascending order.
Ascending order of fractions are 1/6,1/4,5/12
(vii) 2/7, 11/35, 9/14, 13/28
ANSWER:
We have to arrange given fractions in ascending order.
Ascending order of fractions are 2/7, 11/35,13/28, 9/14
(viii) 1/3, 4/9, 5/12, 4/15
ANSWER:
We have to arrange given fractions in ascending order.
Ascending order of fractions are 4/15, 1/3, 5/12, 4/9
8.) Arrange the following fractions in descending order:-
(i) 5/9, 7/9, 1/9
ANSWER:
We have to arrange given fractions indescending order.
Descending order of fractions are 7/9,5/9, 1/9
(ii) 3/11, 5/11, 2/11, 7/11
ANSWER:
We have to arrange given fractions in descending order.
Descending order of fractions are 7/11,5/11,3/11, 2/11
(iii) 2/7, 2/13, 2/9
ANSWER:
We have to arrange given fractions in descending order.
Descending order of fractions are 2/7, 2/9, 2/13
(iv) 1/5, 1/3, 1/8, 1/2
ANSWER:
We have to arrange given fractions in descending order.
Descending order of fractions are1/2, 1/3, 1/5, 1/8
(v) 1/6, 5/12, 5/18, 2/3
ANSWER:
We have to arrange given fractions in descending order.
Descending order of fractions are 2/3, 5/12, 5/18,1/6
(vi) 3/4, 9/20, 11/15, 17/30
ANSWER:
We have to arrange given fractions in descending order.
Descending order of fractions are3/4, 11/15, 17/30, 9/20
9.) Kasvi covered 1/3 of her journey by car, 1/5 by rickshaw and 2/15 on foot. Find by whichmeans,she covered the major part of her journey.
ANSWER:
Kasvi covered 1/3 of her journey by car, 1/5 by rickshaw and 2/15 on foot.
We have to find by which means, she covered the major part of her journey.
We first find LCM of denominator 3, 5 and 15.
LCM of denominator 3, 5 and 15 is 15.
1/3 of her journey by car = 1 x 5/3 x 5 = 5/15 of her journey by car
1/5 by rickshaw = 1 x 3/5 x 3 = 3/15by rickshaw.
2/15 on foot.
Means, she covered the major part of her journey = 5/15 = journey by car
10.) Father distributed his property among his three sons. The eldest one got 3/10.The middle got 1/6 and the youngest got1/5 part of the property. State how the property was distributedin ascending order.
ANSWER:
Given that,
The eldest one got 3/10. The middle got 1/6 and the youngest got 1/5 part of the property.
We first find LCM of denominator 10, 6 and 5
LCM of denominator 10, 6 and 5 is 30.
The eldest one got 3/10 = 3 x 3 /10 x 3 = 9/30
The middle got 1/6 = 1 x 5 /6 x 5 = 5/30
The youngest got 1/5 = 1 x 6 /5 x 6 = 6/30
The property was distributed in ascending order are 5/30,6/30 and 9/30
The property was distributed in ascending order are middle, younger and eldest
Exercise 5.5
1.) Add the following:-
(i) 3/7 + 2/7
ANSWER:
We know,
When denominator is same, we add only numerator.
3/7 + 2/7 = 5/7
(ii) 2/11 + 4/11
ANSWER:
We know,
When denominator is same, we add only numerator.
2/11 + 4/11 = 6/11
(iii) 6/13 + 5/13
ANSWER:
We know,
When denominator is same, we add only numerator.
6/13 + 5/13 = 11/13
(iv) 5/14 + 9/14 + 3/14
ANSWER:
We know,
When denominator is same, we add only numerator.
5/14 + 9/14 + 3/14 = 17/14
(v) 1/4 + 2/3
ANSWER:
We have to make denominator same.
We take LCM of 3 and 4. 3 x 4 = 12
LCM of 3 and 4 = 12
1 x 3/4 x 3 + 2 x 4/3 x 4 = 3/12 + 8/12
3/12 + 8/12 = 11/12
(vi) 1/6 + 5/12
ANSWER:
We have to make denominator same.
We take LCM of 6 and 12
LCM of 6 and 12 = 12
1 x 2 /6 x 2 + 5/12= 2/12 + 5/12
1/6 + 5/12 = 7/12
(vii) 3/10 + 4/15
ANSWER:
We have to make denominator same.
We take LCM of 10 and 15
LCM of 10 and 15 = 30
3 x 3 /10 x 3 + 4 x 2/15x 2
= 9/30 + 8 / 30
3/10 + 4/15 = 17/30
(viii) 3/8 + 1/4
ANSWER:
We have to make denominator same.
We take LCM of 8 and 4
LCM of 8 and 4 = 8
3/8 + 1 x 2/4 x 2 = 3/8 + 2/8
3/8 + 1/4 = 5/8
(ix) 5/9 + 4
ANSWER:
We have to make denominator same.
We take LCM of 9 and 1
LCM of 9 and 1 = 9
5/9 + 4 x 9 = 5 + 36 /9
5/9 + 4 = 41/9
(x) 4/7 + 2/3 + 5/21
ANSWER:
We have to make denominator same.
We take LCM of 7, 3 and 21
LCM of 7, 3 and 21 = 21
4 x 3 /7 x 3 + 2 x 7 /3 x 7 + 5/21
= 12/21 + 14/21 + 5/21
4/7 + 2/3 + 5/21 = 31/21
(xi) 3/4 + 7/12 + 2/3
ANSWER:
We have to make denominator same.
We take LCM of 4, 12 and 3
LCM of 4, 12 and 3 = 12
3 x 3 /4 x 3 + 7/12 + 2 x 4/3 x 4
= 9/12 + 7/12 + 8/12
= 24/12 = 2
3/4 + 7/12 + 2/3 = 2
(xii) 3/5 + 1/3
ANSWER:
We have to make denominator same.
We take LCM of 5 and 3
LCM of 5 and 3 = 15
3 x 3/5 x 3 + 1 x 5/3 x 5
= 9/15 + 5/15
3/5 + 1/3 = 14/15
2.) Subtract the following:-
(i) 5/9 – 2/9
ANSWER:
We know,
When denominator is same, we subtract only numerator.
5/9 – 2/9 = 3/9 = 1/3
(ii) 6/17 – 3/17
ANSWER:
We know,
When denominator is same, we subtract only numerator.
6/17 – 3/17 = 3/17
(iii) 7/10 – 3/10
ANSWER:
We know,
When denominator is same, we subtract only numerator.
7/10 – 3/10 = 4/10 = 2/5
(iv) 11/13 – 6/13 – 2/13
ANSWER:
We know,
When denominator is same, we subtract only numerator.
11/13 + (– 6/13 – 2/13)
11/13 – 8/13
11/13 – 6/13 – 2/13 = 3/13
(v) 5/12 – 1/4
ANSWER:
We have to make denominator same.
We take LCM of 12 and 4
LCM of 12 and 4 = 12
5/12 – 1 x 3 /4 x 3 = 5/12 – 3/12
5/12 – 1/4 = 2/12 = 1/6
(vi) 3/5 – 2/10
ANSWER:
We have to make denominator same.
We take LCM of 5 and 10
LCM of 5 and 10 = 10
3 x 2 /5 x 2 – 2/10
= 6/10 – 2/10
3/5 – 2/10 = 4/10 = 2/5
(vii) 6/7 – 2/3
ANSWER:
We have to make denominator same.
We take LCM of 7 and 3
LCM of 7 and 3 = 21
6 x 3 /7 x 3 – 2 x 7 /3 x 7
= 18/21 – 14/21
6/7 – 2/3 = 4/21
(viii) 5/6 – 1/4
ANSWER:
We have to make denominator same.
We take LCM of 6 and 4
LCM of 6 and 4 = 12
5 x 2/6 x 2 – 1 x 3/4 x 3
= 10/12 – 3/12
5/6 – 1/4 = 7/12
(ix) 8/3 – 5/9
ANSWER:
We have to make denominator same.
We take LCM of 3 and 9
LCM of 3 and 9= 9
8 x 3/3 x 3 – 5/9 = 24/9 – 5/9
8/3 – 5/9 = 19/9
3.) Simplify the following:-
(i) 4 (2/5) + 2 (1/5)
ANSWER:
We are adding full number separate and fractions separate.
4 2/5 + 2 1/5 = (4 + 2) + (2/5 + 1/5)
(4 + 2) + (2/5 + 1/5) = 6 + 3/5
4 (2/5) + 2 (1/5) = 6 (3/5)
(ii) 5 (3/4) + 2 (1/6)
ANSWER:
We are adding full number separate and fractions separate.
5 (3/4) + 2 (1/6) =
7 + (3/4 + 1/6)
We have to make denominator same.
We take LCM of 4 and 6
LCM of 4 and 6 = 12
7 + (3 x 3/4 x 3 + 1 x 2/6 x 2)
7 + (9/12 + 2/12)
5 (3/4) + 2 (1/6) = 7 (11/12)
(i) 6 (1/2) + 2 (2/3)
ANSWER:
We are adding full number separate and fractions separate.
6 (1/2) + 2 (2/3) =
8 + (1/2 + 2/3)
We have to make denominator same.
We take LCM of 2 and 3
LCM of 2 and 3 = 6
8 + (1 x 3 /2 x 3 + 2 x 2/3 x 2)
8 + (3/6 + 4/6)
6 (1/2) + 2 (2/3) = 9 (1/6)
(iv) 4(3/4) – 1 (5/6)
ANSWER:
We are adding full number separate and fractions separate.
4 (3/4) – 1 (5/6) =
3 + (3/4 – 5/6)
We have to make denominator same.
We take LCM of 4 and 6
LCM of 4 and 6 = 12
3 + (3 x 3/4 x 3 – 5 x 2/6 x 2)
3 (9/12 -10/12)
3 – (1/12)
4 (3/4) – 1 (5/6) = 2 (11/12)
(v) 2 (7/10) – 1 (2/15)
ANSWER:
We are adding full number separate and fractions separate.
2 (7/10) – 1 (2/15) =
1 – (7/10 – 2/15)
We have to make denominator same.
We take LCM of 10 and 15
LCM of 10 and 15 = 30
1 + (7 x 3/10 x 3 – 2 x 2/15 x 2)
1+ (21/30 – 4/30)
2 (7/10) – 1 (2/15) = 1 (17/30)
(vi) 5 – 3 (1/2)
ANSWER:
We are adding full number separate and fractions separate.
5 – 3 (1/2) = 1(1/2)
(vii) 7 + 7/4 + 5 (1/6)
ANSWER:
We are adding full number separate and fractions separate.
7 + 7/4 + 5 (1/6)
12 + (7/4 + 1/6)
We have to make denominator same.
We take LCM of 4 and 6
LCM of 4 and 6 = 12
12 + (7 x 3/4 x 3 + 1 x 2/6 x 2)
12 + (21/12 + 2/12)
12 + (23/12)
7 + 7/4 + 5 (1/6) = 13 (11/12)
(vii) 2 (1/8) + 1 (1/2) – 7/16
ANSWER:
We are adding full number separate and fractions separate.
2 (1/8) + 1 (1/2) – 7/16
= (3-7) + (1/8 + 1/2 – 7/16)
-4 + (1/8 + 1/2 – 7/16)
We have to make denominator same.
We take LCM of 8,2 and 16
LCM of8, 2 and 16 = 16
-4 + (1 x 2/8 x 2 + 1 x 8 /2 x 8 – 7/16)
-4 + (2/16 + 8/16 – 7/16)
-4 + (3/16)
2 (1/8) + 1 (1/2) – 7/16 = 3(3/16)
4.) An iron pipe of length 6 2/3 metres long was cut into two pieces. One piece is 4 (3/7) metre long. What is the length of other piece?
ANSWER:
Given that,
An iron pipe of length 6 (2/3) metres long was cut into two pieces.
One piece is 4 (3/7) metre long.
We have to find the length of other piece
The length of other piece = 6 (2/3) metres – 4 (3/7) metre
The length of other piece = (6-4) (2/3 – 3/7)
We have to make denominator same.
We take LCM of 3 and 7
LCM of 3 and 7 = 21
= 2 (2 x 7 /3 x 7 – 3 x 3 /7 x 3)
= 2 (14/21 – 9/21)
The length of other piece = 2 (5/21) metre
5.) Ashok bought 7/10 kg of mangoes and Tarun 11/15 kg of apples. How much fruit did he buy in all?
ANSWER:
Given that,
Ashok bought 7/10 kg of mangoes and Tarun 11/15 kg of apples.
We have to findhow much fruit he bought in all.
Fruit he bought in all = 7/10 kg of mangoes + 11/15 kg of apples.
We have to make denominator same.
We take LCM of 10 and 15
LCM of 10 and 15 = 30
Fruit he bought in all = (7 x 3 /10 x 3 kg of mangoes + 11 x 2/15 x 2 kg of apples)
Fruit he bought in all = (21/30 + 22/30)
Fruit he bought in all = 43/30 = 1 (13/30) kg.
6.) Avi did 3/5 of his homework on Saturday and 1/10 of the same homework on Sunday. How much of the homework did he do over the weekend?
ANSWER:
Given that,
Avi did 3/5 of his homework on Saturday and 1/10 of the same homework on Sunday.
We have to find how much of the homework did he do over the weekend.
Homework did he do over the weekend = 3/5 + 1/10
We have to make denominator same.
We take LCM of 5 and 10
LCM of 5 and 10 = 10
Homework did he do over the weekend = 3 x 2/5 x 2 + 1/10
Homework did he do over the weekend = 6/10 + 1/10
Homework did he do over the weekend = 7/10
7.) Charan spent 1/4 of his pocket money on a movie and 3/8 on a new pen and 1/8 on a pencil. What fraction of his pocket money did he spend?
ANSWER:
Given that,
Charan spent 1/4 of his pocket money on a movie and 3/8 on a new pen and 1/8 on a pencil.
We have to find what fraction of his pocket money he spent
Fraction of his pocket money he spent = 1/4 + 3/8 + 1/8
We have to make denominator same.
We take LCM of 4 and 8
LCM of 4 and 8 = 8
Fraction of his pocket money he spent = 1 x 2 /4 x 2 + 3/8 + 1/8
Fraction of his pocket money he spent = 2/8 + 3/8 + 1/8
Fraction of his pocket money he spent = 6/8 = 3/4
8.) Simar lives at a distance of 4km from the school. Prabhjot lives at a distance of 2/3 less than simar’s distance from the school. How far does prabhjot live from the school?
ANSWER:
Given that,
Simar lives at a distance of 4km from the school. Prabhjot lives at a distance of 2/3 km less than simar’s distance from the school.
We have to find how far prabhjot lives from the school.
Prabhjot lives from the school. = 4km – 2/3 km
We have to make denominator same.
We take LCM of 1 and 3
LCM of 1 and 3= 3
Prabhjot lives from the school. = 4 x 3 km – 2/3 km
Prabhjot lives from the school. = 12/3 – 2/3
Prabhjot lives from the school. = 10/3 = 3 (1/3) km
Exercise 5.6
1.) Multiply:-
(i) 1/5 x 4
ANSWER:
We have to multiply 1/5 x 4
We directly do multiplication of numerator with numerator and denominator withdenominator.
1/5 x 4/1 = 4/5
(ii) 2/7 x 3
ANSWER:
We have to multiply 2/7 x 3
We directly do multiplication of numerator with numerator and denominator with denominator.
2/7 x 3/1 = 6/7
(iii) 5/8 x 2
ANSWER:
We have to multiply 5/8 x 2
We directly do multiplication of numerator with numerator and denominator with denominator.
5/8 x 2/1 = 10 /8
10 /8 = 5/4
5/8 x 2 = 5/4
(iv) 7/12 x 4
ANSWER:
We have to multiply 7/12 x 4
We directly do multiplication of numerator with numerator and denominator with denominator.
7/12 x 4/1 = 28/12
28/12 = 7/3
7/12 x 4 = 7/3
(v) 10 x 4/5
ANSWER:
We have to multiply 10 x 4/5
We directly do multiplication of numerator with numerator and denominator with denominator.
10/1 x 4/5 = 40 / 5 = 8
10 x 4/5 = 8
2.) Divide:-
(i) (1/4) / 5
ANSWER:
Here we have to divide 1/4 / 5
1/4 / 5 = 1/4 x 1/ 5
Now,
We have to multiply 1/4 x 1/ 5
We directly do multiplication of numerator with numerator and denominator with denominator.
1/4 x 1/ 5 = 1 / 20
(1/4) / 5 = 1 / 20
(ii) (3/5) / 3
ANSWER:
Here we have to divide (3/5) / 3
(3/5) / 3 = (3/5) x 1 / 3
Now,
We have to multiply 3/5 x 1 / 3
We directly do multiplication of numerator with numerator and denominator with denominator.
3/5 x 1 / 3= 3 / 15 = 1/5
(3/5) / 3 = 1/5
(iii) (5/8) / 3
ANSWER:
Here we have to divide (5/8) / 3
(5/8) / 3 = (5/8) x 1 / 3
Now,
We have to multiply 5/8 x 1 / 3
We directly do multiplication of numerator with numerator and denominator with denominator.
5/8 x 1 / 3 = 5 / 24
(5/8) / 3 = 5 / 24
(iv) (6/7) / 2
ANSWER:
Here we have to divide (6/7) / 2
(6/7) / 2 = (6/7) x 1 / 2
Now,
We have to multiply 6 / 7 x 1 / 2
We directly do multiplication of numerator with numerator and denominator with denominator.
6 / 7 x 1 / 2 = 6 / 14 = 3/7
(6/7) / 2 = 3 / 7
(v) (12/15) / 6
ANSWER:
Here we have to divide (12/15) / 6
(12/15) / 6= (12/15) x 1 / 6
Now,
We have to multiply 12/15 x 1 / 6
We directly do multiplication of numerator with numerator and denominator with denominator.
12/15 x 1 / 6 = 12 / 90 = 2/15
(12/15) / 6 = 2/15
Multiple Choice Questions
1.) Which of the following does not represent any fraction?
ANSWER:
2.) Which of the following is a proper fraction?
(a) 5/5
(b) 12/11
(c) 7/9
(d) 7
ANSWER: (c) 7/9
3.) Which of the following is a mixed fraction?
(a) 5/8
(b) 2 (3/4)
(c) 7/11
(d) 15/16
ANSWER:(b) 2 (3/4)
4.) The fractions having 1 as numerator are called fractions.
(a) Like
(b) Unlike
(c) Unit
(d) Proper
ANSWER:(c) Unit
5.) The fractions having same denominators are called fractions.
(a) Proper
(b) Unit
(c) Improper
(d) Like
ANSWER:(d) Like
6.) The fraction having different denominators are called fractions.
(a) Unlike
(b) Like
(c) Improper
(d) Unit
ANSWER:(a) Unlike
7.) Express 8 hours as a fraction of 1 day.
(a) 2/3
(b) 1/3
(c) 8/1
(d) 1/8
ANSWER:(b) 1/3
8.) Find: 2/5 of 20
(a) ₹8
(b) ₹10
(c) ₹12
(d)₹40
ANSWER:(a) ₹8
9.) Write 19/4 as mixed fraction
(a) 3 4/5
(b) 4 4/3
(c) 4 3/4
(d) 5 ¼
ANSWER:(c) 4 3/4
10.) 7 2/3 =
(a) 17/3
(b) 23/3
(c) 13/3
(d) 42/3
ANSWER:(b) 23/3
11.) Which of the following diagram represents an improper fraction?
ANSWER:
12.) Which of the following fraction is an equivalent of 5/7
(a) 25/49
(b) 20/35
(c) 35/49
(d) 35/28
ANSWER:(c) 35/49
13.) Replace by the correct number in 5/8 = 20/ Box
(a) 32
(b) 24
(c) 40
(d) 16
ANSWER:(a) 32
14.) Which of the following are in ascending order?
(a) 2/3, 2/7, 2/5
(b) 2/3, 2/5, 2/7
(c) 2/7, 2/3, 2/5
(d) 2/7, 2/5, 2/3
ANSWER:(d) 2/7, 2/5, 2/3
15.) Which of the following are in descending order?
(a) 1/8, 1/3, 1/9
(b) 1/3, 1/8, 1/9
(c) 1/8, 1/9, 1/3
(d) 1/3, 1/9, 1/8
ANSWER:(b) 1/3, 1/8, 1/9
16.) 4/6 + 3/6 =
(a) 7/12
(b) 7/8
(c) 1 1/6
(d) 1 1/12
ANSWER:(c) 1 1/6
17.) 4/9 + 5/9 – 2/9 = …………….
(a) 7/9
(b) 7/18
(c) 11/9
(d) 5/9
ANSWER:(a) 7/9
18.) 2/3 + 1/6 =
(a) 3/9
(b) 5/6
(c) 7/6
(d) 5/9
ANSWER:(b) 5/6
19.) 4 – 1/3 =…………….
(a) 4 1/3
(b) 3 1/3
(c) 4 2/3
(d) 3 2/3
ANSWER:(d) 3 2/3
20.) Divide 1/6 by 2
(a) 1/3
(b) 1/12
(c) 1/18
(d) 12
ANSWER:(b) 1/12
Do you have solved: Your problem in Chapter 4? Here link