Class 6 - Maths - Fractions

**Exercise 7.1**

**Question 1:**

Write the fraction representing the shaded portion:

Answer:

(i) The given figure represents 2 shaded parts out of 4 equal parts.

So, the fraction = 2/4

(ii) The given figure represents 8 shaded parts out of 9 equal parts.

So, the fraction = 8/9

(iii) The given figure represents 4 shaded parts out of 8 equal parts.

So, the fraction = 4/8

(iv) The given figure represents 1 shaded part out of 4 equal parts.

So, the fraction = 1/4

(v) The given figure represents 3 shaded parts out of 7 equal parts.

So, the fraction = 3/7

(vi) The given figure represents 3 shaded parts out of 12 equal parts.

So, the fraction = 3/12

(vii) The given figure represents 10 shaded parts out of 10 equal parts.

So, the fraction = 10/10

(viii) The given figure represents 4 shaded parts out of 9 equal parts.

So, the fraction = 4/9

(ix) The given figure represents 4 shaded parts out of 8 equal parts.

So, the fraction = 4/8

(x) The given figure represents 1 shaded part out of 2 equal parts.

So, the fraction = 1/2

**Question 2:**

Colour the part according to the given fraction:

Answer:

(i) 1/6 means we have to colour one part out of 6 parts in the given figure.

(ii) 1/4 means we have to colour one part out of 4 parts in the given figure.

(iii) 1/3 means we have to colour one part out of 3 parts in the given figure.

(iv) 3/4 means we have to colour three parts out of 4 parts in the given figure.

(v) 4/9 means we have to colour four parts out of 9 parts in the given figure.

**Question 3:**

Identify the error, if any?

Answer:

All the figures are not equally divided. For making fractions, it is necessary that figure is to be

divided in equal parts.

**Question 4:**

What fraction of a day is 8 hours?

Answer:

We know that 1 day = 24 hours.

Therefore, the fraction of 8 hours = 8/24 = 1/3

Question 5:

What fraction of an hour is 40 minutes?

Answer:

Since 1 hour = 60 minutes.

Therefore, the fraction of 40 minutes = 40/60 = 2/3

**Question 6:**

Arya, Abhimanyu and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam.

The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.

(a) How can Arya divide his sandwiches so that each person has an equal share?

(b) What part of a sandwich will each boy receive?

Answer:

(a) Arya will divide each sandwich into three equal parts and give one part of each sandwich to

each one of them.

(b) The part of a sandwich each boy will receive = 1 * (1/3) = 1/3

**Question 7:**

Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

Answer:

Total number of dresses = 30

Work finished = 20

Fraction of finished work = 20/30 = 2/3

**Question 8:**

Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

Answer:

Natural numbers from 2 to 12: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Prime numbers from 2 to 12: 2, 3, 5, 7, 11

Hence, the fraction of prime numbers = 5/11

**Question 9:**

Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

Answer:

Natural numbers from 102 to 113:

102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113

Prime numbers from 102 to 113:

103, 107, 109, 113

Hence fraction of prime numbers = 4/12 = 1/3

**Question 10:**

What fractions of these circles have ‘X’s in them?

Answer:

Total number of circles = 8 and number of circles having ‘X’ = 4 . Hence, the fraction = 4/8

**Question 11:**

Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy

and what fraction did she receive as gifts?

Answer:

Total number of CDs = 3 + 5 = 8

Number of CDs purchased = 3

Fraction of CDs purchased = 3/8

Fraction of CDs received as gifts = 5/8

**Exercise 7.2**

**Question 1:**

Draw number lines and locate the points on them:

(a) 1/2, 1/4, 3/4, 4/4

(b) 1/8, 2/8, 3/8, 7/8

(c) 2/5, 3/5, 8/5, 4/5

Answer:

(a)

(b)

(c)

**Question 2:**

Express the following fractions as mixed fractions:

(a) 20/3 (b) 11/5 (c) 17/7 (d) 28/5 (e) 19/6 (f) 35/9

Answer: (a)

So, 20/3 = 6

(b)

So, 11/5 = 2

(c)

So, 17/7 = 2

(d)

So, 28/5 = 5

(e)

So, 19/6 = 3

(f)

So, 35/9 = 9

**Question 3:**

Express the following fractions as improper fractions:

(a) 7¾ (b) 5 (c) 2 (d) 10 (e) 9 (f) 8

Answer:

(a) 7¾ = 7 + 3/4 = {(7 * 4) + 3}/4 = (28 + 3)/4 = 31/4

(b) 5 = 5 + 6/7 = {(5 * 7) + 6}/7 = (35 + 6)/7 = 41/7

(c) 2 = 2 + 5/6 = {(2 * 6) + 5}/6 = (12 + 5)/6 = 17/6

(d) 10 = 10 + 3/5 = {(10 * 5) + 3}/5 = (50 + 3)/5 = 53/5

(e) 9 = 9 + 3/7 = {(9 * 7) + 3}/7 = (63 + 3)/7 = 66/7

(f) 8 = 8 + 4/9 = {(8 * 9) + 4}/9 = (72 + 4)/9 = 76/9

**Exercise 7.3**

**Question 1:**

Write the fractions. Are all these fractions equivalent:

Answer:

(a) 1/2 , 2/4, 3/6, 4/8

Again, 1/2 = 2/4 = 3/6 = 4/8

Yes, all of these fractions are equivalent.

(b) 4/12, 3/9, 2/6, 1/3, 6/15

Now, 4/12 = 1/3, 3/9 = 1/3, 2/9 = 1/3, 6/15 = 2/5

So, these fractions are not equivalent.

**Question 2:**

Write the fraction and pair up the equivalent fractions to each row:

Answer:

(a) 1/2 (ii) 4/8 = 1/2

(b) 4/6 = 2/3 (iv) 8/12 = 2/3

(c) 3/9 = 1/3 (i) 6/18 = 1/3

(d) 2/8 = 1/4 (v) 4/16 = 1/4

(e) 3/4 (iii) 12/16 = 3/4

**Question 3:**

Replace in each of the following by the correct number:

(a) 2/7 = 8/ (b) 5/8 = 10/ (c) 3/5 = /20

(d) 45/60 = 15/ (e) 18/24 = /4

Answer:

(a) 2/7 = (2*4)/(7*4) = 8/ (b) 5/8 = (5*2)/(8*2)= 10/

(c) 3/5 = (3*4)/(5*4) = /20

(d) 45/60 = (45/3)/(60/3) = 15/ (e) 18/24 = (18/6)/(24/6) = /4

**Question 4:**

Find the equivalent fraction of 3/5 having:

(a) denominator 20 (b) numerator 9 (c) denominator 30 (d) numerator 27

Answer:

(a) 3/5 = (3*4)/(5*4) = 12/20 (b) 3/5 = (3*3)/(5*3) = 9/15

(a) 3/5 = (3*6)/(5*6) = 18/30 (a) 3/5 = (3*9)/(5*9) = 27/45

**Question 5:**

Find the equivalent fraction of 36/48 with:

(a) numerator 9 (b) denominator 4

Answer:

(a) 36/48 = (36/4)/(48/4) = 9/12

(b) 36/48 = (36/12)/(48/12) = 3/4

**Question 6:**

Check whether the given fractions are equivalent:

(a) 5/9, 30/54 (b) 3/10, 12/50 (c) 7/13, 5/11

Answer:

(a) 5/9, 30/54 = (5*6)/(9*6), 30/54 = 30/54, 30/54

So, 5/9, 30/54 are equivalent fractions.

(b) 3/10, 12/50 = (3*5)/(10*5), 12/50 = 15/50, 12/50

So, 3/10, 12/50 are not equivalent fractions.

(a) 7/13, 5/11 = (7*11)/(13*11), (5*13)/(11*13) = 77/143, 65/143

So, 7/13, 5/11 are not equivalent fractions.

**Question 7:**

Reduce the following fractions to simplest form:

(a) 48/60 (b) 150/60 (c) 84/98 (d) 12/52 (e) 7/28

Answer:

(a) 48/60 = 4/5 {48 and 60 are divided by 12}

(b) 150/60 = 5/2 {150 and 60 are divided by 30}

(c) 84/98 = 6/7 {84 and 98 are divided by 14}

(d) 12/52 = 3/13 {12 and 52 are divided by 4}

(e) 7/28 = 1/4 {7 and 28 are divided by 7}

**Question 8:**

Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months,

Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils.

What fraction did each use up? Check is each has used up an equal fraction of her/his

pencils?

Answer:

Ramesh: Sheelu:

Total pencils = 20 Total pencils = 50

Used pencils = 10 Used pencils = 25

Fraction = 10/20 = 1/2 Fraction = 50/25 = 1/2

Jamaal:

Total pencils = 80

Used pencils = 40

Fraction = 40/80 = 1/2

Since, all of them used half of their pencils, therefore each one used up equal fraction of pencils.

**Question 9:**

Match the equivalent fractions and write two more for each:

(i) 250/400 (a) 2/3

(ii) 180/200 (b) 2/5

(iii) 660/990 (c) 1/2

(iv) 180/360 (d) 5/8

(v) 220/550 (e) 9/10

Answer:

(a) 250/400 = 25/40 {250 and 400 are divided by 10}

= 5/8 {25 and 40 are divided by 5}

So, (a) 250/400 = (d) 5/8

(b) 180/200 = 18/20 {180 and 200 are divided by 10}

= 9/10 {18 and 20 are divided by 2}

So, (b) 180/200 = (e) 9/10

(c) 660/990 = 66/99 {660 and 990 are divided by 10}

= 6/9 {66 and 99 are divided by 11}

= 2/3 {6 and 9 are divided by 3}

So, (a) 660/990 = (a) 2/3

(d) 180/360 = 18/36 {180 and 360 are divided by 10}

= 1/2 {18 and 36 are divided by 18}

So, (d) 180/360 = (c) 1/2

(e) 220/550 = 22/55 {220 and 550 are divided by 10}

= 2/5 {22 and 55 are divided by 11}

So, (e) 220/550 = (b) 2/5

**Exercise 7.4**

**Question 1:**

Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘<’, ‘>’, ‘=’ between the fractions:

(c) Show 2/6, 4/6, 8/6 and 6/6 on the number line. Put appropriate signs between the fractions given:

5/6 2/6, 3/6 0, 1/6 6/6, 8/6 5/6

Answer:

(a) 3/8, 6/8, 4/8, 1/8

Ascending order: 1/8 < 3/8 < 4/8 < 6/8

Descending order: 6/8 > 4/8 > 3/8 > 1/8

(b) 8/9, 4/9, 3/9, 6/9

Ascending order: 3/9 < 4/9 < 6/9 < 8/9

Descending order: 8/9 > 6/9 > 4/9 > 3/9

(c) Number line is:

5/6 2/6, 1/6 6/6, 3/6 0/6, 8/6 5/6

**Question 2:**

Compare the fractions and put an appropriate sign:

(a) 3/6 5/6 (b) 1/7 1/4 (c) 4/5 5/5 (d) 3/5 3/7

Answer:

(a) 3/6 5/6

(b) 1/7 1/4

(c) 4/5 5/5

(d) 3/5 3/7

**Question 3:**

Make five more each pairs and put appropriate signs.

Answer:

(a) 9/10 6/10

(b) 1/3 1/6

(c) 1/8 1/5

(d) 7/8 11/8

(e) 11/13 9/13

**Question 4:**

Look at the figures and write ‘<’ or ‘>’ between the given pairs of fractions:

(a) 1/6 1/3 (b) 3/4 2/6 (c) 2/3 2/4 (d) 6/6 3/3 (d) 5/6 5/5

Answer:

(a) 1/6 1/3 (b) 3/4 2/6 (c) 2/3 2/4 (d) 6/6 3/3 (e) 5/6 5/5

Five such more problems are:

(a) 1/2 3/6 (b) 2/3 3/5 (c) 3/4 4/6 (d) 5/6 2/2 (e) 0/1 0/6

Answer:

(a) 1/2 3/6 (b) 2/3 3/5 (c) 3/4 4/6 (d) 5/6 2/2 (e) 0/1 0/6

**Question 5:**

How quickly can you do this? Fill appropriate sign (<, =, >):

(a) 1/2 1/5 (b) 2/4 3/6 (c) 3/5 2/3 (d) 3/4 2/8 (e) 3/5 6/5

(f) 7/9 3/9 (g) 1/4 2/8 (h) 6/10 4/5 (i) 3/4 7/8 (j) 6/10 4/5

(k) 5/7 15/21

Answer:

(a) 1/2 1/5 (b) 2/4 3/6 (c) 3/5 2/3 (d) 3/4 2/8 (e) 3/5 6/5

(f) 7/9 3/9 (g) 1/4 2/8 (h) 6/10 4/5 (i) 3/4 7/8

(j) 6/10 4/5 (k) 5/7 15/21

**Question 6:**

The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form:

(a) 2/12 (b) 3/15 (c) 8/50 (d) 16/100 (e) 10/60 (f) 15/75

(g) 12/60 (h) 16/96 (i) 12/75 (j) 12/72 (k) 3/18 (l) 4/25

Answer:

(a) 2/12 = 1/6 {2 and 12 are divided by 2}

(b) 3/15 = 1/5 {3 and 15 are divided by 3}

(c) 8/50 = 4/25 {8 and 50 are divided by 2}

(d) 16/100 = 4/25 {16 and 100 are divided by 4}

(e) 10/60 = 1/6 {10 and 60 are divided by 10}

(f) 15/75 = 1/5 {15 and 75 are divided by 15}

(g) 12/60 = 1/5 {12 and 60 are divided by 12}

(h) 16/96 = 1/6 {16 and 96 are divided by 16}

(i) 12/75 = 4/25 {12 and 75 are divided by 3}

(j) 12/72 = 1/6 {12 and 72 are divided by 12}

(k) 3/18 = 1/6 {3 and 18 are divided by 3}

(l) 4/25 = 4/25 {It is already is in simplest form}

Now equivalent groups are:

I group: 1/5 {b, f, g}

II group: 1/6 {a, e, h, j, k}

III group: 4/25 {c, d, i, l}

**Question 7:**

Find answers to the following. Write and indicate how you solved them:

(a) Is 5/9 equal to 4/5 ? (b) Is 9/16 equal to 5/9 ?

(c) Is 4/5 equal to 16/20 ? (d) Is 1/15 equal to 4/30 ?

Answer:

(a) 5/9, 4/5

= {(5 * 5)/(45), (4 * 9)/(45)} {LCM(9, 5) = 45}

= 25/45, 36/45

Since, 25/45 ≠ 36/45

So, 5/9 ≠ 4/5

(b) 9/16, 5/9

= {(9 * 9)/(144), (5 * 16)/(144)} {LCM(16, 9) = 144}

= 81/144, 80/144

Since, 81/144 ≠ 80/144

So, 9/16 ≠ 5/9

(c) 4/5, 16/20

16/20 = 4/5 {16 and 20 are divided by 4}

So, 4/5 = 16/20

(d) 1/15 and 4/30

Now, 1/15 = (1*2)/(15*2) = 2/30

Since 2/30 ≠ 4/30

So, 1/15 ≠ 4/30

**Question 8:**

Ila read 25 pages of a book containing 100 pages. Lalita read 2/5 of the same book. Who read less?

Answer:

Illa read 25 pages out of 100 pages.

Fraction of reading the pages = 25/100 = 1/4^{th} part of the book.

Lalita read 2/5^{th} part of the book = 40/100 pages.

Since 1/4 < 2/5

Therefore, Illa read less.

**Question 9:**

Rafiq exercised for 3/6 of an hour, while Rohit exercised for 3/4 of an hour. Who exercised for a longer time?

Answer:

Rafiq exercised 3/6 of an hour.

Rohit exercised 3/4 of an hour.

Since, 3/4 > 3/6

Therefore, Rohit exercised for a longer time.

**Question 10:**

In a class A of 25 students, 20 passed in first class; in another class B of 30 students, 24 passed in first class.

In which class was a greater fraction of students getting first class?

Answer:

In class A, 20 passed out 25, i.e. 20/24 = 4/5

In class B, 24 passed out 30, i.e. 24/30 = 4/5

Hence, each class have same fraction of student getting first class.

**Exercise 7.5**

**Question 1:**

Write the fractions appropriately as additions or subtractions:

Answer:

(a) 1/5 + 2/5 = (1 + 2)/5 = 3/5

(b) 5/5 – 3/5 = (5 - 3)/5 = 2/5

(c) 2/6 + 3/6 = (2 + 3)/6 = 5/6

**Question 2:**

Solve:

(a) 1/18 + 1/18 (b) 8/15 + 3/15 (c) 7/7 – 5/7 (d) 1/22 + 21/22 (e) 12/15 – 7/15

(f) 5/8 + 3/8 (g) 1 – 2/3 (1 = 3/3) (h) 1/4 + 0/4 (i) 3 – 12/5

Answer:

(a) 1/18 + 1/18 = (1 + 1)/18 = 2/18 = 1/9

(b) 8/15 + 3/15 = (8 + 3)/15 = 11/15

(c) 7/7 – 5/7 = (7 - 5)/7 = 2/7

(d) 1/22 + 21/22 = (1 + 21)/22 = 22/22 = 1

(e) 12/15 – 7/15 = (12 - 7)/15 = 5/15 = 1/3

(f) 5/8 + 3/8 = (5 + 3)/8 = 8/8 = 1

(g) 1 – 2/3 (1 = 3/3) = 3/3 – 2/3 = (3 - 2)/3 = 1/3

(h) 1/4 + 0/4 = (1 + 0)/4 = 1/4

(i) 3 – 12/5 = (3*5)/5 – 12/5 = 15/5 – 12/5 = (15 - 12)/5 = 3/5

**Question 3:**

Shubham painted 2/3 of the wall space in his room. His sister Madhavi helped and painted 1/3 of the wall space. How much did they paint together?

Answer:

Fraction of wall painted by Shubham = 2/3

Fraction of wall painted by Madhavi = 1/3

Total painting by both of them = 2/3 + 1/3 = (2 + 1)/3 = 3/3 = 1

Therefore, they painted complete wall.

**Question 4:**

Fill in the missing fractions:

(a) 7/10 - = 3/10 (b) - 3/21 = 5/21

(c) - 3/6 = 3/6 (d) + 5/27 = 12/27

Answer:

Let the blank space is denoted by x

(a) 7/10 – x = 3/10

=> 7/10 – 3/10 = x

=> x = (7 - 3)/10

=> x = 4/10

So, the blank space is 4/10

(b) x – 3/21 = 3/10

=> x = 5/21 + 3/21

=> x = (5 + 3)/21

=> x = 8/21

So, the blank space is 8/21

(c) x – 3/6 = 3/6

=> x = 3/6 + 3/6

=> x = (3 + 3)/6

=> x = 6/6 = 1

So, the blank space is 1

(d) x + 5/27 = 12/27

=> x = 12/27 + 5/27

=> x = (12 + 5)/27

=> x = 17/27

So, the blank space is 17/27

**Question 5:**

Javed was given 5/7 of a basket of oranges. What fraction of oranges was left in the basket?

Answer:

Total = 1

Fraction given to Javed = 5/7

Now, fraction left in the basket = 1 – 5/7 = 7/7 – 5/7 = (7 - 5)/7 = 2/7

**Exercise 7.6**

**Question 1:**

Solve:

(a) 2/3 + 1/7 (b) 3/10 + 7/15 (c) 4/9 + 2/7 (d) 5/7 + 1/3 (e) 2/5 + 1/6 (f) 4/5 + 2/3

(g) 3/4 - 1/3 (h) 5/6 – 1/3 (i) 2/3 + 3/4 + 1/2 (j) 1/2 + 1/3 + 1/6 (k) 1 + 3

(l) 4 + 3 (m) 16/5 – 7/5 (n) 4/3 – 1/2

Answer:

(a) 2/3 + 1/7

= (2*7 + 1*3)/21 {LCM(3, 7) = 21}

= (14 + 3)/21

= 17/21

(b) 3/10 + 7/15

= (3*3 + 7*2)/30 {LCM(10, 15) = 30}

= (9 + 14)/30

= 23/30

(c) 4/9 + 2/7

= (4*7 + 2*9)/63 {LCM(9, 7) = 63}

= (28 + 18)/63

= 46/63

(d) 5/7 + 1/3

= (5*3 + 1*7)/21

= (15 + 7)/21

= 22/21 = 1

(e) 2/5 + 1/6

= (2*6 + 1*5)/30 {LCM(5, 6) = 30}

= (12 + 5)/30

= 17/30

(f) 4/5 + 2/3

= (4*3 + 2*5)/15 {LCM(5, 3) = 15}

= (12 + 10)/15

= 22/15

(g) 3/4 - 1/3

= (3*3 – 1*4)/12 {LCM(4, 3) = 12}

= (9 - 4)/12

= 5/12

(h) 5/6 – 1/3

= (5*1 – 1*2)/6 {LCM(6, 3) = 6}

= (5 - 2)/6

= 3/6 = 1/2

(i) 2/3 + 3/4 + 1/2

= (2*4 + 3*3 + 1*6)/12 {LCM(2, 3, 4) = 12}

= (8 + 9 + 6)/12

= 23/12

(j) 1/2 + 1/3 + 1/6

= (1*3 + 1*2 + 1*1)/6 {LCM(2, 3, 6) = 6}

= (3 + 2 + 1)/6

= 6/6 = 1

(k) 1 + 3

= 4/3 + 11/3

= (4 + 11)/3

= 15/3 = 5

(l) 4 + 3

= 14/3 + 13/4

= (14 * 4 + 13 * 3)/12 {LCM(3, 4) = 12}

= (56 + 39)/12

= 95/12

(m) 16/5 – 7/5

= (16 - 7)/5

= 9/5

(n) 4/3 – 1/2

= (4 * 2 – 1 * 3)/6 {LCM(3, 2) = 6}

= (8 - 3)/6

= 5/6

**Question 2:**

Sarika bought 2/5 meter of ribbon and Lalita 3/4 meter of ribbon. What is the total length of the ribbon they bought?

Answer:

Ribbon bought by Sarita = 2/5 m

Ribbon bought by Lalita = 3/4 m

Total length of the ribbon = 2/5 + 3/4

= (2*4 + 3*5)/20 {LCM(5, 4) = 20}

= (8 + 15)/20

= 23/20

= 1

Hence, they bought 1 m of ribbon.

**Question 3:**

Naina was given 1 piece of cake and Najma was given 1 piece of cake. Find the total amount of cake given to both of them.

Answer:

Cake given by Naina = 1 = 3/2

Cake given by Najma = 1 = 4/3

Total cake taken = 3/2 + 4/3

= (3*3 + 4*2)/6 {LCM(2, 3) = 6}

= (9 + 8)/6

= 17/6

= 2

So, the total consumption of cake is 2

**Question 4:**

Fill in the boxes:

(a) - 5/8 = 1/4 (b) - 1/5 = 1/2 (c) 1/2 - = 1/6

Answer:

Let we denote blank space as x

(a) x – 5/8 = 1/4

=> x = 1/4 + 5/8

=> x = (1*2 + 5*1)/8 {LCM(4, 8) = 8}

=> x = (2 + 5)/8

=> x = 7/8

So, the blank space is 7/8

(b) x – 1/5 = 1/2

=> x = 1/2 + 1/5

=> x = (1*5 + 1*2)/10 {LCM(2, 5) = 10}

=> x = (5 + 2)/10

=> x = 7/10

So, the blank space is 7/10

(c) 1/2 - x = 1/6

=> 1/2 - 1/6 = x

=> x = (1*3 – 1*2)/6 {LCM(2, 3) = 6}

=> x = (3 - 1)/6

=> x = 2/6

So, the blank space is 2/6

**Question 5:**

Complete the addition – subtraction box:

Answer:

(a) 2/3 + 4/3 = (2 + 4)/3 = 6/3

1/3 + 2/3 = (1 + 2)/3 = 3/3

2/3 - 1/3 = (2 - 1)/3 = 1/3

4/3 - 2/3 = (4 - 2)/3 = 2/3

1/3 + 2/3 = (1 + 2)/3 = 3/3

(b) 1/2 + 1/3 = (2 + 3)/6 = 5/6

1/3 + 1/4 = (3 + 4)/12 = 7/12

1/2 - 1/3 = (3 - 2)/6 = 1/6

1/3 - 1/4 = (4 - 3)/12 = 1/12

1/6 + 1/12 = (2 + 1)/12 = 3/12

**Question 6:**

A piece of wire 7/8 meter long broke into two pieces. One piece was 1/4 meter long. How long is the other piece?

Answer:

Total length of wire = 7/8 meter

Length of first part = 1/4 meter

Remaining part = 7/8 – 1/4

= (7*1 – 1*2)/8 {LCM(4, 8) = 8}

= (7 - 2)/8

= 5/8

So, the length of remaining part is 5/8 meters.

**Question 7:**

Nandini house is 9/10 km from her school. She walked some distance and then took a bus for 1/2 km to reach the school. How far did she walk?

Answer:

Total distance between school and house = 9/10 km

Distance covered by bus = 1/2 km

Remaining distance = 9/10 – 1/2

= (9*1 – 1*5)/10 {LCM(2, 10) = 10}

= (9 - 5)/10

= 4/10 = 2/5

So, the distance covered by walking is 2/5 km.

**Question 8:**

Ahsa and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is 5/6^{th} full and Samuel’s shelf is 2/5^{th} full.

Whose bookshelf is more full? By what fraction?

Answer:

Given, Asha’s shelf is 5/6^{th} full and Samuel’s shelf is 2/5^{th} full

Now, 5/6, 2/5

= (5*5, 2*6)/30 {LCM(5, 6) = 30}

= (25, 12)/30

= 25/30, 12/30

Since 25/30 > 12/30

=> 5/6 > 2/5

So, Asha’s bookshelf is more covered than Samuel.

Again, difference = 25/30 - 12/30 = (25 - 12)/30 = 13/30

**Question 9:**

Jaidev takes 2 minutes to walk across the school ground. Rahul takes 7/4 minutes to do same. Who takes less time and by what fraction?

Answer:

Time taken by Jaidev = 2 = 11/5 minutes

Time taken by Rahul = 7/4 minutes

Now, the difference = 11/5 – 7/4

= (11*4 – 7*5)/20 {LCM(4, 5) = 20}

= (44 - 35)/20

= 9/35

So, Rahul takes less time which is 9/20 minutes.

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