# Chapter 7: Fractions

*EXERCISE 7.1*

*EXERCISE 7.1*

*Write the fraction representing the shaded portion.*

**Solution:**

= 2/4

= 8/9

= 4/8

= 1/4

= 3/7

= 3/9

= 10/10

= 1

= 4/9

= 3/8

= 4/8

2. *Color the part according to the given fraction.*

**Solution: **

3. *Identify the error, if any*

**Solution:**

4. *What fraction of a day is 8 hours?*

**Solution:**

Fraction of a day is 8 hours

= 8/24

5. *What fraction of an hour is 40 minutes?*

**Solution:**

Fraction of an hour is 40 min

= 40/60

= 2/3rd.

* 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?*

**Solution:**

** (a) Divide sandwiches equally among three** **people.**

Since there are three people (Arya, Abhimanyu, and Vivek) to eat, Arya should divide each sandwich into 3 equal parts and give 1 part to each person so that they all get an equal share.

** (b) Calculate part of a sandwich will each boy get.**

Since, each sandwich is divided into 3 parts.

Hence,

(a) Arya can divide each sandwich into three equal parts so that each person receives an equal share.

(b) Each boy will receive 1/3 part of a sandwich.

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

**Solution:**

**Total number of dresses Kanchan had to dye = 30**

**Number of dresses she had finished = 20**

**Therefore, the fraction of dresses she has finished **=20/30

=2/3**.**

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

*Solution:*

The prime numbers from

The natural numbers are2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.

The prime numbers are2, 3, 5, 7, 11.

There are 5 prime numbers out of 11 natural numbers.

Therefore, the fractions of prime numbers from 2 to12. are as follows:

Prime number from 2 to 12total number of natural numbers from 2 to 12 /⇒fraction of prime number from 2 to 12=5/11.

Hence, the fraction of prime numbers among natural numbers from 2 to 12 is 5/11.

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

**Solution:**

Natural numbers from 102 to 113:

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

Number of Natural numbers from 102 to 113 = 12

Prime numbers from 102 to 113:

103, 107, 109, 113

Number of prime numbers from 102 to 113 = 4

Hence, fraction of prime numbers from 102 to 113 =4/12=1/3.

10. ** What fraction of these circles have Xs in them**?

Solution:

Total number of circles = 8

Number of circles having X = 4

** Hence, the fraction = 4/8.**

*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?*

Solution:

As per the question

Number of CD’s Kristin purchased = 3

Number of CD’s Kristin received as gifts = 5

Total number of CD’s Kristin has = 3 + 5 = 8

The fraction of her total CDs Kristin purchased =3/8.

The fraction of her total CD’s Kristin received as gifts =5/8.

## EXERCISE 7.2

*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*

**Solution:**

(a) **½, ¼, ¾, 4/4,**

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

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

*2. Express the following as mixed fractions:*

*(a) 20/ 3*

*(b) 11/ 5*

* (c) 17/ 7*

*(d) 28/ 5*

* (e) 19/ 6*

*(f) 35/ 9*

**Solution:**

(a) **20/3**

(b) **11/5**

(c) **17/**7

(d) **28/5**

(e) **19/6**

(f) **35/9**

*3. Express the following as improper fractions:*

Solution:

= (4*7+3)/4

= 31/4

(b) 5(6/7)

= (7*5+6)/7

= 36/7

(c) 2(5/6)

= (6*2+5)

= 17/6

(d) 10(3/5)

= (10*5+3)/5

= 53/5

(e) 9(3/7)

= (9*7+ 3)/7

= 66/7

(f) 8(4/9)

= (8*9+4)/9

= 76/9

## EXERCISE 7.3

*Write the fractions. Are all these fractions equivalent?*

** Solution:**

= 1/2, 2/4, 3/6, 4/8; Yes

** Solution:**

** = **4/12, 3/9, 2/6, 1/3, 6/15; No

2. *Write the fractions and pair up the equivalent fractions from each row.*

**Solution: **

(a) 1/ 2 (b) 4/ 6 (c) 3 /9 (d) 2/ 8 (e) 3/ 4

(i) 6/ 18 (ii) 4/ 8 (iii) 12/ 16 (iv) 8 /12 (v) 4 /16

*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*

**Solution:**

(a) 2/7= 8/?

= (7*8) =2*X

= 56 =2X

= 56/2 = X

=28 = X

(b) 5/8 = 10/?

= (8*10) = 5*X

= 80 = 5X

= 80/5 = X

=16 = X

(c) 3/5 =? /20

= 5*X = (3*20)

= 5X = 60

= X = 60/5

= X = 12

(d) 45/60 = 15/?

= (60*15) = 45*X

= 900 = 45X

= 900/45 = X

= 2 = X

(e) 18/24 =? /4

=(18*4) = 24*X

= 72 = 24X

= 72/24 = X

= 3=X

*4. Find the equivalent fraction of 3/ 5 having*

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

**Solution:**

- 12/ 20 (b) 9 /15 (c) 18 /30 (d) 27/ 45

*5. Find the equivalent fraction of 36 /48 with*

* (a) numerator 9 (b) denominator 4*

**Solution:**

(a) 9 /12 (b) 3/ 4

*6. Check whether the given fractions are equivalent: (a) 5/ 9, 30 /54, (b) 3/ 10 ,12/ 50,*

* (c) 7 /13 ,5 /11*

**Solution:**

(a) equivalent (b) not equivalent (c) not equivalent

*7. Reduce the following fractions to simplest form:*

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

**Solution:**

- 4/ 5 (b) 5/ 2 (c) 6/ 7 (d) 3 /13 (e) 1/ 4

*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 if each has used up an equal fraction of her/his pencils?*

**Solution:**

**As per the question:**

**Number of pencils Ramesh had = 20**

**Number of pencils Ramesh used = 10**

**Fraction of pencils Ramesh used up = **10/20=1/2

**Number of pencils Sheelu had = 50**

**Number of pencils Sheelu used = 25**

**Fraction of pencils Sheelu used up = **25/50=1/2

**Number of pencils Jamaal had = 80**

**Number of pencils Jamaal used = 40**

**Fraction of pencils Jamaal used up = **40/80=1/2

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

*9. Match the equivalent fractions and write two more for each.*

*(1) 250/400 (a) 2/3*

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

*(3) 660/990 (c) 1/2*

*(4) 180/360 (d) 5/8*

*(5) 220/550 (e) 9/10*

**Solution:**

(i)→ (d) (ii) → (e) (iii) → (a) (iv) → (c) (v) → (b)

# EXERCISE 7.4

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

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

**Solution: **

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

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

(c)

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

*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*

* *Solution:

(a) 3/6 < 5/6

(b) 1/7 < 1/4

(c) 4/5 < 5/5

(d) 3/5 > 3/7

3. ** Make five more such pairs and put appropriate signs**.

Solution:

(a) 5/8 < 7/8

Here denominators are same, the fraction with higher numerator will be greater.

(b) 7/3 > 7/8

Here, numerators are same, the fraction with lesser denominator will be greater.

(c) 5/15 > 3/15

Here, denominators are same, the fraction with higher numerator will be greater.

(d) 9/21 > 9/27

Here, numerators are same, the fraction with lesser denominator will be greater.

(e0 5/12 < 8/12

Here, denominators are same, the fraction with higher numerator will be greater.

4. *Look at the figures and write ‘’, ‘=’ between the given pairs of fractions*

**Solution:**

(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

5. *How quickly can you do this? Fill appropriate sign. ( ‘< ‘,’ = ‘, ‘>’)*

**Solution:**

(a) 1/2 > 1/5

(b) 2/4 = 3/6

(c) 2/3 < 2/4

(d) 3/4 > 3/7

(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 = 3/5

(k) 5/7 = 15/21

*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*

**Solution:**

- 2/12 = 1/6
- 3/15 = 1/5
- 8/50 = 4/25
- 16/100 = 4/25
- 10/60 = 1/6
- 15/75 = 1/5
- 12/60 = 1/5
- 16/96 = 1/6
- 12/75 = 4/25
- 12/72 = 1/6
- 3/18 = 1/6
- 4/25 = 4/25

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

* (a) Is 5/ 9 equal to 4 /5?*

* (b) Are 9/ 16 equals to 5/ 9?*

* (c) Is 4/ 5 equals to 16 /20?*

* (d) Is 1 /15 equal to 4/ 30?*

**Solution:**

(i) For 5/9 and 4/5,

⇒5×5 and 4×9

⇒25 and 36

Since, 25<36,

∴59<45

(ii) For 9/16 and 5/9

⇒9×9 ad 5×16

⇒81 and 80

Since, 81>80

∴ 916>59

(iii) For 4/5 and 16/20,

The later fraction can be reduced to its lowest form,

⇒1620=16÷420÷4=45

Thus, the two fractions are equal, 45=16/20

(iv) For 1/15 and 4/30.

The later fraction can be reduced to its lowest form,

⇒430=4÷2/30÷2=2/15

Since, 2/15>1/15

∴430>115

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

**Solution:**

**As per the question**

**Ila read 25 pages out of 100 pages.**

**Fraction of reading the pages **=25/100=1/4th** part of book.**

**Lalita read **2/5th** part of book**

**Number of pages Lalita read = **2/5×100=40

**Ila read 2/5 pages out of 100 pages and Lalita read 40 pages out of 100.**

**Therefore, Ila read less.**

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

**Solution:**

**As per the question**

**Rafiq exercised **3/6** of an hour.**

**Rohit exercised **3/4

**of an hour.**

**Now, the LCM of 6 and 4 is 12.**

**Therefore, the equivalent fractions of **3/6** and **3/4** with the same denominator are:**

3/6=3×2/6×2=612** and **3/4=3×3/4×3=9/12**.**

6/12<9/12

**Therefore **3/4>3/6

**Therefore, Rohit exercised for a longer time.**

*10. In a class A of 25 students, 20 passed with 60% or more marks; in another class B of 30 students, 24 passed with 60% or more marks. In which class was a greater fraction of students getting with 60% or more marks?*

**Solution:**

Step 1: Find the fraction of students in class A who passed with 60% or more marks.

Since, there are 25 students in class A. and 20 students are passed with 60% or more marks.

So, the required fraction is 20/25=4/5.

Hence, the fraction of students in class A who passed with 60% or more marks is 4/5.

Step 2: Find the fraction of students in class B who passed with 60% or more marks.

Since, there are 30 students in class B. and 24 students are passed with 60% or more marks.

So, the required fraction is 24/30=4/5.

Hence, the fraction of students in class B who passed with 60% or more marks is 4/5.

Therefore, in both classes equal fraction of students passed with 60% or more marks [ i.e., 4/5].

## EXERCISE 7.5

*Write these fractions appropriately as additions or subtractions:*

**Solution:**

- (addition)

1/5 + 2/5 = 3/5

- (subtraction)

5/5 – 3/5 = 2/5

- (addition)

2/6 + 3/6 = 5/6

2. *Solve:*

(a) **1/18 + 1/18**

**= 2/18**

(b) **8/15 + 3/15**

**= 11/15**

(c)** 7/7 – 5/7**

**= 2/**

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

**= 22/22**

**= 1**

(e) **12/15 + 7/15**

**= 19/15**

(f) **5/8 + 3/8**

**= 8/8**

**= 1**

(g) **1 – 2/3 (1= 3/3)**

**= 3/3 -2/3**

**= 1/3**

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

**= 1/4**

(i) **3 – 12/5**

**= (3*5) – 12/5**

**= 15 – 12 /5**

**= 3/5**

*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?*

** Solution:**

**As per the question**

**Fraction of wall painted by Shubham = **2/3

**Fraction of wall painted by Madhavi = **1/3

**Total painting done by both of them =**2/3+1/3=2+1/3=3/3=1

**Therefore, they painted the whole wall**

4. *Fill in the missing fractions.*

**Solution: **

(a) 7/10 -? = 3/10

= 7/10 – 10/10 = 3/10

(b) ? – 3/21 = 5/21

= 8/21 – 3/21 = 5/21

(c) ? – 3/6 = 3/6

= 0 – 3/6 = 3/6

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

= 7/27 + 5/27 = 12/27

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

**Solution:**

Javed was given 5/7 of a basket of oranges.

The fraction of oranges given to Javed + The fraction of oranges left in the basket = 1

⇒ The fraction of oranges left = 1 – The fraction of oranges given to Javed

On substituting the values, we get:

Fraction of Orange left =1−5/7

=7/7−5/7=7−5/7=2/7

Thus,27 oranges were left in the basket.

## EXERCISE 7.6

**Solve**

**Solution:**

- 2/3 + 1/7

= (2*7 + 1*3)/3*7

= (14 + 3)/21

= 17/21

- 3/10 + 7/15

= (3*3 + 7*2)/30 ( 30 is LCM of 10 and 15)

= (9 + 14)/30

= 22/30

- 4/9 + 2/7

= (4*7 + 2*9)/9*7

= (28 + 18)/63

= 46/63

- 5/7 +1/3

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

= (15 + 7)/21

= 22/21

- 2/5 +1/6

= (2*6+ 1*5)/6*5

= (12 + 5)/30

= 17/30

- 4/5 + 2/3

= (4*3 + 2*5)/15

= (12 + 10)/15

= 22/15

- 3/4 – 1/3

= (3*3 – 1*4)/12

= (9 – 4)/12

= 5/12

- 5/6 – 1/3

= (5*3 – 1*6)/6*3

= (15 – 6)/18

= 9/18

= 1/2

- 2/3 + 3/4 + 1/2

= (2*4 + 3*3 + 1*6)/12 ( 12 is LCM of 3,4 and 2)

= (8 + 9 + 6)/12

= 23/12

- 1/2 + 1/3 + 1/6

= (1*6 + 1*4 + 1*2)/12 (12 is LCM of 2,3 and 6)

= (6 + 4 + 2)/12

= 12/12

= 1

- +

= 4/3 + 11/3

= 15/3

= 5

- +

= 14/3 + 13/4

= (14*4 + 13*3)/4*3

= (56 + 39)/12

= 95/12

- 16/5 – 7/5

= (16 – 7)/5

= 9/5

- 4/3 – 1/2

= (4*2 – 1*3)/6

= (8 – 3)/6

= 5/6

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

**Solution:**

The total length of the ribbon bought by both of them is 2 / 5 + 3 / 4

Taking LCM of 20

= [(2 × 4) + (3 × 5)] / 20

= (8 + 15) / 20

= 23 / 20 meter

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

**Solution:**

The fraction of cake given to Naina is = 3/2.

The fraction of cake given to Najma is = 4/3.

Total amount of cake given to both of them = 3/2 + 4/3

= (3*3)/(2*3) + (4*2)/(3*2)

= 9/6 + 8/6

= (9 + 8)/6

= 17/6

=

Hence, both of them were given pieces of cake.

4. **Fill in the boxes:**

**Solution:**

- 7/8
- 7/10
- 1/3

**5. Complete the addition-subtraction box.**

**Solution:**

**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?**

**Solution:**

Total length of wire = 7/8 meter

Length of first place = 1/4 meter

Now,

Total length = length of first piece + length of second piece

7/8 = 1/4 + length of second piece

Length of second piece = 7/8 – 1/4

= (7*4 – 1*8)/8*4

= (28 – 8)/32

= 20/32

= 5/8

Therefore, length of second piece = 5/8 metre.

**7. Nandini’s 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?**

**Solution:**

The total distance from Nandini’s house to school is given as 9/10km

Distance Nandini had covered by bus is 1/2 km

Total distance covered by Nandini on foot will be the difference of 9/10 and 1/2

= (9/10 – 1/2) km

= (9*1 – 1*5)/10 (10 is LCM of 2 and 10)

= (9 – 5)/10

= 4/10

= 2/5

Hence distance covered by Nandini on foot will be 2/5 km.

8. **Asha 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?**

**Solution:**

The fraction by which Asha’s bookshelf covered is more than Samuel’s is = 5/6−2/5

= 25/30−12/30

= 13/30

fraction among 5/6 and 2/5 is greater.

5/6=5/6×5/5=25/30 and 2/5=2/5×6/6=12/30.

[∵ L.C.M. of 6 and 5 is 30]

∴ 25/30>12/30

⇒ 5/6>2/5

∴ Asha’s bookshelf is more covered than Samuel.

**9. Jaidev takes 2(1/5) minutes to walk across the school ground. Rahul takes 7/4 minutes to do the same. Who takes less time and by what fraction?**

**Solution:**

**Given,**

Time taken by Jaidev to walk across the school ground = 2(1/5) =11/5 minutes

Time taken by Rahul to walk across the school ground = 7/4 minutes

Now, we will convert the given fractions into like fractions,

Time taken by Jaidev: 11/5 = 11/5 × 4/4 = 44/20

And, Time taken by Rahul: 74 = 7/4 ×5/5 = 35/20

It is clear that,44/20>35/20

So, Rahul takes less time than Jaidev

Difference = 44/20 – 35/20 = 9/20

Hence, Rahul walks across the school ground by 9/20 minutes faster than Jaidev.

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