**Fractions**

**Exercise 7.1**

**Ex 7.1 Question 1.**

Write the fraction representing the shaded portion.

**Solution:**

(I) Total number of parts = 4

Shaded portion = 2

∴ Fraction = 2 / 4

(ii) Total number of parts = 9

Shaded portion = 8

∴ Fraction = 8 / 9

(iii) Total number of parts = 8

Shaded portion = 4

∴ Fraction = 4 / 8

(iv) Total number of parts = 4

Shaded portion = 1

∴ Fraction = 1 / 4

(v) Total number of parts = 7

Shaded portion = 3

∴ Fraction = 3 / 7

(vi) Total number of parts = 12

Shaded portion = 3

∴ Fraction = 3 / 12

(vii) Total number of parts = 10

Shaded portion = 10

∴ Fraction = 10 / 10

(viii) Total number of parts = 9

Shaded portion = 4

∴ Fraction = 4 / 9

(ix) Total number of parts = 8

Shaded portion = 4

∴ Fraction = 4 / 8

(x) Total number of parts = 2

Shaded portion = 1

∴ Fraction = 1 / 2

**Ex 7.1 Question 2.**

Colour the part according to the given fraction.

**Solution:**

**Ex 7.1 Question 3.**

**Identify the error, if any.**

**Solution:**

(a) Since the shaded part is not half.

∴ This is not 1/2.

(b) Since the parts are not equal.

∴ The shaded portion is not 1/4.

(c) Since the part is not equal.

∴ The shaded portion is not 3/4.

**Ex 7.1 Question 4.**

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

**Solution:**

A day has = 24 hours

we have 8 hours,

∴ Required fraction = 8/24

**Ex 7.1 Question 5.**

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

**Solutions:**

1 hour = 60 minutes

∴ required Fraction = 40 / 60

**Ex 7.1 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?**

**Solution:**

(a) Arya has divided his sandwich into three equal parts.

So, each of them will get one part.

(b) Each one of them will receive 1/3 part.

∴ Required fraction = 1/3

**Ex 7.1 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?**

**Solution:**

Total number of dresses to be dyed = 30

Number of dresses finished = 20

∴ Required fraction = 20/30= 2/3

**Ex 7.1 Question 8.**

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

**Solutions:**

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

Total number of natural numbers given = 11

Number of prime numbers = 5

∴ Required Fraction = 5 / 11

**Ex 7.1 Question 9.**

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

**Solutions:**

Natural numbers from 102 to 113 = 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113

Total number of natural numbers given = 12

Number of prime numbers = 4 [103, 107, 109, 113]

∴ Required Fraction = 4 / 12 = 1 / 3

**Ex 7.1 Question 10.**

**What fraction of these circles have X’s in them?**

**Solution:**

Total number of circles in figure = 8

Number of circles having X’s in them = 4

∴ Required Fraction = 4 / 8 = 1 / 2

**Ex 7.1 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?**

**Solutions:**

Number of CDs bought by Kristin from the market = 3

Number of CDs Kristin received as gifts = 5

Total number of CDs Kristin have = 3 + 5 = 8

∴ Fraction of CD Kristin bought = 3 / 8

∴ Fraction of CDs Kristin received as gifts = 5 / 8