In mathematics, a fraction number represents a part of a whole number. A fraction number consists of a denominator and numerator. Knowing these terms and their uses are very much important to understand the concepts of mathematics in higher classes. Apart from solving NCERT questions, students are also advised to solve questions from reference books like RS Aggarwal. To help students understand the concepts faster, we have provided the RS Aggarwal Class 6 solutions chapter 5 fractions.

**Q1)**

**Ans. 1) **(i) The shaded portion is 3 parts of the whole figure.

Therefore, \(\frac{ 3 }{ 4 }\)

(ii) The shaded portion is 1 parts of the whole figure.

Therefore, \(\frac{ 1 }{ 4 }\)

(iii) The shaded portion is 2 parts of the whole figure.

Therefore, \(\frac{ 2 }{ 3 }\)

(iv) The shaded portion is 3 parts of the whole figure.

Therefore, \(\frac{ 3 }{ 10 }\)

(v) The shaded portion is 4 parts of the whole figure.

Therefore, \(\frac{ 4 }{ 9 }\)

(vi) The shaded portion is 3 parts of the whole figure.

Therefore, \(\frac{ 3 }{ 8 }\)

**Q2)**

**Ans. 2)**

**Q3) In the given figure, if we say that the shaded region is \(\frac{ 1 }{ 4 }\) ,then identify the error in it.**

**Ans. 3) **The given rectangle is not divided into four equal parts.

Thus, the shaded region is not equal to \(\frac{ 1 }{ 4 }\) of the whole.

**Q4) Write a fraction for each of the following:**

**(i) three – fourths (ii) four – sevenths**

**(iii) two – fifths (iv) three – tenths**

**(v) one – eighth (vi) five – sixths**

**(vii) eight – ninths (viii) seven – twelfths**

**Ans. 4) **(i) \(\frac{ 3 }{ 4 }\)

(ii) \(\frac{ 4 }{ 7 }\)

(iii) \(\frac{ 2 }{ 5 }\)

(iv) \(\frac{ 3 }{ 10 }\)

(v) \(\frac{ 1 }{ 8 }\)

(vi) \(\frac{ 5 }{ 6 }\)

(vii) \(\frac{ 8 }{ 9 }\)

(viii) \(\frac{ 7 }{ 12 }\)

**Q5) Write down the numerator and the denominator of each of the fractions given below:**

**(i) \(\frac{ 4 }{ 9 }\) (ii) \(\frac{ 6 }{ 11 }\)**

**(iii) \(\frac{ 8 }{ 15 }\) (iv) \(\frac{ 12 }{ 17 }\)**

**(v) \(\frac{ 5 }{ 1 }\)**

**Ans. 5) **Numerator Denominator

(i) 4 9

(ii) 6 11

(iii) 8 15

(iv) 12 17

(v) 5 1

**Q6) Write down the fraction in which **

**(i) numerator = 3, denominator = 8 (ii) numerator = 5, denominator = 12**

**(iii) numerator = 7, denominator = 16 **

**(iv) numerator = 8, denominator = 15**

**Ans. 6) **(i) \(\frac{ 3 }{ 8 }\)

(ii) \(\frac{ 5 }{ 12 }\)

(iii) \(\frac{ 7 }{ 16 }\)

(iv) \(\frac{ 8 }{ 15 }\)

**Q7) Write down the fractional number for each of the following:**

**(i) \(\frac{ 2 }{ 3 }\) (ii) \(\frac{ 4 }{ 9 }\)**

**(iii) \(\frac{ 2 }{ 5 }\) (iv) \(\frac{ 7 }{ 10 }\)**

**(v) \(\frac{ 1 }{ 3 }\) (vi) \(\frac{ 3 }{ 4 }\)**

**(vii) \(\frac{ 3 }{ 8 }\) (viii) \(\frac{ 9 }{ 14 }\)**

**(ix) \(\frac{ 5 }{ 11 }\) (x) \(\frac{ 6 }{ 15 }\)**

**Ans. 7) **(i) two – thirds

(ii) four – ninths

(iii) two – fifths

(iv) seven – tenths

(v) one – thirds

(vi) three – fourths

(vii) three – eighths

(viii) nine – fourteenths

(ix) five – elevenths

(x) six – fifteenths

**Q8) What fractions of an hour is 24 minutes?**

**Ans. 8) **We know: 1 hour = 60 minutes

Therefore, The required fraction = \(\frac{ 24 }{ 60 }\) = \(\frac{ 2 }{ 5 }\)

**Q9) How many natural numbers are there from 2 to 10? What fraction of them are prime numbers?**

**Ans. 9) **There are total 9 numbers from 2 to 10. They are 2, 3, 4, 5, 6, 7, 8, 9, 10.

Out of these natural numbers 2, 3, 5, 7 are the prime numbers.

Therefore, The required fraction = \(\frac{ 4 }{ 9 }\) .

**Q10) Determine:**

**(i) \(\frac{ 2 }{ 3 }\) of 15 pens **

**(ii) \(\frac{ 2 }{ 3 }\) of 27 balls **

**(iii) \(\frac{ 2 }{ 3 }\) of 36 balloons**

**Ans. 10) **(i) \(\frac{ 2 }{ 3 }\)of 15 pens = \(\left (\frac{ 2 }{ 3 } \times 15 \right )\) = 10 pens

(ii) \(\frac{ 2 }{ 3 }\) of 27 balls = \(\left (\frac{ 2 }{ 3 } \times 27 \right )\) = 18 balls

(iii) \(\frac{ 2 }{ 3 }\) of 36 balloons = \(\left (\frac{ 2 }{ 3 } \times 36 \right )\) = 24 balls

**Q11) Determine: **

**(i) \(\frac{ 3 }{ 4 }\) of 16 cups **

**(ii) \(\frac{ 3 }{ 4 }\) of 28 rackets **

**(iii) \(\frac{ 3 }{ 4 }\) of 32 books**

**Ans. 11)**(i) \(\frac{ 3 }{ 4 }\) of 16 cups = \(\left (\frac{ 3 }{ 4 } \times 16 \right )\) = 12 cups

(ii) \(\frac{ 3 }{ 4 }\) of 28 rackets = \(\left (\frac{ 3 }{ 4 } \times 28 \right )\) = 21 rackets

(iii) \(\frac{ 3 }{ 4 }\) of 32 books = \(\left (\frac{ 3 }{ 4 } \times 32 \right )\) = 24 books

**Q12) Neelam has 25 pencils. She gives \(\frac{ 4 }{ 5 }\) of them to Meena . How many pencils does Meena get? How many pencils are left with Neelam ?**

**Ans. 12) **(i) Neelam gives \(\frac{ 4 }{ 5 }\) of 25 pencils to Meena.

\(\left (\frac{ 4 }{ 5 } \times 25 \right )\) = 20 pencils

Thus, Meena gets 20 pencils.

Therefore, Number of pencils left with Neelam = 25 – 20 = 5 pencils

Thus, 5 pencils are left with Neelam

**Q13) Represent each of the following fractions on the number line:**

**(i) \(\frac{ 3 }{ 8 }\) (ii) \(\frac{ 5 }{ 9 }\)**

**(iii) \(\frac{ 4}{ 7 }\) (iv) \(\frac{ 2 }{ 5 }\)**

**(v) \(\frac{ 1 }{ 4 }\)**

**Ans. 13) **Draw a 0 to 1 on a number line. Label point 1 as A and mark the starting point as 0.

(i) Divide the number line from 0 to 1 into 8 equal parts and take out 3 parts from it to reach point R.

(ii) Divide the number line from 0 to 1 into 9 equal parts and take out 5 parts from it to reach point P

(iii) Divide the number line from 0 to 1 into 7 equal parts and take out 4 parts from it to reach point P.

(iv) Divide the number line from 0 to 1 into 5 equal parts and take out 2 parts from it to reach point P.

(v) Divide the number line from 0 to 1 into 4equal parts and take out 1 parts from it to reach point P.

**Exercise 5B**

**Q1) Which of the following are proper fractions ?**

**\(\frac{ 1 }{ 2 }\) , \(\frac{ 3 }{ 5 }\) , \(\frac{ 10 }{ 7 }\) , \(\frac{ 7 }{ 4 }\) , 2 , \(\frac{ 15 }{ 8 }\) , \(\frac{ 16 }{ 16 }\) , \(\frac{ 10 }{ 11 }\) , \(\frac{ 23 }{ 10 }\)**

**Ans. 1) **\(\frac{ 1 }{ 2 }\) , \(\frac{ 3 }{ 5 }\) , \(\frac{ 10 }{ 11 }\)

**Q2) \(\frac{ 3 }{ 2 }\) , \(\frac{ 5 }{ 6 }\) , \(\frac{ 9 }{ 4 }\) , \(\frac{ 8 }{ 8 }\) , 3 , \(\frac{ 27 }{ 16 }\) , \(\frac{ 23 }{ 31 }\) , \(\frac{ 19 }{ 18 }\) , \(\frac{ 10 }{ 13 }\) , \(\frac{ 26 }{ 26 }\)**

**Ans. 2)**A fraction whose numerator is greater than or equal to its denominator is called \(\frac{ 3 }{ 2 }\) , \(\frac{ 9 }{ 4 }\) , \(\frac{ 8 }{ 8 }\) , \(\frac{ 19 }{ 18 }\) and \(\frac{ 26 }{ 26 }\) are improper fractions.

**Q3) Write six improper fractions with denominator 5.**

**Ans. 3) **Clearly , \(\frac{ 6 }{ 5 }\) , \(\frac{ 7 }{ 5 }\) , \(\frac{ 8 }{ 5 }\) , \(\frac{ 11 }{ 5 }\) and \(\frac{ 12 }{ 5 }\) are improper fractions , each with 5 as the denominator.

**Q4) Write six improper fractions with numerator 13.**

**Ans. 4) **Clearly , \(\frac{ 13 }{ 2 }\) , \(\frac{ 13 }{ 3 }\) , \(\frac{ 13 }{ 4 }\) , \(\frac{ 13 }{ 5 }\) , \(\frac{ 13 }{ 6 }\) , \(\frac{ 13 }{ 7 }\) are improper fractions , each with 13 as the numerator.

**Q5) Convert each of the following into an improper fraction:**

**(i) \(5 \frac{ 5 }{ 7 }\) (ii) \(9 \frac{ 3 }{ 8 }\)**

**(iii) \(6 \frac{ 3 }{ 10 }\) (iv) \(3 \frac{ 5 }{ 11 }\)**

**(v) \(10 \frac{ 9 }{ 14 }\) (vi) \(12 \frac{ 7 }{ 15 }\)**

**(vii) \(8 \frac{ 8 }{ 13 }\) (viii) \(51 \frac{ 2 }{ 3 }\)**

**Ans. 5) **We have:

(i) \(5 \frac{ 5 }{ 7 }\) = \(\frac{ (5 \times 7 ) + 5 }{ 7 } = \frac{ 40 }{ 7 }\)

(ii) \(9 \frac{ 3 }{ 8 }\) = \(\frac{ (9 \times 8 ) + 3 }{ 8 } = \frac{ 75 }{ 8 }\)

(iii) \(6 \frac{ 3 }{ 10 }\) = \(\frac{ (6 \times 10 ) + 3 }{ 10 } = \frac{ 63 }{ 10 }\)

(iv) \(3 \frac{ 5 }{ 11 }\) = \(\frac{ (3 \times 11 ) + 5 }{ 11 } = \frac{ 38 }{ 11 }\)

(v) \(10 \frac{ 9 }{ 14 }\) = \(\frac{ ( 10 \times 14 ) + 9 }{ 14 } = \frac{ 149 }{ 14 }\)

(vi) \(12 \frac{ 7 }{ 15 }\) = \(\frac{ ( 12 \times 15 ) + 7 }{ 15 } = \frac{ 187 }{ 15 }\)

(vii) \(8 \frac{ 8 }{ 13 }\) = \(\frac{ (8 \times 13 ) + 8 }{ 13 } = \frac{ 112 }{ 13 }\)

(viii) \(51 \frac{ 2 }{ 3 }\) = \(\frac{ (51 \times 3 ) + 2 }{ 3 } = \frac{ 155 }{ 3 }\)

**Q6) Convert each of the following into a mixed fraction:**

**(i) \(\frac{ 17 }{ 5 }\) (ii) \(\frac{ 62 }{ 7 }\)**

**(iii) \(\frac{ 101 }{ 8 }\) (iv) \(\frac{ 95 }{ 13 }\)**

**(v) \(\frac{ 81 }{ 11 }\) (vi) \(\frac{ 87 }{ 16 }\)**

**(vii) \(\frac{ 103 }{ 12 }\) (viii) \(\frac{ 117 }{ 20 }\)**

**Ans. 6) **(i) On dividing 17 by 5, we get:

Quotient = 3

Remainder = 2

Therefore, \(\frac{ 17 }{ 5 }\) = 3 + \(\frac{ 2 }{ 5 }\) = \(3\frac{ 2 }{ 5 }\)

(ii) On dividing 62 by 7, we get:

Quotient = 8

Remainder = 6

Therefore, \(\frac{ 62 }{ 7 }\) = 8 + \(\frac{ 6 }{ 7 }\) = \(8 \frac{ 6 }{ 7 }\)

(iii) On dividing 101 by 8, we get:

Quotient = 12

Remainder = 5

Therefore, \(\frac{ 101 }{ 8 }\) = 12 + \(\frac{ 5 }{ 8 }\) = \(12 \frac{ 5 }{ 8 }\)

(iv) On dividing 95 by 13, we get:

Quotient = 7

Remainder = 4

Therefore, \(\frac{ 95 }{ 13 }\) = 7 + \(\frac{ 4 }{ 13 }\) = \(7 \frac{ 4 }{ 13 }\)

(v) On dividing 81 by 11, we get:

Quotient = 7

Remainder = 4

Therefore, \(\frac{ 81 }{ 11 }\) = 7 + \(\frac{ 4 }{ 11 }\) = \(7 \frac{ 4 }{ 11 }\)

(vi) On dividing 87 by 16, we get:

Quotient = 5

Remainder = 7

Therefore, \(\frac{ 87 }{ 16 }\) = 5 + \(\frac{ 7 }{ 16 }\) = \(5 \frac{ 7 }{ 16 }\)

(vii) On dividing 103 by 12, we get:

Quotient = 8

Remainder = 7

Therefore, \(\frac{ 103 }{ 12 }\) = 8 + \(\frac{ 7 }{ 12 }\) = \(8 \frac{ 7 }{ 12 }\)

(viii) On dividing 117 by 20, we get:

Quotient = 5

Remainder = 17

Therefore, \(\frac{ 117 }{ 20 }\) = 5 + \(\frac{ 17 }{ 20 }\) = \(5 \frac{ 17 }{ 20 }\)

**Q7) Fill up the blanks with â€˜ > â€™ , â€˜ < â€˜ or â€˜ = â€˜ :**

**(i) \(\frac{ 1 }{ 2 } — 1\) **

**(ii) \(\frac{ 3 }{ 4 } –1\)**

**(iii)\(1 — \frac{ 6 }{ 7 }\)**

**(iv) \(\frac{ 6 }{ 6 } –1\)**

**(v) ) \(\frac{ 3016 }{ 3016 } –1\)**

**(vi) )\(\frac{ 11 }{ 5 } –1\)**

**Ans. 7) **An improper fraction is greater than 1. Hence, it is always greater than a proper fraction, which is less than 1.

(i) \(\frac{ 1 }{ 2 }\)< 1

(ii) \(\frac{ 3 }{ 4 }\)< 1

(iii) 1 >\(\frac{6 }{ 7 }\)

(iv) \(\frac{ 6 }{ 6 }\) = 1

(v) \(\frac{ 3016 }{ 3016 }\) = 1

(vi) \(\frac{ 11 }{ 5 }\)> 1

**Q8) Draw number lines and locate the following points:**

**(i) \(\frac{ 1 }{ 4 }\) , \(\frac{ 1 }{ 2 }\) , \(\frac{ 3 }{ 4 }\) , \(\frac{ 4 }{ 4 }\)**

**(ii) \(\frac{ 1 }{ 8 }\) , \(\frac{ 2 }{ 8 }\) , \(\frac{ 3 }{ 8 }\) , \(\frac{ 4 }{ 8 }\) , \(\frac{ 5 }{ 8 }\) , \(\frac{ 7 }{ 8 }\) , \(\frac{ 7 }{ 8 }\)**

**(iii) \(\frac{ 2 }{ 5 }\) , \(\frac{ 3 }{ 5 }\) , \(\frac{ 4 }{ 5 }\) , \(\frac{ 8 }{ 5 }\)**

**Ans. 8) **(i) Draw a number line. Mark 0 as the starting point and 1 as the ending point. Then divide 0 to 1 in four equal parts, where each part is equal to \(\frac{1 }{ 4 }\)

Show the consecutive parts as \(\frac{ 1 }{ 4 }\) , \(\frac{ 1 }{ 2 }\) , \(\frac{ 3 }{ 4 }\) and at 1 show \(\frac{ 4 }{ 4 }\)

= 1.

(ii) Draw 0 to 1 on a number line. Divide the segment into 8 equal parts, each part corresponds to 1/8. Show the consecutive parts as 1/8 , 2/8 , 3/8 , 4/8 , 5/8 , 6/8 , 7/8 and 8/8. Highlight the required ones only.

(iii) Draw 0 to 2 on a number line. Divide the line segment between 0 and 1 into 5 equal parts , where each part is equal to 1/5.

Show 2/5 , 3/5 , 4/5 and 8/5 3 parts away from 1 towards 2. ( 1< 8/5 < 2 )