RS Aggarwal Class 6 Solutions 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 ‘ > ’ , ‘ < ‘ or ‘ = ‘ :

(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 )


Practise This Question

Identify the disease shown in the given image and its cause.