# RS Aggarwal Solutions Class 6 Ex 5D

Mark against the correct answer in each of the following:

Q1 ) A fraction equivalent to $\frac{ 3 }{ 5 }$ is

(a) $\frac{3 + 2}{5 + 2}$

(b) $\frac{3 -2}{5 – 2}$

(c) $\frac{3 \times 2}{5 \times 2}$

(d) none of these

Ans. 1) (c) $\frac{3 \times 2}{5 \times 2}$

Q2) A fraction equivalent to $\frac{ 8 }{ 2 }$ is

(a) $\frac{ 8 + 4 }{ 12 + 4 }$

(b) $\frac{ 8 -4 }{ 12 – 4 }$

(c) $\frac{ 8 \div 4 }{ 12 \div 4 }$

(d) none of these

Ans. 2) (c) $\frac{ 8 \div 4 }{ 12 \div 4 }$

Q3) A fraction equivalent to $\frac{ 24 }{ 36 }$

(a) $\frac{ 3 }{ 4 }$

(b) $\frac{ 2 }{ 3 }$

(c) $\frac{ 8 }{ 9 }$

(d) none of these

Ans. 3) (b) $\frac{ 2 }{ 3 }$

Factors of 24 are 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24 .

Factors of 36 are 1 , 2 , 3, 4 , 6 , 9 , 12 , 18 , 36.

Common Factors of 24 and 36 are 1 , 2 , 3, 4 , 6 , 12.

H.C.F. = 12

Dividing both the numerator and the denominator by 12 :

$\frac{ 24 }{ 36 }$

= $\frac{ 24 \div 12 }{ 36 \div 12 }$

=$\frac{ 2 }{ 3 }$

Q4) If $\frac{ 3 }{ 4 }$ is equivalent to $\frac{ x }{ 20 }$ then the value of x is

(a) 15 (b) 18 (c) 12 (d) none of these

Ans. 4) (a) 15

Explanation:

$\left (\frac{ 3 }{ 4 } = \frac{ x }{ 20 } \right )$

We have:

20 = 4 x 5

So, we have to multiply the numerator by 5.

Therefore, x = 3 x 5 = 15

Q5) If $\frac{ 45 }{ 60 }$ is equivalent to $\frac{ 3 }{ x }$ then the value of x is

(a) 4 (b) 5 (c) 6 (d) 20

Ans. 5) (a) 4

Explanation:

$\left (\frac{ 45 }{ 60 } = \frac{ 3 }{ x } \right )$

Now, 3 = 45 / 15

So, we have to divide the denominator by 15.

Therefore, x = 60 / 15 = 4

Q6) Which of the following are like fractions?

(a) $\frac{ 2 }{ 5 } , \frac{ 2 }{ 7 } , \frac{ 2 }{ 9 } , \frac{ 2 }{ 11 }$

(b) $\frac{ 2 }{ 3 } , \frac{ 3 }{ 4 } , \frac{ 4 }{ 5 } , \frac{ 5 }{ 6 }$

(c) $\frac{ 1 }{ 8 } , \frac{ 3 }{ 8 } , \frac{ 5 }{ 8 } , \frac{ 7 }{ 8 }$

(d) none of these

Ans. 6) (c) $\frac{ 1 }{ 8 } , \frac{ 3 }{ 8 } , \frac{ 5 }{ 8 } , \frac{ 7 }{ 8 }$

( Fractions having the same denominator are called like fractions .)

Q7) Which of the following is a proper fraction?

(a) $\frac{ 5 }{ 3 }$

(b) 5

(c) $1 \frac{ 2 }{ 5 }$

(d) none of these

Ans. 7) (d) none of these

In a proper fraction , the numerator is less than the denominator.

Q8) Which of the following is a proper fraction?

(a) $\frac{ 7 }{ 8 }$

(b) $1 \frac{ 7 }{ 8 }$

(c)$\frac{ 8 }{ 7 }$

(d) none of these

Ans. 8) (a) $\frac{ 7 }{ 8 }$

In a proper fraction, the numerator is less than the denominator.

Q9) Which of the following statements are correct ?

(a) $\frac{ 3 }{ 4 } > \frac{ 3 }{ 5 }$

(b) $\frac{ 3 }{ 4 } < \frac{ 3 }{ 5 }$

(c) $\frac{ 3 }{ 4 } and \frac{ 3 }{ 5 }$ cannot be compared

Ans. 9) (b) $\frac{ 3 }{ 4 } < \frac{ 3 }{ 5 }$

Between the two fractions with the same numerator, the one with smaller denominator is the greater.

Q10) The smallest of the fractions $\frac{ 3 }{ 5 } , \frac{ 2 }{ 3 } , \frac{ 5 }{ 6 } , \frac{ 7 }{ 10 }$ is

(a) $\frac{ 2 }{ 3 }$

(b) $\frac{ 7 }{ 10 }$

(c) $\frac{ 3 }{ 5 }$

(d) $\frac{ 5 }{ 6 }$

Ans. 10) (c) $\frac{ 3 }{ 5 }$

L.C.M. of 5, 3, 6 and 10 = ( 2 x 3 x 5 ) = 30

Thus, we have:

$\frac{ 3 }{ 5 } = \frac{ 3 \times 6 }{ 5 \times 6 } = \frac{ 18 }{ 30 }$

$\frac{ 2 }{ 3 } = \frac{ 2 \times 10 }{ 3 \times 10 } = \frac{ 20 }{ 30 }$

$\frac{ 5 }{ 6 } = \frac{ 5 \times 5 }{ 6 \times 5 } = \frac{ 25 }{ 30 }$

$\frac{ 7 }{ 10 } = \frac{ 7 \times 3 }{ 10 \times 3 } = \frac{ 21 }{ 30 }$

Therefore, The smallest fraction = $\frac{ 18 }{ 30 }$

= $\frac{ 3 }{ 5 }$

Q11) The largest of the fractions $\frac{ 4 }{ 5 } , \frac{ 4 }{ 7 } , \frac{ 4 }{ 9 } , \frac{ 4 }{ 11 }$ is

(a) $\frac{ 4 }{ 11 }$

(b) $\frac{ 4 }{ 5 }$

(c) $\frac{ 4 }{ 7 }$

(d) $\frac{ 4 }{ 9 }$

Ans. 11) (b) $\frac{ 4 }{ 5 }$

Among the given fractions with same numerator, the one with smallest denominator is the greatest .

Q12) The smallest of the fractions $\frac{ 6 }{ 11 } , \frac{ 7 }{ 11 } , \frac{ 8 }{ 11 } , \frac{ 9 }{ 11 }$ is

(a) $\frac{ 6 }{ 11 }$

(b) $\frac{ 7 }{ 11 }$

(c) $\frac{ 8 }{ 11 }$

(d) $\frac{ 9 }{ 11 }$

Ans. 12) (a) $\frac{ 6 }{ 11 }$

Among like fractions, the fraction with the smallest numerator is the smallest.

Q13) The smallest of the fractions $\frac{ 3 }{ 4 } , \frac{ 5 }{ 6 } , \frac{ 7 }{ 12 } , \frac{ 2 }{ 3 }$ is

(a) $\frac{ 2 }{ 3 }$

(b) $\frac{ 3 }{ 4 }$

(c) $\frac{ 5 }{ 6 }$

(d) $\frac{ 7 }{ 12 }$

Ans. 13) (d) $\frac{ 7 }{ 12 }$

Explanation:

L.C.M. of 4, 6, 12 and 3 = ( 2 x 2 x 3 ) = 12

Thus , we have:

$\frac{ 3 }{ 5 } = \frac{ 3 \times 6 }{ 5 \times 6 } = \frac{ 18 }{ 30 }$

$\frac{ 2 }{ 3 } = \frac{ 2 \times 10 }{ 3 \times 10 } = \frac{ 20 }{ 30 }$

$\frac{ 5 }{ 6 } = \frac{ 5 \times 5 }{ 6 \times 5 } = \frac{ 25 }{ 30 }$

$\frac{ 7 }{ 12 }$

Clearly, $\frac{ 7 }{ 12 }$ is the smallest fraction.

Q14) $4 \frac{ 3 }{ 5 }$ = ?

(a) $\frac{ 17 }{ 5 }$

(b) $\frac{ 23 }{ 5 }$

(c) $\frac{ 17 }{ 3 }$

(d) none of these

Ans. 14) (b) $\frac{ 23 }{ 5 }$

Q15) $\frac{ 34 }{ 7 }$ = ?

(a) $3 \frac{ 4 }{ 7 }$

(b) $7 \frac{ 3 }{ 4 }$

(c) $4 \frac{ 6 }{ 7 }$

(d) none of these

Ans. 15) (c) $4 \frac{ 6 }{ 7 }$

On dividing 34 by 7:

Quotient = 4

Remainder = 6

$\frac{ 34 }{ 7 } \; = \; 4 \; + \; \frac{ 6 }{ 7 } \; = \; 4 \frac{ 6 }{ 7 }$

Q16) $\frac{ 5 }{ 8 } + \frac{ 1 }{ 8 }$ = ?

(a) $\frac{ 3 }{ 8 }$

(b) $\frac{ 3 }{ 4 }$

(c) 6

(d) none of these

Ans. 16) (b) $\frac{ 3 }{ 4 }$

Explanation:

Addition of like fractions = Sum of the numerators / Common denominator

= $\frac{ 5 }{ 8 } + \frac{ 1 }{ 8 }$

= $\frac{ ( 5 + 1 ) }{ 8 } \; = \; \frac{ 6 }{ 8 } \; = \; \frac{ 3 }{ 4 }$

Q17 ) $\frac{ 5 }{ 8 } – \frac{ 1 }{ 8 }$ = ?

(a) $\frac{ 1 }{ 4 }$

(b) $\frac{ 1 }{ 2 }$

(c) $\frac{ 1 }{ 16 }$

(d) none of these

Ans. 17) (b) $\frac{ 1 }{ 2 }$

Explanation:

$\frac{ 5 }{ 8 } – \frac{ 1 }{ 8 }$

= $\frac{ ( 5 – 1 ) }{ 8 } \; = \; \frac{ 4 }{ 8 } \; = \; \frac{ 1 }{ 2 }$

Q18) $3 \frac{ 3 }{ 4 } – 2 \frac{ 1 }{ 4 }$ = ?

(a) $1 \frac{ 1 }{ 2 }$

(b) $1 \frac{ 1 }{ 4 }$

(c) $\frac{ 1 }{ 4 }$

(d) none of these

Ans. 18) (a) $1 \frac{ 1 }{ 2 }$

Explanation:

$3 \frac{ 3 }{ 4 } – 2 \frac{ 1 }{ 4 }$

$3 \frac{ 3 }{ 4 } – 2 \frac{ 1 }{ 4 }$

$\frac{ ( 15 – 9 ) }{ 4 }$

$\frac{ 6 }{ 4 } = \frac{ 3 }{ 2 } = 1 \frac{ 1 }{ 2 }$

Q19) $\frac{ 5 }{ 6 } + \frac{ 2 }{ 3 } – \frac{ 4 }{ 9 }$ = ?

(a) $1 \frac{ 1 }{ 3 }$

(b) $1 \frac{ 1 }{ 6 }$

(c) $1 \frac{ 1 }{ 9 }$

(d) $1 \frac{ 1 }{ 18 }$

Ans. 19) (d) $1 \frac{ 1 }{ 18 }$

Explanation:

$\frac{ 5 }{ 6 } + \frac{ 2 }{ 3 } – \frac{ 4 }{ 9 }$

( L.C.M. of 3, 6 and 9 = ( 2 x 3 x 3 ) = 18 )

= $\frac{ (15 + 12 – 8) }{ 18 }$

[ 18 / 6 = 3 , 3 x 5 = 15 ] , [ 18 / 3 = 6 , 6 x 2 = 12 ] and [ 18 / 9 = 2 , 2 x 4 = 8 ]

= $\frac{ (27 – 8) }{ 18 } = \frac{ 19 }{ 18 } = 1\frac{ 1 }{ 18 }$

Q20) Which is greater: $3\frac{ 1 }{ 3 } \; or \; \frac{ 33 }{ 10 }$ ?

(a) $3 \frac{ 1 }{ 3 }$

(b) $\frac{ 33 }{ 10 }$

(c) both are equal

Ans. 20) (a) $3 \frac{ 1 }{ 3 }$

Explanation:

Let us compare $3 \frac{ 1 }{ 3 }$and $\frac{ 33 }{ 10 }$

or $\frac{ 10 }{ 3 }$ and $\frac{ 33 }{ 10 }$ .

10 x 10 = 100 and 3 x 33 = 99

Clearly, 100 < 99

Therefore, $\frac{ 10 }{ 3 } < \frac{ 33 }{ 10 }$ or

$3 \frac{ 1 }{ 3 } < \frac{ 33 }{ 10 }$

#### Practise This Question

Fill in the blanks:-

i)Number of factors of a given number is _____________

ii)Every multiple of a number is ____________ that number.

iii)Number of multiples of a given number is __________ .

iv)Every number is a multiple of ______________ .