RS Aggarwal Solutions Class 6 Ex 5B

Q1) Define like and unlike fractions and give five examples of each.

Ans. 1) Like Fractions:

Fractions having the same denominator are called like fractions.

Examples: \( \frac { 3 }{ 11 }\) , \( \frac { 5 }{ 11 }\) , \( \frac { 7 }{ 11 }\) , \( \frac { 9 }{ 11 }\) , \( \frac { 10 }{ 11 }\)

Unlike Fractions:

Fractions having different denominators are called unlike fractions.

Examples: \( \frac { 3 }{ 4 }\) , \( \frac { 4 }{ 5 }\) , \( \frac { 6 }{ 7 }\) , \( \frac { 9 }{ 11 }\) , \( \frac { 2 }{ 13 }\)

Q2) Convert \( \frac { 3 }{ 5 }\) , \( \frac { 7 }{ 10 }\) , \( \frac { 8 }{ 15 }\) and \( \frac { 11 }{ 30 }\) into like fractions.

Ans. 2) The given fractions are \( \frac { 3 }{ 5 }\) , \( \frac { 7 }{ 10 }\) , \( \frac { 8 }{ 15 }\) and \( \frac { 13 }{ 30 }\)

L.C.M. of 5, 10, 15 and 30 = ( 5 x 2 x 3 ) = 30

So, we convert the given fractions into equivalent fractions with 30 as the denominator. (But, one of the fractions already has 30 as its denominator. So, there is no need to convert it into an equivalent fraction. )

Thus, we have:

\( \frac { 3 }{ 5 } = \frac { 3 \times 6 }{ 5 \times 6 } = \frac { 18 }{ 30 }\)

\( \frac { 7 }{ 10 } = \frac { 7 \times 3 }{ 10 \times 3 } = \frac { 21 }{ 30 }\)

\( \frac { 8 }{ 15 } = \frac { 8 \times 2 }{ 15 \times 2 } = \frac { 16 }{ 30 }\)

Hence, the required like fractions are \( \frac { 18 }{ 30 }\) , \( \frac { 21 }{ 30 }\) , \( \frac { 16 }{ 30 }\) and \( \frac { 11 }{ 30 }\) .

Q3) Convert \( \frac { 1 }{ 4 }\) , \( \frac { 5 }{ 8 }\) , \( \frac { 7 }{ 12 }\) and \( \frac { 13 }{ 24 }\) into like fractions.

Ans. 3) The given fractions are \( \frac { 1 }{ 4 }\) , \( \frac { 5 }{ 8 }\) , \( \frac { 7 }{ 12 }\) and \( \frac { 13 }{ 24 }\)

L.C.M. of 4, 8, 12 and 24 = ( 4 x 2 x 3 ) = 24

So, we convert the given fractions into equivalent fractions with 24 as the denominator. (But, one of the fractions already has 24 as the denominator. So, there is no need to convert it into an equivalent fraction. )

Thus, we have:

\( \frac { 1 }{ 4 } = \frac { 1 \times 6 }{ 4 \times 6 } = \frac { 6 }{ 24 }\)

\( \frac { 5 }{ 8 } = \frac { 5 \times 3}{ 8 \times 3 } = \frac { 15 }{ 24 }\)

\( \frac { 7 }{ 12 } = \frac { 7 \times 2 }{ 12 \times 2 } = \frac { 14 }{ 24 }\)

Hence, the required like fractions are \( \frac { 6 }{ 24 }\) , \( \frac { 15 }{ 24 }\) , \( \frac { 14 }{ 24 }\) and \( \frac { 13 }{ 24 }\)

Q4) Fill in the pace holders with the correct symbol > or < :

(i) \( \frac { 8 }{ 9 } — \frac { 5 }{ 9 }\)
(ii) \( \frac { 9 }{ 10 } — \frac { 7 }{ 10 }\)
(iii) \( \frac { 3 }{ 7 } — \frac { 6 }{ 7 }\)

(iv)\( \frac { 11 }{ 15 }– \frac { 8 }{ 15 }\)

(v) \( \frac { 6 }{ 11 }– \frac { 5 }{ 11 }\)

(vi) \( \frac { 11 }{ 20 }– \frac { 17 }{ 20 }\)
Ans. 4) (i) >

(ii) >

(iii) <

(iv) >

(v) >

(vi) <

Q5) Fill in the place holders with the correct symbol > or < :

(i) \( \frac { 3 }{ 4 } \;– \;\frac { 3 }{ 5 }\)

(ii) \( \frac { 7 }{ 8 } \;–\;\frac { 7 }{ 10 }\)

(iii) \( \frac { 4 }{ 11 } \;–\;\frac { 4 }{ 9 }\)

(iv) \( \frac { 8 }{ 11 } \;–\;\frac { 8 }{ 13 }\)

(v) \( \frac { 5 }{ 12 } \;–\;\frac { 5 }{ 8 }\)

(vi) \( \frac { 11 }{ 14 } \;–\;\frac { 11 }{ 15 }\)

Ans. 5) Between two fractions with the same numerator, the one with the smaller denominator is the greater of the two.

(i) >

(ii) >

(iii) <

(iv) >

(v) <

(vi) >

Compare the fractions given below :

Q6) \( \frac { 4 }{ 5 }\) , \( \frac { 5 }{ 7 }\)

Ans. 6) \( \frac { 4 }{ 5 }\) , \( \frac { 5 }{ 7 }\)

By cross multiplying :

5 x 5 = 25 and 4 x 7 = 28

Clearly, 28 > 25

Therefore, \( \frac { 4 }{ 5 }\)> \( \frac { 5 }{ 7 }\)

Q7) \( \frac { 3 }{ 8 }\) , \( \frac { 5 }{ 6 }\)

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

By cross multiplying :

3 x 6 = 18 and 5 x 8 = 40

Clearly, 18 < 40

Therefore, \( \frac { 3 }{ 8 }\)<\( \frac { 5 }{ 6 }\)

Q8) \( \frac { 7 }{ 11 }\) , \( \frac { 6 }{ 7 }\)

Ans. 8) \( \frac { 7 }{ 11 }\) , \( \frac { 6 }{ 7 }\)

By cross multiplying :

7 x 7 = 49 and 11 x 6 = 66

Clearly, 49 < 66

Therefore, \( \frac { 7 }{ 11 }\)< \( \frac { 6 }{ 7 }\)

Q9) \( \frac { 5 }{ 6 }\) , \( \frac { 9 }{ 11 }\)

Ans. 9) \( \frac { 5 }{ 6 }\) , \( \frac { 9 }{ 11 }\)

By cross multiplying :

5 x 11 = 55 and 9 x 6 = 54

Clearly, 55 > 54

Therefore, \( \frac { 5 }{ 6 }\)< \( \frac { 9 }{ 11 }\)

Q10) \( \frac { 2 }{ 3 }\) , \( \frac { 4 }{ 9 }\)

Ans. 10) \( \frac { 2 }{ 3 }\) , \( \frac { 4 }{ 9 }\)

By cross multiplying :

2 x 9 = 18 and 4 x 3 = 12

Clearly, 18 > 12

Therefore, \( \frac { 2 }{ 3 }\)> \( \frac { 4 }{ 9 }\)

Q11) \( \frac { 6 }{ 13 }\) , \( \frac { 2 }{ 4 }\)

Ans. 11) \( \frac { 6 }{ 13 }\) , \( \frac { 2 }{ 4 }\)

By cross multiplying :

6 x 4 = 24 and 13 x 3 = 39

Clearly, 24 < 39

Therefore, \( \frac { 6 }{ 13 }\)< \( \frac { 3 }{ 4 }\)

Q12) \( \frac { 3 }{ 4 }\) , \( \frac { 5 }{ 6 }\)

Ans. 8) \( \frac { 3 }{ 4 }\) , \( \frac { 5 }{ 6 }\)

By cross multiplying :

3 x 6 = 18 and 4 x 5 = 20

Clearly, 18 < 20

Therefore, \( \frac { 3 }{ 4 }\)< \( \frac { 5 }{ 6 }\)

Q13) \( \frac { 5 }{ 8 }\) , \( \frac { 7 }{ 12 }\)

Ans. 13) \( \frac { 5 }{ 8 }\) , \( \frac { 7 }{ 12 }\)

By cross multiplying :

5 x 12 = 60 and 8 x 7 = 56

Clearly, 60 > 56

Therefore, \( \frac { 5 }{ 8 }\)>\( \frac { 7 }{ 12 }\)

Q14) \( \frac { 4 }{ 9 }\) , \( \frac { 6 }{ 7 }\)

Ans. 14) L.C.M. of 9 and 6 = ( 3 x 3 x 2 ) = 18

Now, we convert \( \frac { 4 }{ 9 }\) and \( \frac { 6 }{ 7 }\) into equivalent fractions having 18 as the denominator.

Therefore, \( \frac { 4 }{ 9 } = \frac { 4 \times 2 }{ 9 \times 2 } = \frac { 8 }{ 18 }\) and \( \frac { 5 }{ 6 } = \frac { 5 \times 3 }{ 6 \times 3 } = \frac { 15 }{ 18 }\)

Clearly, \( \frac { 8 }{ 18 }\)<\( \frac { 15 }{ 18 }\)

Therefore \( \frac { 4 }{ 9 }\)< \( \frac { 5 }{ 6 }\)

Q15) \( \frac { 4 }{ 5 }\) , \( \frac { 7 }{ 10 }\)

Ans. 15) L.C.M. of 5 and 10 = ( 5 x 2 ) = 10

Now, we convert \( \frac { 4 }{ 5 }\) into an equivalent fractions having 10 as the denominator as the other fraction has already 10 as its denominator.

Therefore, \( \frac { 4 }{ 5 } = \frac { 4 \times 2 }{ 5 \times 2 } = \frac { 8 }{ 10 }\)

Clearly, \( \frac { 8 }{ 10 }\)>\( \frac { 7 }{ 10 }\)

Therefore, \( \frac { 4 }{ 5 }\)> \( \frac { 7 }{ 10 }\)

Q16) \( \frac { 7 }{ 8 }\) , \( \frac { 9 }{ 10 }\)

Ans. 14) L.C.M. of 8 and 10 = ( 2 x 5 x 2 x 2 ) = 40

Now, we convert \( \frac { 7 }{ 8 }\) and \( \frac { 9 }{ 10 }\) into equivalent fractions having 40 as the denominator.

Therefore, \( \frac { 7 }{ 8 } = \frac { 7 \times 5 }{ 8 \times 5 } = \frac { 35 }{ 40 }\) and \( \frac { 9 }{ 10 } = \frac { 9 \times 4 }{ 10 \times 4 } = \frac { 36 }{ 40 }\)

Clearly, \( \frac { 35 }{ 40 }\)<\( \frac { 36 }{ 40 }\)

Therefore \( \frac { 7 }{ 8 }\)< \( \frac { 9 }{ 10 }\)

Q17) \( \frac { 11 }{ 12 }\) , \( \frac { 11 }{ 15 }\)

Ans. 17) L.C.M. of 12 and 15 = ( 2 x 2 x 3 x 5 ) = 60

Now, we convert \( \frac { 11 }{ 12 }\) and \( \frac { 13 }{ 15 }\) into equivalent fractions having 60 as the denominator.

Therefore, \( \frac { 11 }{ 12 } = \frac { 11 \times 5 }{ 12 \times 5 } = \frac { 55 }{ 60 }\) and \( \frac { 13 }{ 15 } = \frac { 13 \times 4 }{ 15 \times 4 } = \frac { 52 }{ 60 }\)

Clearly, \( \frac { 55 }{ 60 }\)>\( \frac { 52 }{ 60 }\)

Therefore \( \frac { 11 }{ 12 }\)> \( \frac { 13 }{ 15 }\) .

Arrange the following fractions in ascending order:

Q18) \( \frac { 1 }{ 2 }\) , \( \frac { 3 }{ 4 }\) , \( \frac { 5 }{ 6 }\) and \( \frac { 7 }{ 8 }\)

Ans. 18)

The given fractions are \( \frac { 1 }{ 2 }\) , \( \frac { 3 }{ 4 }\) , \( \frac { 5 }{ 6 }\) and \( \frac { 7 }{ 8 }\)

L.C.M. of 2, 4, 6 and 8 = ( 2 x 2 x 2 x 3 ) = 24

We convert each of the given fractions into an equivalent fraction with denominator 24. Now, we have:

\( \frac { 1 }{ 2 } = \frac { 1 \times 12 }{ 2 \times 12 } = \frac { 12 }{ 24 }\)

\( \frac { 3 }{ 4 } = \frac { 3 \times 6 }{ 4 \times 6 } = \frac { 18 }{ 24 }\)

\( \frac { 5 }{ 6 } = \frac { 5 \times 4 }{ 6 \times 4 } = \frac { 20 }{ 24 }\)

\( \frac { 7 }{ 8 } = \frac { 7 \times 3 }{ 8 \times 3 } = \frac { 21 }{ 24 }\)

Clearly, \( \frac { 12 }{ 24 }\)< \( \frac { 18 }{ 24 }\)< \( \frac { 20 }{ 24 }\)<\( \frac { 21 }{ 24 }\)

Therefore, \( \frac { 1 }{ 2 }\)< \( \frac { 3 }{ 4 }\)< \( \frac { 5 }{ 6 }\)<\( \frac { 7 }{ 8 }\)

Hence, the given fractions can be arranged in the ascending order as follows:

\( \frac { 1 }{ 2 }\) , \( \frac { 3 }{ 4 }\) , \( \frac { 5 }{ 6 }\) , \( \frac { 7 }{ 8 }\)

Q19) \( \frac { 2 }{ 3 }\) , \( \frac { 5 }{ 6 }\) , \( \frac { 7 }{ 9 }\) and \( \frac { 11 }{ 18 }\)

Ans. 19) The given fractions are \( \frac { 2 }{ 3 }\) , \( \frac { 5 }{ 6 }\) , \( \frac { 7 }{ 9 }\) and \( \frac { 11 }{ 18 }\)

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

We convert each of the given fractions whose denominator is not equal to 18 into an equivalent fraction with denominator 18. Now, we have:

\( \frac { 2 }{ 3 } = \frac { 2 \times 6 }{ 3 \times 6 } = \frac { 12 }{ 18 }\)

\( \frac { 5 }{ 6 } = \frac { 5 \times 3 }{ 6 \times 3 } = \frac { 15 }{ 18 }\)

\( \frac { 7 }{ 9 } = \frac { 7 \times 2 }{ 9 \times 2 } = \frac { 14 }{ 18 }\)

Clearly, \( \frac { 11 }{ 18 }\)< \( \frac { 12 }{ 18 }\)< \( \frac { 14 }{ 18 }\)<\( \frac { 15 }{ 18 }\)

Therefore, \( \frac { 11 }{ 18 }\)< \( \frac { 2 }{ 3 }\)< \( \frac { 7 }{ 9 }\)<\( \frac { 5 }{ 6 }\)

Hence, the given fractions can be arranged in the ascending order as follows:

\( \frac { 11 }{ 18 }\) , \( \frac { 2 }{ 3 }\) , \( \frac { 7 }{ 9 }\) , \( \frac { 5 }{ 6 }\)

Q20) \( \frac { 2 }{ 5 }\) , \( \frac { 3 }{ 4 }\) , \( \frac { 11 }{ 15 }\) and \( \frac { 17 }{ 30 }\)

Ans. 20) The given fractions are \( \frac { 2 }{ 5 }\) , \( \frac { 7 }{ 10 }\) , \( \frac { 11 }{ 15 }\) and \( \frac { 17 }{ 30 }\)

L.C.M. of 5, 10, 15 and 30 = ( 2 x 5 x 3 ) = 30

So, we convert each of the given fractions whose denominator is not equal to 30 into an equivalent fraction with denominator 30.

Now, we have:

\( \frac { 2 }{ 5 } = \frac { 2 \times 6 }{ 5 \times 6 } = \frac { 12 }{ 30 }\)

\( \frac { 7 }{ 10 } = \frac { 7 \times 3 }{ 10 \times 3 } = \frac { 21 }{ 30 }\)

\( \frac { 11 }{ 15 } = \frac { 11 \times 2 }{ 15 \times 2 } = \frac { 22 }{ 30 }\)

Clearly, \( \frac { 12 }{ 30 }\)< \( \frac { 17 }{ 30 }\)< \( \frac { 21 }{ 30 }\)<\( \frac { 22 }{ 30 }\)

Therefore, \( \frac { 2 }{ 5 }\)< \( \frac { 17 }{ 30 }\)< \( \frac { 7 }{ 10 }\)<\( \frac { 11 }{ 15 }\)

Hence, the given fractions can be arranged in the ascending order as follows:

\( \frac { 2 }{ 5 }\) , \( \frac { 17 }{ 30 }\) , \( \frac { 7 }{ 10 }\) , \( \frac { 11 }{ 15 }\)

Q21) \( \frac { 2 }{ 5 }\) , \( \frac { 3 }{ 4 }\) , \( \frac { 11 }{ 15 }\) and \( \frac { 17 }{ 30 }\)

Ans. 20) The given fractions are \( \frac { 2 }{ 5 }\) , \( \frac { 7 }{ 10 }\) , \( \frac { 11 }{ 15 }\) and \( \frac { 17 }{ 30 }\)

L.C.M. of 5, 10, 15 and 30 = ( 2 x 5 x 3 ) = 30

So, we convert each of the given fractions whose denominator is not equal to 30 into an equivalent fraction with denominator 30.

Now, we have:

\( \frac { 3 }{ 4 } = \frac { 3 \times 8 }{ 4 \times 8 } = \frac { 24 }{ 32 }\)

\( \frac { 7 }{ 8 } = \frac { 7 \times 4 }{ 8 \times 4 } = \frac { 28 }{ 32 }\)

\( \frac { 11 }{ 16 } = \frac { 11 \times 2 }{ 16 \times 2 } = \frac { 22 }{ 32 }\)

Clearly, \( \frac { 22 }{ 32 }\)< \( \frac { 23 }{ 32 }\)< \( \frac { 24 }{ 32 }\)<\( \frac { 28 }{ 32 }\)

Therefore, \( \frac { 11 }{ 16 }\)< \( \frac { 23 }{ 32 }\)< \( \frac { 3 }{ 4 }\)<\( \frac { 7}{ 8 }\)

Hence, the given fractions can be arranged in the ascending order as follows:

\( \frac { 11 }{ 16 }\) , \( \frac { 23 }{ 32 }\) , \( \frac { 3 }{ 4 }\) , \( \frac { 7 }{ 8 }\)

Arrange the following fractions in descending order:

Q22) \( \frac { 3 }{ 4 }\) , \( \frac { 5 }{ 8 }\) , \( \frac { 11 }{ 12 }\) and \( \frac { 17 }{ 24 }\)

Ans. 22) The given fractions are \( \frac { 3 }{ 4 }\) , \( \frac { 5 }{ 8 }\) , \( \frac { 11 }{ 12 }\) and \( \frac { 17 }{ 24 }\)

L.C.M. of 4, 8, 12 and 24 = ( 2 x 2 x 2 x 3 ) = 24

So, we convert each of the fractions whose denominator is not equal to 24 into equivalent fractions with denominator 24.

Now, we have:

\( \frac { 3 }{ 4 } = \frac { 3 \times 6 }{ 4 \times 6 } = \frac { 18 }{ 24 }\)

\( \frac { 7 }{ 8 } = \frac { 7 \times 3 }{ 8 \times 3 } = \frac { 15 }{ 24 }\)

\( \frac { 11 }{ 12 } = \frac { 11 \times 2 }{ 12 \times 2 } = \frac { 22 }{ 24 }\)

Clearly, \( \frac { 22 }{ 24 }\)> \( \frac { 18 }{ 24 }\)> \( \frac { 17 }{ 24 }\)>\( \frac { 15 }{ 24 }\)

Therefore, \( \frac { 11 }{ 12 }\)> \( \frac { 3 }{ 4 }\)> \( \frac { 17 }{ 24 }\)>\( \frac { 5 }{ 8 }\)

Hence, the given fractions can be arranged in the descending order as follows:

\( \frac { 11 }{ 12 }\) , \( \frac { 3 }{ 4 }\) , \( \frac { 17 }{ 24 }\) , \( \frac { 5 }{ 8 }\)

Q23)\( \frac { 7 }{ 9 }\) , \( \frac { 5 }{ 12 }\) , \( \frac { 11 }{ 18 }\) and \( \frac { 17 }{ 36 }\)

Ans. 23) The given fractions are \( \frac { 7 }{ 9 }\) , \( \frac { 5 }{ 12 }\) , \( \frac { 11 }{ 18 }\) and \( \frac { 17 }{ 36 }\)

L.C.M. of 9, 12, 18 and 36 = ( 3 x 3 x 2 x 2 ) = 36

We convert each of the fractions whose denominator is not equal to 30 into an equivalent fractions with denominator 36.

Now, we have:

\( \frac { 7 }{ 9 } = \frac { 7 \times 4 }{ 9 \times 4 } = \frac { 28 }{ 36 }\)

\( \frac { 5 }{ 12 } = \frac { 5 \times 3 }{ 12 \times 3 } = \frac { 15 }{ 36 }\)

\( \frac { 11 }{ 18 } = \frac { 11 \times 2 }{ 18 \times 2 } = \frac { 22 }{ 36}\)

Clearly, \( \frac { 28 }{ 36 }\)> \( \frac { 22 }{ 36 }\)> \( \frac { 17 }{ 36 }\)>\( \frac { 15 }{ 36 }\)

Therefore, \( \frac { 7 }{ 9 }\)> \( \frac { 11 }{ 18 }\)> \( \frac { 17 }{ 36 }\)>\( \frac { 5 }{ 12 }\)

Hence, the given fractions can be arranged in the descending order as follows:

\( \frac { 7 }{ 9 }\) , \( \frac { 11 }{ 18 }\) , \( \frac { 17 }{ 36 }\) , \( \frac { 5 }{ 12 }\)

Q24) \( \frac { 2 }{ 3 }\) , \( \frac { 3 }{ 5 }\) , \( \frac { 7 }{ 10 }\) and \( \frac { 8 }{ 15 }\)

Ans. 24) The given fractions are \( \frac { 2 }{ 3 }\) , \( \frac { 3 }{ 5 }\) , \( \frac { 7 }{ 10 }\) and \( \frac { 8 }{ 15 }\)

L.C.M. of 3, 5, 10 and 15 = ( 2 x 3 x 5 ) = 30

So, we convert each of the fractions whose denominator is not equal to 30 into an equivalent fractions with denominator 30.

Thus, we have:

\( \frac { 2 }{ 3 } = \frac { 2 \times 10 }{ 3 \times 10 } = \frac { 20 }{ 30 }\)

\( \frac { 3 }{ 5 } = \frac { 3 \times 6 }{ 5 \times 6 } = \frac { 18 }{ 30 }\)

\( \frac { 7 }{ 10 } = \frac { 7 \times 3 }{ 10 \times 3 } = \frac { 21 }{ 30}\)

\( \frac { 8 }{ 15 } = \frac { 8 \times 2 }{ 15\times 2 } = \frac { 16 }{ 30 }\)

Clearly, \( \frac { 21 }{ 30 }\)> \( \frac { 20 }{ 30 }\)> \( \frac { 18 }{ 30 }\)>\( \frac { 16 }{ 30 }\)

Therefore, \( \frac { 7 }{ 10 }\)> \( \frac { 2 }{ 3 }\)> \( \frac { 3 }{ 5 }\)>\( \frac { 8 }{ 15 }\)

Hence, the given fractions can be arranged in the descending order as follows:

\( \frac { 7 }{ 10 }\) , \( \frac { 2 }{ 3 }\) , \( \frac { 3 }{ 5 }\) , \( \frac { 8 }{ 15 }\)

Q25) \( \frac { 5 }{ 7 }\) , \( \frac { 9 }{ 14 }\) , \( \frac { 17 }{ 21 }\) and \( \frac { 31 }{ 42 }\)

Ans. 22) The given fractions are \( \frac { 5 }{ 7 }\) , \( \frac { 9 }{ 14 }\) , \( \frac { 17 }{ 21 }\) and \( \frac { 31 }{ 42 }\)

L.C.M. of 7, 14, 21 and 42 = ( 2 x 3 x 7 ) = 42

We convert each of the fractions whose denominator is not equal to 42 into equivalent fractions with denominator 42.

Thus, we have:

\( \frac { 5 }{ 7 } = \frac { 5 \times 6 }{ 7 \times 6 } = \frac { 30 }{ 42 }\)

\( \frac { 9 }{ 14 } = \frac { 9 \times 3 }{ 14 \times 3 } = \frac { 27 }{ 42 }\)

\( \frac { 17 }{ 21 } = \frac { 17 \times 2 }{ 21\times 2 } = \frac { 34 }{ 42}\)

Clearly, \( \frac { 34 }{ 42 }\)> \( \frac { 31 }{ 42 }\)> \( \frac { 30 }{ 42 }\)>\( \frac { 27 }{ 42 }\)

Therefore, \( \frac { 17 }{ 21 }\)> \( \frac { 31 }{ 42 }\)> \( \frac { 5 }{ 7 }\)>\( \frac { 9 }{ 14 }\)

Hence, the given fractions can be arranged in the descending order as follows:

\( \frac { 17 }{ 21 }\) , \( \frac { 31 }{ 42 }\) , \( \frac { 5 }{ 7 }\) , \( \frac { 9 }{ 14 }\)

Q26) \( \frac { 1 }{ 12 }\) , \( \frac { 1 }{ 23 }\) , \( \frac { 1 }{ 7 }\) , \( \frac { 1 }{ 9 }\) , \( \frac { 1 }{ 17 }\) , \( \frac { 1 }{ 50 }\)

Ans. 26) The given fractions are \( \frac { 1 }{ 12 }\) , \( \frac { 1 }{ 23 }\) , \( \frac { 1 }{ 7 }\) , \( \frac { 1 }{ 9 }\) , \( \frac { 1 }{ 17 }\) and \( \frac { 1 }{ 50 }\)

As the fractions have the same numerator, we can follow the rule for the comparison of such fractions. This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.

Clearly, \( \frac { 1 }{ 7 }\)> \( \frac { 1 }{ 9 }\)> \( \frac { 1 }{ 12 }\)> \( \frac { 1 }{ 12 }\)> \( \frac { 1 }{ 23 }\)> \( \frac { 1 }{ 50 }\)

Hence, the given fractions can be arranged in the descending order as follows:

\( \frac { 1 }{ 7 }\) , \( \frac { 1 }{ 9 }\) , \( \frac { 1 }{ 12 }\) , \( \frac { 1 }{ 12 }\) , \( \frac { 1 }{ 23 }\) , \( \frac { 1 }{ 50 }\)

Q27) \( \frac { 3 }{ 7 }\) , \( \frac { 3 }{ 11 }\) , \( \frac { 3 }{ 5 }\) , \( \frac { 3 }{ 13 }\) , \( \frac { 3 }{ 4 }\) , \( \frac { 3 }{ 17 }\)

Ans. 26) The given fractions are \( \frac { 3 }{ 7 }\) , \( \frac { 3 }{ 11 }\) , \( \frac { 3 }{ 5 }\) , \( \frac { 3 }{ 13 }\) , \( \frac { 3 }{ 4 }\) and \( \frac { 3 }{ 17 }\)

As the fractions have the same numerator, so we can follow the rule for the comparison of such fractions.

This rule states that when two fractions have the same numerator, the fraction having the smaller denominator is the greater one.

Clearly, \( \frac { 3 }{ 4 }\)> \( \frac { 3 }{ 5 }\)> \( \frac { 3 }{ 7 }\)> \( \frac { 3 }{ 11 }\)> \( \frac { 3 }{ 13 }\)> \( \frac { 3 }{ 17 }\)

Hence, the given fractions can be arranged in the descending order as follows:

\( \frac { 3 }{ 4 }\) , \( \frac { 3 }{ 5 }\) , \( \frac { 3 }{ 7 }\) , \( \frac { 3 }{ 7 }\) , \( \frac { 3 }{ 11 }\) , \( \frac { 3 }{ 17 }\)

Q28) Laila read 30 pages of a book containing 100 pages while Sarita read \( \frac { 2 }{ 5 }\) of the book. Who read more?

Ans. 28) Lalita read 30 pages of a book having 100 pages.

Sarita read \( \frac { 2 }{ 5 }\) of the same book.

\( \frac { 2 }{ 5 }\) of 100 pages = \( \frac { 2 }{ 5 }\) x 100 = \( \frac { 200 }{ 5 }\) = 40 pages

Hence, Sarita read more pages than Lalita as 40 is greater than 30.

Q29) Rafiq exercised for \( \frac { 2 }{ 3 }\) hour, while Rohit exercised for \( \frac { 3 }{ 4 }\) hour. Who exercised for longer time?

Ans. 29) To know who exercised for a longer time, we have to compare \( \frac { 2 }{ 3 }\) hour with \( \frac { 3 }{ 4 }\) hour

On cross multiplying:

4 x 2 = 8 and 3 x 3 = 9

Clearly, 8 < 9

Therefore, \( \frac { 2 }{ 3 }\) hour < \( \frac { 3 }{ 4 }\) hour

Hence, Rohit exercised for a longer time.

Q30) In a school 20 students out of 25 passed in VI A, while 24 out of 30 passed in VI B. Which section gave a better result?

Ans. 30) Fraction of student who passed in VI A = \( \frac { 20 }{ 25 }\) = \( \frac { 20 \div 5 }{ 25 \div 5 } = \frac { 4 }{ 5 }\)

Fraction of student who passed in VI B = \( \frac { 24 }{ 30 }\) = \( \frac { 24 \div 6 }{ 30 \div 6 } = \frac { 4 }{ 5 }\)

In both the sections, the fraction of students who passed is the same, so both the sections have the same result.


Practise This Question

When the chemicals in a cell get used up, then: