## Maharashtra State Board Class 8 Maths Solutions Chapter 1 Rational and Irrational Numbers Practice Set 1.2

Question 1.

Compare the following numbers.

i. 7, -2

ii. 0, \(\frac { -9 }{ 5 }\)

iii. \(\frac { 8 }{ 7 }\), 0

iv. \(-\frac{5}{4}, \frac{1}{4}\)

v. \(\frac{40}{29}, \frac{141}{29}\)

vi. \(-\frac{17}{20},-\frac{13}{20}\)

vii. \(\frac{15}{12}, \frac{7}{16}\)

viii. \(-\frac{25}{8},-\frac{9}{4}\)

ix. \(\frac{12}{15}, \frac{3}{5}\)

x. \(-\frac{7}{11},-\frac{3}{4}\)

Solution:

i. 7, -2

If a and b are positive numbers such that a < b, then -a > -b.

Since, 2 < 7 ∴ -2 > -7

ii. 0, \(\frac { -9 }{ 5 }\)

On a number line, \(\frac { -9 }{ 5 }\) is to the left of zero.

∴ 0 > \(\frac { -9 }{ 5 }\)

iii. \(\frac { 8 }{ 7 }\), 0

On a number line, zero is to the left of \(\frac { 8 }{ 7 }\) .

∴ \(\frac { 8 }{ 7 }\) > 0

iv. \(-\frac{5}{4}, \frac{1}{4}\)

We know that, a negative number is always less than a positive number.

∴ \(-\frac{5}{4}<\frac{1}{4}\)

v. \(\frac{40}{29}, \frac{141}{29}\)

Here, the denominators of the given numbers are the same.

Since, 40 < 141

∴ \(\frac{40}{29}<\frac{141}{29}\)

vi. \(-\frac{17}{20},-\frac{13}{20}\)

Here, the denominators of the given numbers are the same.

Since, 17 < 13

∴ -17 < -13

∴ \(-\frac{17}{20}<-\frac{13}{20}\)

vii. \(\frac{15}{12}, \frac{7}{16}\)

Here, the denominators of the given numbers are not the same.

LCM of 12 and 16 = 48

Alternate method:

15 × 16 = 240

12 × 7 = 84

Since, 240 > 84

∴ 15 × 16 > 12 × 7

viii. \(-\frac{25}{8},-\frac{9}{4}\)

Here, the denominators of the given numbers are not the same.

LCM of 8 and 4 = 8

ix. \(\frac{12}{15}, \frac{3}{5}\)

Here, the denominators of the given numbers are not the same.

LCM of 15 and 5 = 15

x. \(-\frac{7}{11},-\frac{3}{4}\)

Here, the denominators of the given numbers are not the same.

LCM of 11 and 4 = 44

**Maharashtra Board Class 8 Maths Solutions Chapter 1 Rational and Irrational Numbers Practice Set 1.2 Questions and Activities**

Question 1.

Verify the following comparisons using a number line. (Textbook pg. no, .3)

i. 2 < 3 but – 2 > – 3

ii. \(\frac{5}{4}<\frac{7}{4}\) but \(\frac{-5}{4}<\frac{-7}{4}\)

Solution:

We know that, on a number line the number to the left is smaller than the other.

∴ 2 < 3 and -3 < -2

i.e. 2 < 3 and -2 > -3