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## Karnataka State Syllabus Class 7 Maths Chapter 9 Rational Numbers Ex 9.1

Question 1.

List five rational numbers between:

a) -1 and 0

Solution:

we see that

∴ Five rational numbers between -1 and 0 are

ii) -2 and -1

Solution:

we see that

∴ Five Rational Numbers between -2 and -1 are

iii)

Solution:

we see that

Thus five rational numbers between

iv)

Solution:

we see that

Thus 5 Rational Numbers in between \(\frac{1}{2}\) and \(\frac{2}{3}\) are

Question 2.

Write four more rational numbers in each of the following patterns :

i)

Solution:

Thus we came to know the pattern in the above numbers ie., both numerator and denominator should be multiplied by same whole number.

∴ The four more rational numbers would be

ii)

Solution:

Thus we observe the pattern in these numbers.

The other numbers would be,

iii)

Solution:

Thus we observe the pattern in these numbers. The other numbers would be,

iv)

Solution:

Thus we observe the pattern in these numbers

The other numbers would be

Question 3.

Give four rational numbers equivalent to :

i) \(\frac{-2}{7}\)

Four rational numbers equivalent to \(\frac{-2}{7}\) are

ii) \(\frac{5}{-3}\)

Four rational numbers equivalent to \(\frac{5}{-3}\) are

iii) \(\frac{4}{9}\)

Solution:

Four rational numbers equivalent to \(\frac{4}{9}\) are

Question 4.

Draw the number line and represent the following rational numbers on it :

i) \(\frac{3}{4}\)

Solution:

ii) \(\frac{-5}{8}\)

Solution:

iii) \(\frac{-7}{4}\)

Solution:

iv) \(\frac{7}{8}\)

Solution:

Question 5.

The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.

Solution:

The rational number represented by

The rational number represented by

The rational number represented by

The rational number represented by

The rational number represented by P Q R S is equal to respectively.

Question 6.

Which of the following pairs represent the same rational number ?

i)

Solution:

\(\frac{-7}{21}\) is negative rational number and \(\frac{3}{9}\) is a positive Rational Number. Therefore this pair does not represent the same rational number.

ii)

Solution:

∴ The above pair of numbers represent the same rational number.

iii)

Solution:

∴ The above pair of numbers represent the same rational number.

iv)

Solution:

∴ The above pair of numbers represent the same rational number.

v)

Solution:

∴ The above pair of numbers represent the same rational number.

vi)

Solution:

\(\frac{1}{3}\) is a positive rational number and \(\frac{-1}{9}\) is a negative Rational Number.

Therefore this pair does not represent the same rational number.

vii)

Solution:

is a positive rational number and \(\frac{5}{-9}\) is a negative rational number.

Question 7.

Rewrite the following rational numbers in the simplest form :

i) \(\frac{-8}{6}\)

The H. C. F of 6 and 8 is 2.

Then its simplest form would be,

ii) \(\frac{25}{45}\)

The H. C. F of 25 and 45 is 5.

Then its simplest form would be,

iii) \(\frac{-44}{72}\)

The H. C. F of 44 and 72 is 4.

Then its simplest form would be

iv)

The H. C. F of 8 and 10 is 2.

Then Its simplest form would be

Question 8.

Fill in the boxes with the correct symbol out of >, <, and =.

i)

Solution:

\(\frac{-5}{7}\) is a negative rational number

\(\frac{2}{3}\) is a positive rational number.

ii)

Solution:

To make the equal denominator

iii)

Solution:

iv)

Solution:

v)

Solution:

vi)

Solution:

vii)

Solution:

0 is greater than the negative numbers,

Question 9.

Which is greater in each of the following

i)

Solution:

L.C.M of 3 & 2 is 6

ii)

L. C. M of 6 and 3 is 6

iii)

Solution:

L. C M of 4 and 3 is 12

iv)

Solution:

(∵ All positive numbers are greater than all negative numbers.)

v)

Solution:

Question 10.

Write the following rational numbers in ascending order :

i)

-3 < -2 < -1

∴ Ascending Order is

ii)

Solution:

L. C. M of 3 & 9 is 9

iii)

Solution:

Denominator same, So the numerators are

-42 < -21 < -12