Gujarat Board GSEB Textbook Solutions Class 7 Maths Chapter 9 Rational Numbers InText Questions and Answers.

Gujarat Board Textbook Solutions Class 7 Maths Chapter 9 Rational Numbers InText Questions

Try These (Page 174)

Question 1.
Is the number (frac { 2 }{ -3 }) rational? Think about it.
Solution:
Yes, (frac { 2 }{ -3 }) is a rational number,
∵ 2 and – 3 are integers and – 3 ≠ 0.

Question 2.
List ten rational numbers.
Solution:
Following are ten rational numbers:
(frac { 1 }{ 3 }), (frac { 2 }{ -3 }), (frac { 4 }{ 5 }), (frac { 1 }{ -6 }), (frac { -3 }{ – 4 }) 5.8, 2(frac { 4 }{ 5 }), 0.93, 18 and 11.07.
Note.
1. ‘0’ can be written as (frac { 0 }{ 2 }) or (frac { 0 }{ 15 }), etc. Hence, it is a rational number.
2. A natural number can be written as 5 = (frac { 5 }{ 1 }) or 108
= (frac { 108 }{ 1 })
Hence, it is also a rational number.

Try These (Page 175)

Question 1.
Fill in the boxes:

Solution:

Try These (Page 175)

Question 1.
Is 5 a positive rational number?
Solution:
Yes, 5 or (frac { 5 }{ 1 }) is having both its numerator and denominator as positive.
∴ It is a positive rational number.

Question 2.
List five more positive rational numbers.
Solution:
(frac { 1 }{ 7 }), (frac { 3 }{ 8 }), (frac { 5 }{ 17 }), (frac { 2 }{ 9 }) and (frac { 5 }{ 18 }) are positive rational numbers.

Try These (Page 176)

Question 1.
Is – 8 a negative rational number?
Solution:
Yes, – 8 or (frac { -8 }{ 1 }) is a negative rational number, because its numerator is a negative integer.

Question 2.
List five more negative rational numbers.
Solution:
Five negative rational numbers are as follows:
(frac { – 5 }{ 9 }), (frac { -6 }{ 11 }), (frac { -3 }{ 13 }), (frac { 3 }{ -10 }) and (frac { -1 }{ 7 })

Try These (Page 176)

Question 1.
Which of these are negative rational numbers?
(i) (frac { -2 }{ 3 })
(ii) (frac { 5 }{ 7 })
(iii) (frac { 3 }{ -5 })
(iv) 0
(v) (frac { 6 }{ 11 })
(vi) (frac { -2 }{ -9 })
Solution:
(i) (frac { -2 }{ 3 }) is a negative rational number.
(ii) (frac { 5 }{ 7 }) is a positive rational number.
(iii) (frac { 3 }{ -5 }) is a negative rational number.
(iv) 0 is neither a positive nor a negative rational number.
(v) (frac { 6 }{ 11 }) is a positive rational number.
(vi) (frac { -2 }{ -9 }) is a positive rational number.

∴ (i) (frac { -2 }{ 3 }) and (ii) (frac { 3 }{ -5 }) are negative rational numbers.

Try These (Page 178)

Question 1.
Find the standard form of:
(i) (frac { -18 }{ 45 })
(ii) (frac { -12 }{ 18 })
Solution:
(i) Since HCF of 18 and 45 is 9.
∴ (frac { -18 }{ 45 }) = (frac { (-18)÷9 }{ 45÷9 }) = (frac { -2 }{ 5 })
Thus, the standard form of is (frac { -18 }{ 45 }) is (frac { -2 }{ 5 })

(ii) Since, HCF of 12 and 18 is 6.
∴ (frac { -12 }{ 18 }) = (frac { (-12)÷6 }{ 18÷6 }) = (frac { -2 }{ 3 })
Thus, the standard form of (frac { -12 }{ 18 }) is (frac { -2 }{ 3 })

Try These (Page 181)

Question 1.
Find five rational numbers between (frac { -5 }{ 7 }) and (frac { -3 }{ 8 }).
Solution:
First we convert the given rational numbers with common denominators.
∵ LCM of 7 and 8 is 56.

Thus, the five rational numbers, between (frac { -5 }{ 7 }) and (frac { -3 }{ 8 }) are:
(frac { -39 }{ 56 }), (frac { -38 }{ 56 }), (frac { -37 }{ 56 }), (frac { -36 }{ 56 }), (frac { -35 }{ 56 })
or (frac { -39 }{ 56 }), (frac { -19 }{ 28 }), (frac { -37 }{ 56 }), (frac { -9 }{ 14 }), (frac { -5 }{ 8 })

Try These (Page 185)

Question 1.
Find:
(i) (frac { -13 }{ 7 }) + (frac { 6 }{ 7 })
(ii) (frac { 19 }{ 5 }) + (frac { -7 }{ 5 })
Solution:

Question 2.
Find:
(i) (frac { -3 }{ 7 }) + (frac { 2 }{ 3 })
(ii) (frac { -5 }{ 6 }) + (frac { -3 }{ 11 })
Solution:
(i) (frac { -3 }{ 7 }) + (frac { 2 }{ 3 })
∵ LCM of 7 and 3 is 21.
∴ (frac { -3 }{ 7 }) = (frac { (-3)×3 }{ 7×3 }) = (frac { -9 }{ 21 })
and (frac { 2 }{ 3 }) = (frac { 2×7 }{ 3×7 }) = (frac { 14 }{ 21 })
∴ (frac { -3 }{ 7 }) + (frac { 2 }{ 3 }) = (frac { -9 }{ 21 }) + (frac { 14 }{ 21 })
= (frac { -9+14 }{ 21 })
= (frac { 5 }{ 21 })

(ii) (frac { -5 }{ 6 }) + (frac { -3 }{ 11 })
Since, LCM of 6 and 11 is 66.

Try These (Page 186)

Question 1.
What will be the additive inverse of (frac { -3 }{ 9 })? (frac { -9 }{ 11 })?(frac { 5 }{ 7 })?
Solution:
Additive inverse of (frac { -3 }{ 9 }) is (frac { 3 }{ 9 })
Additive inverse of (frac { -9 }{ 11 }) is (frac { 9 }{ 11 })
Additive inverse of (frac { 5 }{ 7 }) is (frac { -5 }{ 7 })

Try These (Page 187)

Question 1.
Find:
(i) (frac { 7 }{ 9 }) – (frac { 2 }{ 5 })
(ii) 2(frac { 1 }{ 5 }) – (frac { -1 }{ 3 })
Solution:

Try These (Page 188)

Question 1.
What will be
(i) (frac { -3 }{ 5 }) x 7?
(ii) (frac { -6 }{ 5 }) x (-2)?
Solution:
(i) (frac { -3 }{ 5 }) x 7 = (frac { (-3)×7 }{ 5 }) = (frac { -21 }{ 5 })
(ii) (frac { -6 }{ 5 }) x (-2) = (frac { -6×(-2) }{ 5 }) = (frac { 12 }{ 5 })

Note:
We multiply two rational numbers in the following way:
(i) Multiply the numerators of the rational numbers.
(ii) Multiply the denominators of the rational numbers.
(iii) Then product =
For example:

Try These (Page 188)

Question 1.
Find:
(i) (frac { -3 }{ 4 }) x (frac { 1 }{ 7 })
(ii) (frac { 2 }{ 3 }) x (frac { -5 }{ 9 })
Solution:

Try These (Page 189)

Question 1.
What will be the reciprocal of (frac { -6 }{ 11 }) and (frac { -8 }{ 5 })?
Solution:
(i) Reciprocal of (frac { -6 }{ 11 }) is (frac { 11 }{ -6 })
(ii) Reciprocal of (frac { -8 }{ 5 }) is (frac { -5 }{ 8 }).
To divide one rational number by the other rational number, we multiply the rational number by the reciprocal of the other. For example,

Try These (Page 190)

Question 1.
Find:
(i) (frac { 2 }{ 3 }) x (frac { -7 }{ 8 })
(ii) (frac { -6 }{ 7 }) x (frac { 5 }{ 7 })
Solution: