Gujarat Board GSEB Textbook Solutions Class 8 Maths Chapter 1 Rational Numbers Textbook Questions and Answers.

Gujarat Board Textbook Solutions Class 8 Maths Chapter 1 Rational Numbers Ex 1.1

Question 1.
Using appropriate properties find:
(i) (-frac{2}{3} times frac{3}{5}+frac{5}{2}-frac{3}{5} times frac{1}{6})
(ii) (frac{2}{5} timesleft(-frac{3}{7}right)-frac{1}{6} times frac{3}{2}+frac{1}{14} times frac{2}{5})
Solution:
(i) (-frac{2}{3} times frac{3}{5}+frac{5}{2}-frac{3}{5} times frac{1}{6})
= (left[-frac{2}{3} times frac{3}{5}+left(frac{-3}{5}right) times frac{1}{6}right]+frac{5}{2})
(Using commutative)
= (left[-frac{2}{3} times frac{3}{5}+left(frac{-3}{5}right) times frac{1}{6}right]+frac{5}{2}) = (frac { 5 }{ 2 })
= (left(frac{-3}{5}right)left[frac{2}{3}+frac{1}{6}right]+frac{5}{2}) (Using distributivity)
= (left(frac{-3}{5}right)left[frac{4+1}{6}right]+frac{5}{2}=left(frac{-3}{5}right)left[frac{5}{6}right]+frac{5}{2})
= (frac{-3}{5} times frac{5}{6}+frac{5}{2}=frac{-1}{2}+frac{5}{2}=frac{-1+5}{2}=frac{4}{2}) = 2

(ii) (frac{2}{5} timesleft(-frac{3}{7}right)-frac{1}{6} times frac{3}{2}+frac{1}{14} times frac{2}{5})
= (frac{2}{5} timesleft(frac{-3}{7}right)-frac{1}{4}+frac{1}{14} times frac{2}{5})
= (frac{2}{5} timesleft(frac{-3}{7}right)+frac{1}{14} times frac{2}{5}-frac{1}{4})
(Using commutative)
= (frac{2}{5}left[frac{-3}{7}+frac{1}{14}right]-frac{1}{4}) (Using distributivity

Question 2.
Write the additive inverse of each of the following:

1. (frac { 2 }{ 8 })
2. (frac { -5 }{ 9 })
3. (frac { -6}{ -5 })
4. (frac { 2 }{ -9 })
5. (frac { 19 }{ -6 })

Solution:

Question 3.
Verify that – (-x) = x for:

1. x = (frac { 11 }{ 15 })
2. x = – (frac { 13 }{ 17 })

Solution:

Question 4.
Find the multiplicative inverse of the following:

1. – 13
2. (frac { -13 }{ 19 })
3. (frac { 1 }{ 5 })
4. (frac { -5 }{ 8 }) × (frac { -3 }{ 7 })
5. -1 × (frac { -2 }{ 5 })
6. -1

Solution:

Question 5.
Name the property under multiplication used in each of the following:

1. (frac { 1 }{ 2 }) × 1 = 1 × (frac { -4 }{ 5 }) = – (frac { 4 }{ 5 })
2. – (frac { 13 }{ 17 }) × (frac { 13 }{ 17 })
3. (frac{-19}{29} times frac{29}{-19}) = 1

Solution:

Question 6.
Multiply (frac { 6 }{ 13 }) by the reciprocal of (frac { -7 }{ 16 })
Solution:

Question 7.
Tell what property allows you to compute
(frac { 1 }{ 3 }) ×(left(6 times frac{4}{3}right)) as (left(frac{1}{3} times 6right) times frac{4}{3})
Solution:
In computing (frac { 1 }{ 3 }) ×(left(6 times frac{4}{3}right)) as (left(frac{1}{3} times 6right) times frac{4}{3}) , we use the associativity.

Question 8.
Is (frac { 8 }{ 9 }) the multiplicative invers of -1(frac { 1 }{ 8 }) ?
Why or Why not?
Solution:
Since, -1(frac { 1 }{ 8 }) = (frac { -9 }{ 8 }) and (frac { 8 }{ 9 }) × (frac { 8 }{ 9 }) × (frac { -9 }{ 8 }) = -1
[Which is not equal to 1]
∴ (frac { 8 }{ 9 }) is not the multiplicative invers of (frac { -9 }{ 8 })
[∴ The product of (frac { -9 }{ 8 }) and its multiplication invers must be equal to 1]

Question 9.
Is 0.3 the multiplicative inverse of 3 (frac { 1 }{ 3 }) ? Why or why not?
Solution:
0.3 = (frac { 3 }{ 10 }) and 3(frac { 1 }{ 3 }) = (frac { 10 }{ 3 })
and, multiplicative invers of 3 (frac { 1 }{ 3 }) or (frac { 10 }{ 3 }) = (frac { 3 }{ 10 }) = 0.3
∴the multiplicative inverse of 3(frac { 1 }{ 3 }) is 0.3

Question 10.
Write:

1. The rational number that does not have a reciprocal.
2. The rational numbers that are equal to their reciprocals.
3. The rational number that is equal to its negative.

Solution:

1. The rational number zero (0) does not have a reciprocal.
2. The rational numbers 1 and (-1) are equal to their reciprocals respectively.
3. ∵ [A rational number] + [Negative of the rational number] = 0 [ ∵ [0] = [0] = 0 ]
   So, Negative of 0 is 0. Hence, 0 is equal to its negative.

Question 11.
Fill in the blanks:

1. Zero has _______ reciprocal
2. The numbers _______ and _____ are their own reciprocals.
3. The reciprocal of -5 is ______
4. Reciprocal of (frac { 1 }{ x }) , where x ≠ 0 is ______.
5. The reciprocal of a positive rational number is always a _______
6. The reciprocal of a positive rational number is ______

Solution:

1. Zero has no reciprocal.
2. The numbers 1 and -1 are their own reciprocals.
3. The reciprocal of -5 is (frac { -1 }{ 5 })
4. The reciprocal of (frac { 1 }{ x }) where x ≠ 0 is x.
5. The product of two rational numbers is always a rational number.
6. The reciprocal of a positive rational number is positive.