exercise 1.1 class 8
Question 2:
Write the additive inverse of each of the following:
\(\displaystyle (i) {2 \over 8} (ii) {-5 \over 9} (iii) {-6 \over -5} (iv) {2 \over -9} (v) {19 \over -6} \)
Solution:
\(\displaystyle (i) {2 \over 8}\)
Additive inverse = \( \displaystyle {- 2 \over 8}\)
\(\displaystyle (ii) {-5 \over 9}\)
Additive inverse = \( \displaystyle {5 \over 9}\)
\(\displaystyle (iii) {-6 \over -5}={6 \over 5}\)
Additive inverse = \( \displaystyle {-6 \over 5}\)
\( \displaystyle (iv) {2 \over -9}\)
Additive inverse = \(\displaystyle {2 \over 9}\)
\(\displaystyle (v) {19 \over -6}\)
Additive inverse = \( \displaystyle {{19 \over 6}}\)
Question 3:
Verify that −(−x) = x for.
(i) \(\displaystyle x={11 \over 15}\) (ii) \(\displaystyle x={-13 \over 17}\)
Solution:
(i)\(\displaystyle x={11 \over 15}\)
The additive inverse of \(\displaystyle x={11 \over 15}\) is \(\displaystyle -x=-{11 \over 15}\) as \(\displaystyle {11 \over 15}+{-11 \over 15}=0\)
This equality \(\displaystyle {11 \over 15}+{-11 \over 15}=0\) represents that the additive inverse of \( \displaystyle {-11 \over 15} \) is \(\displaystyle {11 \over 15} \) or it can be said that \( \displaystyle -(-{11 \over 15})={11 \over 15}\) i.e., −(−x) = x.
(ii) \(\displaystyle x={-13 \over 17}\)
The additive inverse of \(\displaystyle x={-13 \over 17}\) is \(\displaystyle -x={13 \over 17}\) as \(\displaystyle {-13 \over 17}+{13 \over 17}=0\)
This equality \(\displaystyle {-13 \over 17}+{13 \over 17}=0\) represents that the additive inverse of \( \displaystyle {13 \over 17} \) is \(\displaystyle {-13 \over 17} \) i.e., −(−x) = x.
Question 4:
Find the multiplicative inverse of the following.
(i)\(\displaystyle -13 \)
(ii)\( \displaystyle {-13 \over 19}\)
(iii)\(\displaystyle {1 \over 5} \)
(iv)\(\displaystyle {-5 \over 8}×{-3 \over 7} \)
(v)\(\displaystyle -1 × {-2 \over 5} \)
(vi)\(\displaystyle −1\)
Solution:
(i) \(\displaystyle -13 \)
Multiplicative inverse = \(\displaystyle -{1\over 13} \)
(ii)\( \displaystyle {-13 \over 19}\)
Multiplicative inverse =\( -{19 \over 13}\)
(iii)\(\displaystyle {1 \over 5} \)
Multiplicative inverse = \(\displaystyle { 5} \)
(iv)\(\displaystyle {-5 \over 8}×{-3 \over 7} ={15 \over 56}\)
Multiplicative inverse=\(\displaystyle {56 \over 15} \)
(v)\(\displaystyle -1 × {-2 \over 5} \)
Multiplicative inverse=\(\displaystyle {5 \over 2} \)
(vi) \(\displaystyle −1\)
Multiplicative inverse = \( \displaystyle −1\)
Question 5:
Name the property under multiplication used in each of the following:
(i) \(\displaystyle {-4 \over 5} × 1 = 1 × {-4 \over 5}={-4 \over 5} \)
(ii)\(\displaystyle {-13 \over 17} × {-2 \over 7}={-2 \over 7} × {-13 \over 17} \)
(iii)\(\displaystyle {-19 \over 29} × {29 \over -19} =1\)
Answer:
(i)Multiplicative identity.
(ii) Commutativity
(iii) Multiplicative inverse
Question 6:
Multiply by \(\displaystyle {6\over 13}\) the reciprocal of \(\displaystyle {-7 \over 16}\).
Answer:
\(\displaystyle {6\over 13} × ( \) the reciprocal of \(\displaystyle {-7 \over 16} )\)
=\(\displaystyle {6\over 13} × {-16 \over 7} ={-96 \over 91}\)
Question 7:
Tell what property allows you to compute \(\displaystyle {1 \over 3}×(6×{4 \over 3})\) as \(\displaystyle {1 \over 3}×6)×{4 \over 3}\) .
Answer:
Associativity
Question 8:
Is \(\displaystyle {8 \over 9}\) the multiplicative inverse of \(\displaystyle -1{1 \over 8}\) ? Why or why not?
Answer:
If it is the multiplicative inverse, then the product should be \(\displaystyle 1\).
However, here, the product is not \(\displaystyle 1\) as
\(\displaystyle {8 \over 9} × (-1{1 \over 8})={8 \over 9} × (-{9 \over 8})=-1\neq 1\)
Question 9:
Is \(\displaystyle 0.3\) the multiplicative inverse of \(\displaystyle 3{1 \over 3}\)? Why or why not?
Answer:
\(\displaystyle 3{1 \over 3}={10 \over 3}\)
\(\displaystyle 0.3 × 3{1 \over 3} = 0.3 × {10 \over 3}={3 \over 10} × {10 \over 3}=1\)
Here, the product is 1. Hence, 0.3 is the multiplicative inverse of \(\displaystyle 3{1 \over 3}\).
Question 10:
Write:
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Answer:
(i) \(0\) is a rational number but its reciprocal is not defined.
(ii) \(1\) and \(-1\) are the rational numbers that are equal to their reciprocals.
(iii) \(0\) is the rational number that is equal to its negative.
Question 11:
Fill in the blanks.
(i) Zero has __________ reciprocal.
(ii) The numbers __________ and __________ are their own reciprocals
(iii) The reciprocal of -5 is __________.
(iv) Reciprocal of \(\displaystyle {1\over x}\), where \(\displaystyle { x \neq 0}\) is __________.
(v) The product of two rational numbers is always a __________.
(vi) The reciprocal of a positive rational number is __________.
Answer:
(i) No
(ii) 1, −1
(iii)\(\displaystyle -{1\over 5}\)
(iv) x
(v) Rational number
(vi) Positive rational number
