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Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 1 Chapter 1 Rational Numbers Ex 1.2

Question 1.
Fill in the blanks:
(i) The multiplicative inverse of $$2 \frac{3}{5}$$ is _____.
(ii) If -3 × $$\frac{6}{-11}=\frac{6}{-11}$$ × x, then x is _______.
(iii) If distributive property is true for $$\left(\frac{3}{5} \times \frac{-4}{9}\right)+\left(x \times \frac{15}{17}\right)=\frac{3}{5} \times(y+z)$$, then x, y, z are _____, _____ and ____.
(iv) If x × $$\frac{-55}{63}=\frac{-55}{63}$$ × x = 1, then x is called the _____ of $$\frac{55}{63}$$.
(v) The multiplicative inverse of -1 is ______.
Solution:
(i) $$\frac{5}{13}$$
(ii) -3
(iii) $$\frac{3}{5}, \frac{-4}{9}$$ and $$\frac{15}{13}$$
(iv) Mulitplicative inverse
(v) -1

Question 2.
Say True or False.
(i) $$\frac{-7}{8} \times \frac{-23}{27}=\frac{-23}{27} \times \frac{-7}{8}$$ illustrates the closure property of rational number.
(ii) Associative property is not true for subtraction of rational numbers.
(iii) The additive inverse of $$\frac{-11}{-17}$$ is $$\frac{11}{17}$$.
(iv) The product of two negative rational numbers is a positive rational number.
(v) The multiplicative inverse exists for all rational numbers.
Solution:
(i) False
(ii) True
(iii) False
(iv) True
(v) False

Question 3.
Verify the closure property for addition and multiplication of the rational numbers $$\frac{-5}{7}$$ and $$\frac{8}{9}$$
Solution:
Let a = $$\frac{-5}{7}$$ and b = $$\frac{8}{9}$$ be the given rational numbers.

∴ Closure property is true for addition of rational numbers.
Closure property for multiplication

∴ Closure property is true for multiplication of rational numbers.

Question 4.
Verify the associative property for addition and multiplication of the rational numbers $$\frac{-10}{11}, \frac{5}{6}, \frac{-4}{3}$$.
Solution:

a × (b × c) = $$\frac{100}{99}$$
From (1) and (2) a × (b × c) = (a × b) × c is true for rational numbers.
Thus associative property is true for addition and multiplication of rational numbers.

Question 5.
Check the commutative property for addition and multiplication of the rational numbers $$\frac{-10}{11}$$ and $$\frac{-8}{33}$$.
Solution:
Let a = $$\frac{-10}{11}$$ and b = $$\frac{-8}{33}$$ be the given rational numbers.

From (1) and (2)
a + b = b + a and hence addition is commutative for rational numbers.

From (3) and (4) a × b = b × a
Hence multiplication is commutative for rational numbers.

Question 6.
Verify the distributive property a × (b + c) = (a × b) + (a × c) for the rational numbers a = $$\frac{-1}{2}$$ ,b = $$\frac{2}{3}$$ and c = $$\frac{-5}{6}$$.
Solution:
Given the rational number a = $$\frac{-1}{2}$$ ,b = $$\frac{2}{3}$$ and c = $$\frac{-5}{6}$$.

From (1) and (2) we have a × (b + c) = (a × b) + (a × c) is true.
Hence multiplication is distributive over addition for rational numbers Q.

Question 7.
Evaluate:

Solution:

Question 8.
Evaluate using appropriate properties.

Solution:

Question 9.
Use commutative and distributive properties to simplify $$\frac{4}{5} \times \frac{-3}{8}-\frac{3}{8} \times \frac{1}{4}+\frac{19}{20}$$
Solution:
Since multiplication is commutative

Objective Type Questions

Question 10.
Mulitplicative inverse of 0 (is)
(A) 0
(B) 1
(C) -1
(D) does not exist
Solution:
(D) does not exist

Question 11.
Which of the following illustrates the inverse property for addition?

Solution:
(A) $$\frac{1}{8}-\frac{1}{8}$$ = 0

Question 12.
Closure property is not true for division of rational numbers because of the number
(A) 1
(B) -1
(C) 0
(D) $$\frac{1}{2}$$
Solution:
(C) 0

Question 13.
$$\frac{1}{2}-\left(\frac{3}{4}-\frac{5}{6}\right) \neq\left(\frac{1}{2}-\frac{3}{4}\right)-\frac{5}{6}$$ illustrates that subtraction does not satisfy the ____ law of rational numbers.
(A) commutative
(B) closure
(C) distributive
(D) associative
Solution:
(D) associative

Question 14.
$$\left(1-\frac{1}{2}\right) \times\left(\frac{1}{2}-\frac{1}{4}\right) \div\left(\frac{3}{4}-\frac{1}{2}\right)$$ = ______________

Solution:
(A) $$\frac{1}{2}$$