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

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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:
Closure property for addition.
Let a = \(\frac{-5}{7}\) and b = \(\frac{8}{9}\) be the given rational numbers.
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 1
∴ Closure property is true for addition of rational numbers.
Closure property for multiplication
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 2
∴ Closure property is true for multiplication of rational numbers.

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Question 4.
Verify the associative property for addition and multiplication of the rational numbers \(\frac{-10}{11}, \frac{5}{6}, \frac{-4}{3}\).
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 3
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 4
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.
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 5
From (1) and (2)
a + b = b + a and hence addition is commutative for rational numbers.
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 6
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 = \(\frac{-5}{6}\).
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 7
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:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 8
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 9
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 10

SamacheerKalvi.Guru

Question 8.
Evaluate using appropriate properties.
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 11
Solution:
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 12
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 13
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 14

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
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 15

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?
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 16
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

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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.
\(\left(1-\frac{1}{2}\right) \times\left(\frac{1}{2}-\frac{1}{4}\right) \div\left(\frac{3}{4}-\frac{1}{2}\right)\) = ____
Samacheer Kalvi 8th Maths Term 1 Chapter 1 Rational Numbers Ex 1.2 17
Solution:
(A) \(\frac{1}{2}\)

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