Tamilnadu State Board New Syllabus Samacheer Kalvi 8th Maths Guide Pdf Chapter 1 Numbers Ex 1.3 Textbook Questions and Answers, Notes.
Tamilnadu Samacheer Kalvi 8th Maths Solutions Chapter 1 Numbers Ex 1.3
Question 1.
Verify the closure property for addition and multiplication for the rational numbers \(\frac{-5}{7}\) and \(\frac{8}{9}\).
Answer:
closure property for addition
Let a = \(\frac{-5}{7}\) and b = \(\frac{8}{9}\)
∴ Closure property is true for addition of rational numbers.
Closure property for multiplication
∴ Closure property is true for rnultiplìcation of rational numbers.
Question 2.
Verify the commutative property for addition and multiplication for the rational numbers \(\frac{-10}{11}\) and \(\frac{-8{33}\).
Answer:
Let a = \(\frac{-10}{11}\) and \(\frac{-8{33}\) be the given rational numbers.
From (1) and (2)
a + b = b + a and hence additionis commutative for rational numbers
From (3) and (4) a × b = b × a
Hence multiplication is commutative for rational numbers.
Question 3.
Verify the associative property for addition and multiplication for the rational numbers \(\frac{-7}{9}, \frac{5}{6}\) and \(\frac{-4}{3}\).
Answer:
From (1) and (2), (a + b) + c = a + (b + c) is true for rational numbers.
From (1) and (2) (a × b) × c = (a × b) × c is true for rational numbers.
Thus associative property.
Question 4.
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 = \(\frac{-5}{6}\).
Answer:
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 5.
Verify the identity property for addition and multiplication for the rational numbers \(\frac{15}{19}\) and \(\frac{-18}{25}\).
Answer:
Identify property for addition verified.
Identify property for multiplication verified.
Question 6.
Verify the additive and multiplicative inverse property for the rational numbers \(\frac{-7}{17}\) and \(\frac{17}{27}\).
Answer:
Additive inverse for rational numbers verified.
Mulplicative inverse for rational numbers verified.
Objective Type Questions
Question 7.
Closure property is not true for division of rational numbers because of the number
(A) 1
(B) 1
(C) 0
(D) \(\frac { 1 }{ 2 }\)
Answer:
(C) 0
Question 8.
\(\frac{1}{2}-\left(\frac{3}{4}-\frac{5}{6}\right) \neq\left(\frac{1}{2}-\frac{3}{4}\right)-\frac{5}{6}\) illustrates that subtraction does not satisfy the ________ property for rational numbers.
(A) commutative
(B) closure
(C) distributive
(D) associative
Answer:
(D) associative
Question 9.
Which of the following illustrates the inverse property for addition?
(A) \(\frac{1}{8}-\frac{1}{8}=0\)
(B) \(\frac{1}{8}+\frac{1}{8}=\frac{1}{4}\)
(C) \(\frac{1}{8}+0=\frac{1}{8}\)
(D) \(\frac{1}{8}-0=\frac{1}{8}\)
Answer:
(A) \(\frac{1}{8}-\frac{1}{8}=0\)
Question 10.
\(\frac{3}{4} \times\left(\frac{1}{2}-\frac{1}{4}\right)=\frac{3}{4} \times \frac{1}{2}-\frac{3}{4} \times \frac{1}{4}\) illustrates that multiplication is distributive over
(A) addition
(B) subtraction
(C) multiplication
(D) division
Answer:
(B) subtraction