Verify that x × y + z = x × y + x × z for: x = 4 7 , y = - 3 8 , z = 12 - 13

Given, x = 4 7 , y = - 3 8 , z = 12 - 13 Show that = x × y + z = x × y + x × z So, 4 7 × - 3 8 + 12 - 13 = 4 7 × - 3 8 + 4 7 × 12 - 13 ∵ 12 × ( - 1 ) - 13 × ( - 1 ) = - 12 13 4 7 × - 3 8 + - 12 13 = 4 7 × - 3 8 + 4 7 × - 12 13 4 7 × - 39 - 96 104 = - 12 56 + - 48 91 4 7 × - 135 104 = - 156 - 384 728 - 540 728 = - 540 728 LHS = RHS Hence, verified.

Verify that x × y + z = x × y + x × z for: x = 4 5 , y = - 6 7 , z = - 2 3

Given, x = 4 5 , y = - 6 7 , z = - 2 3 Show that = x × y + z = x × y + x × z Therefore, 4 5 × ( - 6 7 + - 2 3 ) = ( 4 5 × - 6 7 ) + ( 4 5 × - 2 3 ) 4 5 × ( - 18 + ( - 14 ) 21 ) = - 24 35 + - 8 15 4 5 × - 32 21 = - 72 - 56 105 - 128 105 = - 128 105 LHS = RHS Hence, verified.

Divide the sum of - 5 4 and - 1 3 by their difference.

According to the question, - 5 4 + - 1 3 ÷ - 5 4 - - 1 3 ⇒ - 5 × 3 + - 1 × 4 12 ÷ - 5 × 3 - - 1 × 4 12 ⇒ - 15 + - 4 12 ÷ - 15 + 4 12 ⇒ - 19 12 ÷ - 11 12 ⇒ - 19 12 × 12 - 11 ⇒ 19 11 Hence, result is 19 11 .

By what number should - 28 15 be multiplied to get the multiplicative inverse of - 5 7 ?

According to the question, - 28 15 × Multiply with a number to get = Multiplication inverse of - 5 7 Let the number be x . ⇒ - 28 15 × x = Multiplication inverse of - 5 7 ⇒ - 28 15 × x = 7 - 5 ⇒ x = 7 - 5 × 15 - 28 ⇒ x = 3 4 Hence, the number is 3 4 .

Find five rational numbers between - 1 2 and 1 2 .

We convert - 1 2 and 1 2 into its equivalent fraction. Multiply 4 at both numerator and denominator of both numbers. - 4 2 × 4 ⇒ - 4 8 and 4 × 1 2 × 4 ⇒ 4 8 then rational numbers lies between - 1 2 and 1 2 are: - 4 8 < - 3 8 < - 2 8 < - 1 8 < 0 8 < 1 8 < 2 8 < 3 8 < 4 8 Hence, the five rational numbers lies between these two rational numbers i . e - 1 2 < - 3 8 < - 1 4 < - 1 8 < 0 < 1 8 < 1 2

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START UP MATHEMATICS>Chapter 1 - Rational Numbers>REVIEW EXERCISES

Monicaa Abhijit Solutions for Chapter: Rational Numbers, Exercise 10: REVIEW EXERCISES

Author:Monicaa Abhijit

Monicaa Abhijit Mathematics Solutions for Exercise - Monicaa Abhijit Solutions for Chapter: Rational Numbers, Exercise 10: REVIEW EXERCISES

Attempt the practice questions on Chapter 1: Rational Numbers, Exercise 10: REVIEW EXERCISES with hints and solutions to strengthen your understanding. START UP MATHEMATICS solutions are prepared by Experienced Embibe Experts.