What is the standard form of 4 - 12 ?

Given, the rational number, 4 - 12 , = 4 - 12 Divide the numerator and denominator with - 4 , = 4 ÷ - 4 - 12 ÷ - 4 = - 1 3 Therefore, Standard form of 4 - 12 is - 1 3 .

Give the additive inverse of - 2 - 5 .

Given, - 2 - 5 . Now, we can write - 2 - 5 = 2 5 . We need to find the additive inverse of 2 5 . We know that if the sum of two rational numbers is 0 , then the two numbers are called additive inverses of each other. This means for every rational number a b , there is a rational number - a b such that a b + - a b is 0 . So, the additive inverse of 2 5 = - 2 5 . Hence, the required additive inverse is - 2 5 .

Examine if 4 - 9 and - 20 45 represent the same rational number.

Given, 4 - 9 = 4 × - 1 - 9 × - 1 = - 4 9 and Divide the numerator and denominator by 5 , we get - 20 45 = - 20 ÷ 5 45 ÷ 5 = - 4 9 Hence, 4 - 9 and - 20 45 represent the same rational number - 4 9 .

Does the rational number - 3 5 lie between 1 2 and - 1 2 ?

Given, numbers are 1 2 and - 1 2 , 1 2 = 1 × 5 2 × 5 = 5 10 and - 1 2 = - 1 × 5 2 × 5 = - 5 10 Rational numbers between 5 10 and - 5 10 are - 4 10 , - 3 10 , - 2 10 , - 1 10 , 0 , 1 10 , 2 10 , 3 10 , 4 10 or - 2 5 , - 3 10 , - 1 5 , - 1 10 , 0 , 1 10 , 1 5 , 3 10 , 2 5 Hence, - 3 5 does not lie between 1 2 and - 1 2 .

Give reciprocal of - 28 40 in standard form.

Given, the rational number - 28 40 , Reciprocal of - 28 40 = 40 - 28 Divide the rational number by 4 , we get = 10 × 4 - 7 × 4 = 10 - 7 = - 10 7 Hence, standard form of reciprocal of - 28 40 is - 10 7 or - 1 3 7 .

Divide the sum of - 8 15 and - 10 15 by their product.

Given, Sum of = - 8 15 + - 10 45 = - 8 15 - 10 45 = 34 35 Product of = - 8 15 × - 10 45 = 80 675 = 16 135 Now, division of - 34 35 by 16 135 = - 34 45 ÷ 16 135 = - 34 45 × 135 16 = - 51 8 = - 6 3 8 Therefore, the solution is - 6 3 8 .