Question 1

What is the additive identity for rational numbers?

Accepted Answer

The correct answer is 0. Adding 0 to any rational number gives the same rational number ($a + 0 = a$).

Question 2

What is the multiplicative identity for rational numbers?

Accepted Answer

The correct answer is 1. Multiplying any rational number by 1 gives the same rational number ($a 	imes 1 = a$).

Question 3

What is the additive inverse of $\frac{7}{11}$?

Accepted Answer

The correct answer is $-\frac{7}{11}$. The additive inverse of a rational number $\frac{a}{b}$ is $-\frac{a}{b}$ such that $\frac{a}{b} + (-\frac{a}{b}) = 0$.

Question 4

What is the multiplicative inverse (reciprocal) of $-\frac{5}{9}$?

Accepted Answer

The correct answer is $-\frac{9}{5}$. The multiplicative inverse of a non-zero rational number $\frac{a}{b}$ is $\frac{b}{a}$ because $\frac{a}{b} 	imes \frac{b}{a} = 1$.

Question 5

Which rational number does NOT have a reciprocal?

Accepted Answer

The correct answer is 0. The reciprocal of 0 would be $\frac{1}{0}$, which is undefined.

Rational Numbers