Question

If $\frac{x}{y}$ is the additive inverse of $\frac{c}{d}$, then, $\frac{x}{y}-\frac{c}{d}=0$. State whether the statement is true (T) or false (F)

• A. True
• B. False

Answer 1

The correct option is B False

Explanation

An additive inverse number is a number that on adding to the original number gives zero in the result.

Let a number be $x$ then its additive inverse number is $-x$

$$\begin{gathered} \Rightarrow x+(-x) \\ \Rightarrow x-x=0 \end{gathered}$$

Example: Let $\frac{x}{y}$be $\frac{3}{5}$ and $\frac{c}{d}$ be $\frac{-3}{5}$ then,

$$\begin{gathered} \frac{x}{y}-\frac{c}{d} \\ =\frac{3}{5}-(-\frac{3}{5}) \\ =\frac{3}{5}+\frac{3}{5} \\ =\frac{6}{5}\ne 0 \end{gathered}$$

Hence, the given statement is False.