Question

Which of the following statements is incorrect, if $a,b,c$ and $d$ are any rational numbers?

• A. $\frac{a}{b}+\frac{c}{d}=\frac{c}{d}+\frac{a}{b}$
• B. $\frac{a}{b}\times \frac{c}{d}=\frac{c}{d}\times \frac{a}{b}$
• C. $\frac{a}{b}-\frac{c}{d}=\frac{c}{d}-\frac{a}{b}$
• D. none of these

Answer 1

The correct option is C $\frac{a}{b}-\frac{c}{d}=\frac{c}{d}-\frac{a}{b}$

For rational number, subtraction is not commutative.

i.e. $p-q\ne q-p$.
$\therefore \frac{a}{b}-\frac{c}{d}=\frac{c}{d}-\frac{a}{b}$ is not true.

Thus, it is an incorrect statement.