Question
If $\frac{\text{P}}{\text{q}}$ is a rational number and $m$ is a non-zero integer, then $\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}$ is a rational number not equivalent to $\frac{\text{P}}{\text{q}}.$
✓
Answer
Let $m = 1, 2, 3,...$
When $m = 2,$ then,
$\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}=\frac{\text{P}\times1}{\text{q}\times1}=\frac{\text{P}}{\text{q}}$
When $m = 2,$
then, $\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}=\frac{\text{P}\times2}{\text{q}\times2}=\frac{\text{P}}{\text{q}}$For any non-zero value of $m,$
$\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}$ is always equivalent to $\frac{\text{P}}{\text{q}}.$
When $m = 2,$ then,
$\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}=\frac{\text{P}\times1}{\text{q}\times1}=\frac{\text{P}}{\text{q}}$
When $m = 2,$
then, $\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}=\frac{\text{P}\times2}{\text{q}\times2}=\frac{\text{P}}{\text{q}}$For any non-zero value of $m,$
$\frac{\text{P}\times\text{m}}{\text{q}\times\text{m}}$ is always equivalent to $\frac{\text{P}}{\text{q}}.$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Which is larger?
(a) 6.78 or 6.87
(b) 7.90 or 17.900
(a) 6.78 or 6.87
(b) 7.90 or 17.900
Multiply: $\frac{3}{4}\text{ by }\frac{5}{7}$
→In figure, $\triangle\text{ABC}$ is isosceles with $AB = AC$. State if $\triangle\text{ABC}\cong\triangle\text{ACB}.$ If yes, state three relations that you use to arrive at your answer.
→For the following statements, write $(T)$ for true and $(F)$ for false: The smallest integer is zero.
→Which of these are negative rational numbers?
0
0
Write a pair of negative integers, whose difference gives 8.
Fill in the blanks: $($_____$) ÷ (-4) = 24$
→$\triangle\text{ABC}$ is isosceles with $AB = AC$. Line segment $AD$ bisects $\angle\text{A}$ and meets the base $BC$ in $D$.
Is it true to say that $BD = DC$?
→Is it true to say that $BD = DC$?
Give the order of rotational symmetry for the figure:
Express the following properties with variables $x, y$ and $z:$ Associative property of multiplication.
→