MATHS M.C.Q. [1 Marks Each]

Number that lies between $0$ and $-1,$
$-\frac{2}{3}= -0.666...$

Total length of the rope $=4\frac{1}{4}\text{m}=\frac{9}{2}\text{m}$
Number of total pieces $= 9$
Let the length of each piece be $y\ m.$
As per the question,
$\text{9y}=\frac{9}{2}$
$\text{y}=\frac{9}{2\times9}$
$\text{y}=\frac{1}{2}\text{m}$
Therefore, the length of each piece is $\frac{1}{2}\text{m}.$

The additive inverse of $4$ is $-4.$

We know that, if a and b are the additive inverse of each other,
Then $a + b = 0$
Suppose, $x$ is the additive inverse of $\frac{-7}{19}$
Then, $\text{x}-\frac{7}{19}=0$
$\Rightarrow\text{x}=\frac{7}{19}$
Hence, additive inverse of $\frac{-7}{19}$ is $\frac{7}{19}.$

 Here, $\frac{\text{x}+\text{y}}{2}$ is a rational number.
Then, it always lies in between $x$ and $y$ either $x < y$ or $y < x.$

A rational number can be represented in the form $\frac{\text{p}}{\text{q}}$ where $p$ and $q$ are integers and $q$ is not equal to zero.

$\frac{2}{3}\times\Big(\frac{-6}{7}\times\frac{3}{5}\Big)=\Big(\frac{2}{3}\times\frac{-6}{7}\Big)\times\frac{3}{5}$
$[$by associative property under multiplication, $a × (b × c) = (a × b) × c]$
$\Rightarrow\frac{2}{3}\times\frac{-18}{35}=\frac{-12}{21}\times\frac{3}{5}$
So, $a × (b × c) = (a × b) × c$
Hence, the given expression shows that rational numbers are associative under multiplication.