Question

Which of the following numbers lie between -1 and -2?
a) \[\dfrac{-1}{2}\]
b) \[\dfrac{-3}{2}\]
c) \[\dfrac{1}{2}\]
d) \[\dfrac{3}{2}\]

Answer 1

Hint: In this type of questions first we must convert all the given fractions to decimals and then compare them with given range or we can convert all the numbers to fractions and compare and we must also know that negative numbers decrease as the magnitude of those numbers increases,
For e.g. \[-4 < -3\] as both numbers are negative and in magnitude \[4 > 3\].

Complete step-by-step solution -
Explanation:
Step 1: converting all the fractions into decimals we get
\[-\dfrac{1}{2}~=\text{ }-0.5\]
\[~-\dfrac{3}{2}=-1.5\]
\[~\dfrac{1}{2}=0.5\]
\[~\dfrac{3}{2}=1.5\]
Step 2: we know that a number between -2 and -1 will be negative so \[-0.5\] or \[-1.5\] can be answer
Step 3: now we need a number to lie between -2 and -1 Let’s assume the number is x, so x must satisfy the following condition,
\[x \le -1\] and \[x\ge -2\]
Step 4: we compare the numbers according to the above conditions we get,
\[(-0.5~>-1)\] and \[(-0.5>-2)\]
 \[(-1.5<-1)\] and \[(-1.5>-2)\]
\[(0.5>~-1)\] and \[(0.5>-2)\]
\[(1.5~>-1)\] and \[(1.5\text{ }>-2)\]
Hence, we get -1.5 as the correct answer as it satisfies the given conditions and option b is correct.

Note: We can also do this by converting the given whole numbers to fractions and then comparing with options given, where -2 can be written as $-\dfrac{4}{2}$ and -1 can be written as $-\dfrac{2}{2}$
$\dfrac{-4}{2}<\dfrac{-3}{2}<\dfrac{-2}{2}<\dfrac{-1}{2}<\dfrac{1}{2}<\dfrac{3}{2}$
As we can see only \[\dfrac{-3}{2}\] lies between -2 and -1 it will be the answer.