Question
Find two rational numbers lying between $\frac{-1}{3}$ and $\frac{1}{2}$.
✓
Answer
Required number $=\frac{1}{2}\times\Big(\frac{-1}{3}+\frac{1}{2}\Big)$
$=\frac{1}{2}\times\Big(\frac{-2+3}{6}\Big)$
$=\frac{1}{2}\times\frac{1}{6}$
$=\frac{1}{12}$
$\frac{-1}{3}<\frac{1}{12}<\frac{1}{2}$
Required number between $\frac{-1}{3}$ and $\frac{1}{2}$:
$=\frac{1}{2}\times\Big(\frac{-1}{3}+\frac{1}{12}\Big)$
$=\frac{1}{2}\times\Big(\frac{1-4}{12}\Big)$
$=\frac{1}{2}\times\Big(\frac{-3}{12}\Big)$
$=\frac{-3}{24}$
$=\frac{-3\div3}{24\div3}$
$=\frac{-1}{8}$
Thus, $\frac{1}{12}$ and $\frac{-1}{8}$ are two rational numbers between $\frac{-1}{3}$ and $\frac{1}{2}$.
$=\frac{1}{2}\times\Big(\frac{-2+3}{6}\Big)$
$=\frac{1}{2}\times\frac{1}{6}$
$=\frac{1}{12}$
$\frac{-1}{3}<\frac{1}{12}<\frac{1}{2}$
Required number between $\frac{-1}{3}$ and $\frac{1}{2}$:
$=\frac{1}{2}\times\Big(\frac{-1}{3}+\frac{1}{12}\Big)$
$=\frac{1}{2}\times\Big(\frac{1-4}{12}\Big)$
$=\frac{1}{2}\times\Big(\frac{-3}{12}\Big)$
$=\frac{-3}{24}$
$=\frac{-3\div3}{24\div3}$
$=\frac{-1}{8}$
Thus, $\frac{1}{12}$ and $\frac{-1}{8}$ are two rational numbers between $\frac{-1}{3}$ and $\frac{1}{2}$.
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
$ABCDE$ is a regular pentagon. The bisector of angle A meets the side $CD$ at $M$. Find $\angle\text{AMC}.$
→Quadrilateral EFGH is a rectangle, in which J is the point of intersection of the diagonals. Find the value of $x$ if $J F=(8 x+4)$ and $E G=(24 x-8).$
→A sum amounts to $Rs. 756.25$ at $10\%$ per annum in $2$ years, compounded annually. Find the sum.
→Solve:
$ a^2-8 a b+16 b^2-25 c^2 $
→$ a^2-8 a b+16 b^2-25 c^2 $
Which of the two rational numbers is greater in the given pair$?$
$\frac{-1}{3}\ \text{or}\ \frac{4}{-5}$
→$\frac{-1}{3}\ \text{or}\ \frac{4}{-5}$
Find the least number of $4$ digits which is a perfect square.
→Find the square root of the following by prime factorization.$47089$
→The difference between the ages of two cousins is $10$ years. $15$ years ago, if the elder one was twice as old as the younger one, find their present ages.
→A garrison of $200$ men had provisions for $45$ days. After $15$ days, $40$ more men join the garrison. Find the number of days for which the remaining food will last.
→Amit was given an increment of $20\%$ on his salary. If his new salary is $Rs. 15300,$ what was his salary before the increment$?$
→