Question
Find two rational number between $-3$ and $-2.$
✓
Answer
First rational number between $-3$ and $-2$
$=\frac{1}{2}[-3+(-2)]$
$=\frac{1}{2}(-3-2)$
$=\frac{1}{2}(-5)$
$=\frac{-5}{2}$
$\therefore-3<\frac{-5}{2}<-2$
Second rational number between $-3$ and $\frac{-5}{2}$
$=\frac{1}{2}\Big[-3+\Big(\frac{-5}{2}\Big)\Big]$
$=\frac{1}{2}\Big[-3-\frac{5}{2}\Big]$
$=\frac{1}{2}\Big[\frac{-6-5}{2}\Big]$
$=\frac{1}{2}\times\frac{-11}{2}$
$=\frac{-11}{4}$
$=\frac{1}{2}[-3+(-2)]$
$=\frac{1}{2}(-3-2)$
$=\frac{1}{2}(-5)$
$=\frac{-5}{2}$
$\therefore-3<\frac{-5}{2}<-2$
Second rational number between $-3$ and $\frac{-5}{2}$
$=\frac{1}{2}\Big[-3+\Big(\frac{-5}{2}\Big)\Big]$
$=\frac{1}{2}\Big[-3-\frac{5}{2}\Big]$
$=\frac{1}{2}\Big[\frac{-6-5}{2}\Big]$
$=\frac{1}{2}\times\frac{-11}{2}$
$=\frac{-11}{4}$
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
Verify Euler's relation for the following: A tetrahedron.
How many bricks of size $22\ cm \times 10\ cm \times 7\ cm$ are required to construct a wall $11\ m$ long, $3.5\ m$ high and $40\ cm$ thick, if the cement and sand used in the construction occupy $\Big(\frac{1}{10}\Big)\text{th}$ part of the wall?
→If x denotes the digit at hundreds place of the number $\overline{67\text{x}19}$ such that the number is divisible by $11.$ Find all possible values of $x.$
→If $x$ and $y$ vary inversely as: $x = 5$ when $y = 15$, find x when $y = 12$
→The units digit of a two-digit number is $3$ and seven time the sum of the digits is the number itself. Find the number.
→Find the number of sides of a regular polygon when each of its angles has a measures of:- $160^\circ $
→Campus and Welfare Committee of school is planning to develop a blue shade for painting the entire school building. For this purpose various shades are tried by mixing containers of blue paint and white paint. In each of the following mixtures, decide which is a lighter shade of blue and also find the lightest blue shade among all of them.
If one container has one litre paint and the building requires $105$ litres for painting, how many container of each type is required to paint the building by darkest blue shade?
→If one container has one litre paint and the building requires $105$ litres for painting, how many container of each type is required to paint the building by darkest blue shade?
Three cubes each of side $10\ cm$ are joined end to end. Find the surface area of the resultant figure.
→Factorise the expression and divide them as directed:$ 12 x y\left(9 x^2-16 y^2\right) \div 4 x y(3 x+4 y)$
→As part of his science project, Prithvi was supposed to record the temperature every hour one Saturday from $6\ am$ to midnight. At noon, he was taking lunch and forgot to record the temperature. At $8:00\ pm$, his favourite show came on and so forgot again. He recorded the data so collected on a graph sheet as shown below.
$a.$ Why does it make sense to connect the points in this situation?
$b.$ Describe the overall trend, or pattern, in the way the temperature changes over the time period shown on the graph.
$c.$ Estimate the temperature at noon and $8 \ pm.$
→$a.$ Why does it make sense to connect the points in this situation?
$b.$ Describe the overall trend, or pattern, in the way the temperature changes over the time period shown on the graph.
$c.$ Estimate the temperature at noon and $8 \ pm.$