Question

What number is mid-way between $\dfrac{1}{2}$ and 1?

Answer 1

Hint: We know that the average of two numbers is always in mid-way between the two numbers. So, we can find the average of given two numbers to solve this problem. We can also solve this problem, by plotting the given points on the number line, and then bisecting the line.

Complete step by step answer:
To calculate a number mid-way between two numbers, we can calculate the average of these two numbers. We know that this average will always be in the middle of those two numbers.
To find the number exactly in the middle of $\dfrac{1}{2}$ and 1, we need to calculate the average of $\dfrac{1}{2}$ and 1.
We know that the average of any two numbers, a and b is = $\dfrac{a+b}{2}$.
So, we know that the average will be = $\dfrac{\dfrac{1}{2}+1}{2}=\dfrac{\left( \dfrac{3}{2} \right)}{2}=\dfrac{3}{4}$.
Hence, the number $\dfrac{3}{4}$ is mid-way between $\dfrac{1}{2}$ and 1.
Also, we can solve this problem using the number line method.
Let us first plot the two given numbers $\dfrac{1}{2}$ and 1 on the number line.
Now, we can plot the midpoint of $\dfrac{1}{2}$ and 1, that is, $\dfrac{3}{4}$.

We can also find the number mid-way between $\dfrac{1}{2}$ and 1, by using the concept of fractions.
We know that we can express 1 as $\dfrac{4}{4}$, and the number $\dfrac{1}{2}$ as $\dfrac{2}{4}$. So, now if we compare these two numbers with each other, we can easily say that the number exactly in the centre of $\dfrac{1}{2}$ and 1 is $\dfrac{3}{4}$.

Hence, we are now sure that the number mid-way between $\dfrac{1}{2}$ and 1 is $\dfrac{3}{4}$.

Note: We must plot the points very carefully on the number line. To find the midpoint on the number line, we can use the concept of constructing a perpendicular line bisector using a compass.