Question

What number is halfway between $\dfrac{1}{2}$and $\dfrac{3}{4}$ on a number line?

Answer 1

Hint: To find a number which is halfway of two numbers , we should calculate the average of those two numbers. That means if the numbers are $a$ and $b$, then the number which is halfway is $\dfrac{{a + b}}{2}$.

Complete step-by-step solution:
Consider the numbers to be $a$ and $b$,
$a = \dfrac{1}{2}$
$b = \dfrac{3}{4}$
So, halfway between $\dfrac{1}{2}and\dfrac{3}{4}$is
$
   = \dfrac{1}{2} \times \left( {\dfrac{1}{2} + \dfrac{3}{4}} \right) \\
   = \dfrac{1}{2} \times \left( {\dfrac{2}{4} + \dfrac{3}{4}} \right) \\
   = \dfrac{1}{2} \times \left( {\dfrac{{2 + 3}}{4}} \right) \\
   = \dfrac{1}{2} \times \dfrac{5}{4} \\
   = \dfrac{5}{8} \\
 $
Hence, the number is $\dfrac{5}{8}$.
To plot the point on the number line we should equalise the denominator of the three fractions. Hence, the fractions can be reframed as $\dfrac{5}{8}$ is the halfway of $\dfrac{4}{8}and\dfrac{6}{8}$.

Note: Another method to calculate halfway is to find the HCF of both the fractions . Then the fractions would be $\dfrac{2}{4} \text{ and } \dfrac{3}{4}$. The average of $2$ and $3$ is $2.5$ which is not a whole number. So we again multiply the numerator and denominator with $2$. Now, the fraction is $\dfrac{4}{8}$ and $\dfrac{6}{8}$. Now we clearly know that the number between $4$ and $6$ is $5$. Hence, the answer is $\dfrac{5}{8}$.