Question

If $3$ is added to both the numerator and the denominator of the fraction
$\frac{5}{9}$, then will the value of the fraction increase or decrease?

• A. Both are equal
  
• B. Decrease
  
• C. Cannot be determined
  
• D. Increase

Answer 1

The correct option is D Increase

Let’s write $\frac{5}{9}$ as a decimal expansion.


If $3$ is added to the numerator and denominator of $\frac{5}{9}$ , we get:

$\frac{5}{9}=\frac{5+3}{9+3}=\frac{8}{12}$

Decimal value of $\frac{8}{12}$.


As we can see that $\frac{5}{9}$ is smaller than $\frac{8}{12}$ ,

so the value of the fraction will increase.
Note: When we add a constant say $‘k^{\prime }$ to numerator. and denominator of a proper fraction (value $<1$) the value tends towards $1$, i.e it will keep on increasing but always remain smaller than $1.$