Question

CSATEasyPrelims 2019Maths

If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is

Explanation

Proper Fraction: A proper fraction is when the numerator is smaller than the denominator/ If you add the same positive number (let’s say $a$ ) to both the numerator and the denominator, the fraction becomes: $\frac{x+a}{y+a}$ where $x$ is the original numerator and $y$ is the original denominator.

Effect of Adding a:

The numerator increases by $a$ .
The denominator increases by $a$ , but since the denominator was already larger than the numerator, the denominator still remains larger than the numerator.

When you add the same number to both, the fraction increases because the denominator increases slower than the numerator in relation to the total value of the fraction. Thus, the new fraction is always greater than the original one.