Question

Which of the following fractions is the largest?
A. $${\displaystyle \frac{29}{30}}$$
B. $${\displaystyle \frac{29}{23}}$$
C. $${\displaystyle \frac{29}{27}}$$
D. $${\displaystyle \frac{29}{25}}$$

Answer 1

Hint: Compare the four options on the basis of the numerators and denominators of the fractions The denominator which is the least among these will have the greatest fraction.

Complete step-by-step answer:
Given are 4 fractions $${\displaystyle \frac{29}{30}}$$, $${\displaystyle \frac{29}{23}}$$, $${\displaystyle \frac{29}{27}}$$, $${\displaystyle \frac{29}{25}}$$. We need to compare these 4 fractions and find which the largest fraction is. All the fractions given here have the same numerator. As the denominator gets larger, the fraction gets smaller.
To compare fractions with like numerators, look at the denominators. The fraction with the smaller denominator is the larger fraction.
Here, out of $${\displaystyle \frac{29}{30}}$$, $${\displaystyle \frac{29}{23}}$$, $${\displaystyle \frac{29}{27}}$$, $${\displaystyle \frac{29}{25}}$$, the least denominator is 23.
Thus we can conclude that $${\displaystyle \frac{29}{23}}$$ is the largest fraction.
We can arrange these fractions from largest to smallest by seeing their denominators.
$${\displaystyle \frac{29}{23}}>{\displaystyle \frac{29}{25}}>{\displaystyle \frac{29}{27}}>{\displaystyle \frac{29}{30}}.$$
Thus we found the largest fraction as $${\displaystyle \frac{29}{23}}$$ and the smallest fraction as $${\displaystyle \frac{29}{30}}.$$
It is easier to compare fractions with numerators and denominators than dividing the fraction and converting to decimal form and then comparing it.
Thus the largest fraction = $${\displaystyle \frac{29}{23}}$$.
Option B is the correct answer.

Note: If the fractions were $${\displaystyle \frac{30}{29}}$$, $${\displaystyle \frac{23}{29}}$$, $${\displaystyle \frac{27}{29}}$$, $${\displaystyle \frac{25}{29}}$$, i.e. where the denominators are same and numerators are unlike, then the largest fraction is the one with the greatest numerator.
So here $${\displaystyle \frac{30}{29}}>{\displaystyle \frac{27}{29}}>{\displaystyle \frac{25}{29}}>{\displaystyle \frac{23}{29}}.$$
Here, the greatest fraction is $${\displaystyle \frac{30}{29}}$$ and the smallest fraction is $${\displaystyle \frac{23}{29}}.$$