Question

Which bottle has the more oil?

• A. $\frac{3}{6}$
• B. $\frac{4}{9}$
• C. Both are equal
• D. Can't be determined

Answer 1

The correct option is A $\frac{3}{6}$

Fraction of oil in Bottle 1 = $\frac{3}{6}$
Fraction of oil in Bottle 2 = $\frac{5}{9}$

The multiples of 6 and 9
6$:$6, 12, 18, 24...
9$:$9, 18, 27, 36...
The common factor of 6 and 9 is 18.
Hence, $\frac{3}{6}=\frac{3\times 3}{6\times 3}=\frac{9}{18}$

$\text{and}\frac{5}{9}=\frac{5\times 2}{9\times 2}$
$=\frac{8}{18}$

When two fractions have the same denominator, the fraction which has the bigger numerator has more value.
Since, 9$>$8
$\Rightarrow \frac{9}{18}>\frac{8}{18}$
Therefore, $\frac{3}{6}>\frac{4}{9}$