Question

Complete the given fraction equations and choose the option that describes the equations correctly.

Fraction equation$1:\left[\right]\frac{\left[\right]}{\left[\right]}\times \frac{\left[\right]}{\left[\right]}=2\frac{3}{15}$
Fraction equation$2:\left[\right]\frac{\left[\right]}{\left[\right]}\times \frac{\left[\right]}{\left[\right]}=1\frac{4}{24}$

• A. $2\frac{1}{5}$ in fraction equation $1$ is scaled up by $3$ times.
• B. Both options A and B are incorrect.
• C. Both options A and B are correct.
• D. $1\frac{1}{6}$ in fraction equation $2$ is scaled up by $4$ times.

Answer 1

The correct option is C Both options A and B are correct.

Let' s check option A : $2\frac{1}{5}$ in fraction equation $1$ is scaled up by $3$ times.
Let's convert $2\frac{1}{5}$ into an improper fraction.
$2\frac{1}{5}=2+\frac{1}{5}=\frac{2\times 5}{1\times 5}+\frac{1}{5}=\frac{10}{5}+\frac{1}{5}=\frac{11}{5}$
$2\frac{1}{5}$ scaled up by $3$ times is written as:
$2\frac{1}{5}\times \frac{3}{3}=\frac{11}{5}\times \frac{3}{3}=\frac{33}{15}$
$\frac{33}{15}$ as a mixed fraction $=2\frac{3}{15}$
So, $2\frac{1}{5}\times \frac{3}{3}=2\frac{3}{15}$, which is equal to the right-hand side of fraction equation $1$
Therefore, we can conclude that $2\frac{1}{5}$ is scaled up by $3$ times

Let's check option B: $1\frac{1}{6}$ in fraction equation $2$ is scaled up by $4$ times.
Let's convert $1\frac{1}{6}$ into an improper fraction
$1\frac{1}{6}=1+\frac{1}{6}=\frac{1\times 6}{1\times 6}+\frac{1}{6}=\frac{6}{6}+\frac{1}{6}=\frac{7}{6}$
$1\frac{1}{6}\times \frac{4}{4}=\frac{7}{6}\times \frac{4}{4}=\frac{28}{24}$
$\frac{28}{24}$ as a mixed fraction $=1\frac{4}{24}$
Therefore, we can conclude that $1\frac{1}{6}$ in fraction equation $2$ is scaled up by $4$ times.