Question

Which of the following fractions will complete the given equation?
$\left[\right]\frac{\left[\right]}{\left[\right]}\times \frac{\left[\right]}{\left[\right]}=\frac{14}{8}$

• A. $1\frac{1}{4}\times \frac{3}{3}$
• B. $1\frac{3}{4}\times \frac{2}{2}$
• C. $2\frac{3}{5}\times \frac{3}{3}$
• D. All of the above.

Answer 1

The correct option is B $1\frac{3}{4}\times \frac{2}{2}$

Let's convert $1\frac{3}{4}$ into a improper fraction.
$1\frac{3}{4}=1+\frac{3}{4}=\frac{1\times 4}{1\times 4}+\frac{3}{4}=\frac{4}{4}+\frac{3}{4}=\frac{7}{4}$
$1\frac{3}{4}\times \frac{2}{2}=\frac{7}{4}\times \frac{2}{2}=\frac{14}{8}$
Hence, option A is correct.

Option B:
Let's convert $1\frac{1}{4}$ into an improper fraction.
$1\frac{1}{4}=1+\frac{1}{4}=\frac{1\times 4}{1\times 4}+\frac{4}{4}+\frac{1}{4}=\frac{5}{4}$
$1\frac{1}{4}\times \frac{3}{3}=\frac{5}{4}\times \frac{3}{3}=\frac{15}{12}$
This does not satisfy the equation given in option.
Hence, option B is incorrect.

Option C:
Let's convert $2\frac{3}{5}$ into an improper fraction.
$2\frac{3}{5}=2+\frac{3}{5}=\frac{2\times 5}{1\times 5}+\frac{3}{5}=\frac{10}{5}+\frac{3}{5}=\frac{13}{5}$
$2\frac{3}{5}\times \frac{3}{3}=\frac{13}{5}\times \frac{3}{3}=\frac{39}{15}$
Hence, option C is incorrect.