Question

Which of the following fractions will fill in the blanks in fraction A and fraction B?
$FractionA:\frac{\left[\right]}{\left[\right]}\times \frac{\left[\right]}{\left[\right]}=2\frac{5}{20}$
$FractionB:\frac{\left[\right]}{\left[\right]}\times \frac{\left[\right]}{\left[\right]}=5\frac{12}{20}$

• A. $FractionA:5\frac{3}{5}\times \frac{5}{5}$
  $FractionB:2\frac{1}{4}\times \frac{5}{5}$
• B. $FractionA:2\frac{1}{4}\times \frac{5}{4}$
  $FractionB:5\frac{3}{5}\times \frac{4}{4}$
• C. $FractionA:5\frac{3}{5}\times \frac{4}{4}$
  $FractionB:2\frac{1}{4}\times \frac{5}{5}$
• D. None of the above

Answer 1

The correct option is B $FractionA:2\frac{1}{4}\times \frac{5}{4}$

$FractionB:5\frac{3}{5}\times \frac{4}{4}$
Let’s check if option A can complete the given blanks.
$FractionA=2\frac{1}{4}\times \frac{5}{5}$
Let's convert $2\frac{1}{4}$ into an improper fraction.
$2\frac{1}{4}=2+\frac{1}{4}=\frac{2\times 4}{1\times 4}+\frac{1}{4}=\frac{8}{4}+\frac{1}{4}=\frac{9}{4}$
$2\frac{1}{4}\times \frac{5}{5}=\frac{9}{4}\times \frac{5}{5}=\frac{45}{20}$

$\frac{45}{20}asamixedfraction=2\frac{5}{20}$

$So,whenfractionA=2\frac{1}{4}\times \frac{5}{5},theansweris2\frac{5}{20}$

Fraction B:
Let's convert $5\frac{3}{5}$ into an improper fraction.

$5\frac{3}{5}=5+\frac{3}{5}=\frac{5\times 5}{1\times 5}+\frac{3}{5}=\frac{25}{5}+\frac{3}{5}=\frac{28}{5}$
$5\frac{3}{5}\times \frac{4}{4}=\frac{28}{5}\times \frac{4}{4}=\frac{112}{20}$
Let's convert $\frac{112}{20}$ into a mixed fraction.

$Mixedfraction=\text{quotient}\times \frac{\text{reminder}}{\text{divisor}}$

Therefore, $\frac{112}{20}=5\frac{12}{20}$
$So,whenfractionB=5\frac{3}{5}\times \frac{4}{4},theansweris5\frac{12}{20}$.
$Hence,fractionA:2\frac{1}{4}\times \frac{5}{5}=2\frac{5}{20}$ and $FractionB:5\frac{3}{5}\times \frac{4}{4}=5\frac{12}{20}$