Question

Ashley ate $2\frac{1}{4}$ of a cake, while Abby ate $1\frac{2}{3}$ of a cake. What is the total amount of cake consumed by Abby and Ashley?
Express the answer as the improper fraction

• A. $\frac{35}{12}$
• B. $\frac{42}{12}$
• C. $\frac{47}{12}$
• D. $\frac{47}{4}$

Answer 1

The correct option is C $\frac{47}{12}$

Cake eaten by Abby $=1\frac{2}{3}$
Cake eaten by Ashley $=2\frac{1}{4}$

Let's convert each of the fraction into the improper fraction
$1\frac{2}{3}=\frac{3\times 1+2}{3}=\frac{5}{3}$

$2\frac{1}{4}=\frac{4\times 2+1}{4}=\frac{9}{4}$

Total cake eaten $=\frac{5}{3}+\frac{9}{4}$
As these are unlike fractions, convert them into the like fractions as follows

$\frac{5}{3}=\frac{5\times 4}{3\times 4}=\frac{20}{12}$

$\frac{9}{4}=\frac{9\times 3}{4\times 3}=\frac{27}{12}$

$\therefore \frac{5}{3}+\frac{9}{4}=\frac{20}{12}+\frac{27}{12}$

Now, add the two fractions
As the denominators of the fractions are the same, so the numerators can be added directly and the denominator remains the same.

$=\frac{20+27}{12}$

$=\frac{47}{12}$