Question

$\text{John cuts out}\frac{3}{5}\text{th of a cake. Then he shares}\frac{3}{4}\text{th of his portion of cake, with his friend Anna.}\text{What fraction of the cake does Anna have?}$

• A. $\frac{9}{20}$
• B. $\frac{3}{20}$
• C. $\frac{11}{20}$
• D. $\frac{7}{20}$

Answer 1

The correct option is A $\frac{9}{20}$

$\text{John's portion of the cake}=\frac{3}{5}$

$\text{Fraction of John's portion of cake, shared with}\text{Anna}=\frac{3}{4}$

$\text{Fraction of cake with Anna}=\frac{3}{5}\times \frac{3}{4}$

$\text{Calculating}\frac{3}{5}\times \frac{3}{4}\text{using visual models,}\text{we get:}$


$\text{Total parts}=20$

$\text{Total area}=1\times 1=1\text{sq. unit}$

$\text{Area of each section}=\frac{1}{20}\text{sq. unit}$

$\text{Area of overlapping section}=\frac{1}{20}\times 9=\frac{9}{20}\text{sq. units}$

$\therefore \text{The fraction of cake with Anna is}\frac{9}{20}$