Question

A student multiplied two mixed fractions in the following manner :

$2\frac{4}{7}\times 3\frac{1}{4}=6\frac{1}{7}$. What error the students has done?

Answer 1

Step: Find the error​

To check : $2\frac{4}{7}\times 3\frac{1}{4}=6\frac{1}{7}$

Convert mixed fractions into improper fractions :

$2\frac{4}{7}=\frac{(2\times 7)+4}{7}=\frac{14+4}{7}=\frac{18}{7}$

$3\frac{1}{4}=\frac{(3\times 4)+1}{4}=\frac{12+1}{4}=\frac{13}{4}$

$\therefore 2\frac{4}{7}\times 3\frac{1}{4}=\frac{18}{7}\times \frac{13}{4}=\frac{234}{28}$

$=\frac{117}{14}=8\frac{5}{14}$

But given that,

$2\frac{4}{7}\times 3\frac{1}{4}=6\frac{1}{7}$

Hence, the error is that mixed fractions are not converted into proper fractions.