Evaluate the following and express the answer as a mixed fraction:

$4\frac{2}{3}\ \times\ 1\frac{1}{11}$

Given: $4 \frac{2}{3}\ \times\ 1 \frac{1}{11}$

To do: Here we have to evaluate the given expression and express the answer as a mixed fraction.

Solution:

$4\frac{2}{3}\ \times\ 1\frac{1}{11}$

Convert mixed numbers to improper fractions: $4 \frac{2}{3}\ =\ \frac{14}{3}$

$\frac{14}{3} \times 1 \frac{1}{11}$

Convert mixed numbers to improper fractions: $1 \frac{1}{11}\ =\ \frac{12}{11}$

$\frac{14}{3}\ \times\ \frac{12}{11}$

Factor the number: $12\ =\ 3\ \times\ 4$

$=\ \frac{14}{3}\ \times\ \frac{3\ \times\ 4}{11}$

Cross-cancel common factor: 3

$=\ \frac{14}{1}\ \times\ \frac{4}{11}$

Apply the fraction rule: $\frac{a}{b}\ \times\ \frac{c}{d}\ =\ \frac{a\ \times\ c}{b\ \times\ d}$

$\frac{14}{1}\ \times\ \frac{4}{11}\ =\ \frac{14\ \times\ 4}{1\ \times\ 11}$

Multiply the numbers: $14\ \times\ 4\ =\ 56$

$=\ \frac{56}{1\ \times\ 11}$

Multiply the numbers: $1\ \times\ 11\ =\ 11$

$=\ \frac{56}{11}$

Convert improper fractions to mixed numbers: $\frac{56}{11}\ =\ 5 \frac{1}{11}$

$=\ \mathbf{5\frac{1}{11}}$

So, value of the given expression is $5 \frac{1}{11}$.

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Updated on: 10-Oct-2022

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