How to Multiply a Fraction by a Whole Number

It is not difficult to multiply fractions by whole numbers. Here is how you can multiply a fraction by a whole number by following the simple steps.

Write the whole number as a fraction.
Multiply the numerators and denominators of the two fractions.
Simplify the answer if possible.
For Example,

$\\\mathbf{Given\ the\ Fraction\ and\ Whole\ Number\ is\ \frac{5}{7}X3} \\ \\\mathbf{Write\ the\ whole\ number\ as\ a\ fraction\ \frac{5}{7}X\frac{3}{1}} \\ \\\mathbf{Multiply\ the\ numerators\ and\ denominators\ of\ the\ two\ fractions\ \frac{5 x 3}{7 x 1}} \\ \\\mathbf{Answer\ can\ not\ be\ simplified\ any\ further\ so\ the\ final\ answer\ is\ \ \frac{15}{7}}$

Add the given fraction to the number of times $\frac{1}{7}$ it needed to be multiplied by.
Write the multiplication as an addition.
Add the numerators and keep the denominators the same.
For Example,

$\\\mathbf{Given\ the\ Fraction\ and\ Whole\ Number\ is\ \frac{5}{7}\ x\ 3} \\ \\\mathbf{Write\ the\ multiplication\ as\ an\ addition.\ \frac{5}{7}\ x\ {3} = \frac{5}{7} + \frac{5}{7} + \frac{5}{7}} \\ \\\mathbf{Add\ the\ numerators\ and\ keep\ the\ denominators\ same\ \frac{(5 + 5 + 5)}{7}} \\ \\\mathbf{Answer\ can\ not\ be\ simplified\ any\ further\ so\ the\ final\ answer\ is\ \ \frac{15}{7}}$

How to Multiply Mixed Fraction by a Whole Number

Convert the Mixed Fractions into Improper Fractions.
Write the whole number as a fraction.
Multiply the numerators and denominators of the two fractions.
Convert the answer back to Mixed Fractions.
Simplify the answer if possible.
For Example,

$\\\mathbf{Given\ the\ Mixed\ Fraction\ and\ Whole\ Number\ is\ 2\frac{1}{3}\ x\ 5} \\ \\\mathbf{Convert\ the\ Mixed\ Fractions\ into\ Improper\ Fractions\ \frac{7}{3}\ x\ 5} \\ \\\mathbf{Write\ the\ whole\ number\ into\ Fraction.\ \frac{7}{3}\ x\ \frac{5}{1}} \\ \\\mathbf{Multiply\ the\ numerators\ and\ denominators\ of\ the\ two\ fractions\ is\ \frac{7 x 5}{3 x 1} = \frac{35}{3}} \\ \\\mathbf{Convert\ the\ answer\ back\ to\ Mixed\ Fraction\ 11\ \frac{2}{3}} \\ \\\mathbf{The\ answer\ can\ not\ be\ simplified\ further\ so\ the\ final\ answer\ is\ 11\ \frac{2}{3}}$