# How to Multiply a Fraction by a Whole Number

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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.

## How to Multiply a Fraction by a Whole Number

### Multiply the Numerators and Denominators

1. Write the whole number as a fraction.

2. Multiply the numerators and denominators of the two fractions.

3. Simplify the answer if possible.

For Example,

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

1. Add the given fraction to the number of times17 it needed to be multiplied by.

2. Write the multiplication as an addition.

3. Add the numerators and keep the denominators the same.

For Example,

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

## How to Multiply Mixed Fraction by a Whole Number

1. Convert the Mixed Fractions into Improper Fractions.

2. Write the whole number as a fraction.

3. Multiply the numerators and denominators of the two fractions.

4. Convert the answer back to Mixed Fractions.

5. Simplify the answer if possible.

For Example,

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