Multiplication is the basic operations in elementary arithmetic and a fraction represents a part of a whole. To multiply fractions, multiply the numerators together and multiply the denominators together, not necessarily in that order, and then simplify the product if necessary, as to leave it in the simplest form.

Here we discussed about the multiplication of the fractions. To multiply signed fractions, we follow both the rules for multiplying fractions and those for multiplying signed integers.

Here we discussed about the multiplication of the fractions. To multiply signed fractions, we follow both the rules for multiplying fractions and those for multiplying signed integers.

There is more than one way to multiply with fractions:There is more than one way to multiply with fractions:

- Multiply fractions by whole numbers.
- Multiply fractions by fractions.
- Multiply fractions by mixed fractions.

## How to Multiply Fractions

**Steps for Multiplying Fractions:**

**Step 1:**Multiply the numerators.

**Step 2:**Multiply the denominators.

**Step 3:**Write the answer as a fraction, reduced it if possible.

### Solved Examples

**Question 1:**Multiply $\frac{3}{5}$ and 7

**Solution:**

Step 1:

Write 7 as a fraction with a denominator of 1.

7 = $\frac{7}{1}$

Step 2: Multiply numerators together and denominators together

$\frac{3}{5}$ * $\frac{7}{1}$ = $\frac{3 * 7}{5 * 1}$

= $\frac{21}{5}$

Write 7 as a fraction with a denominator of 1.

7 = $\frac{7}{1}$

Step 2: Multiply numerators together and denominators together

$\frac{3}{5}$ * $\frac{7}{1}$ = $\frac{3 * 7}{5 * 1}$

= $\frac{21}{5}$

**Question 2:**Multiply $\frac{6}{15}$ and $\frac{9}{2}$

**Solution:**

Step 1:

Multiply numerators together and denominators together

$\frac{6}{15}$ * $\frac{9}{2}$ = $\frac{6 * 9}{15 * 2}$

= $\frac{54}{30}$

Step 2: Reduced the fraction

$\frac{54}{30}$ = $\frac{2 * 3 * 3 * 3}{2 * 3 * 5}$

= $\frac{ 3 * 3}{ 5}$

= $\frac{9}{ 5}$

=> $\frac{6}{15}$ * $\frac{9}{2}$ = $\frac{9}{ 5}$

Multiply numerators together and denominators together

$\frac{6}{15}$ * $\frac{9}{2}$ = $\frac{6 * 9}{15 * 2}$

= $\frac{54}{30}$

Step 2: Reduced the fraction

$\frac{54}{30}$ = $\frac{2 * 3 * 3 * 3}{2 * 3 * 5}$

= $\frac{ 3 * 3}{ 5}$

= $\frac{9}{ 5}$

=> $\frac{6}{15}$ * $\frac{9}{2}$ = $\frac{9}{ 5}$

**Question 3:**Multiply $\frac{31}{4}$ and $\frac{5}{2}$

**Solution:**

Multiply numerators together and denominators together

$\frac{31}{4}$ * $\frac{5}{2}$ = $\frac{31 * 5}{4 * 2}$

= $\frac{155}{8}$

=> $\frac{31}{4}$ * $\frac{5}{2}$ = $\frac{155}{8}$

$\frac{31}{4}$ * $\frac{5}{2}$ = $\frac{31 * 5}{4 * 2}$

= $\frac{155}{8}$

=> $\frac{31}{4}$ * $\frac{5}{2}$ = $\frac{155}{8}$

## Multiplying Fractions

**Mixed number must be reduced to improper fractions, and whole numbers to the form of fractions.**

### Solved Examples

**Question 1:**Solve $3\tfrac{4}{5}$ * $\frac{4}{5}$

**Solution:**

Step 1: Change mixed number to improper fraction

Step 2: Multiply numerators together and denominators together

$\frac{19}{5}$ * $\frac{4}{5}$ = $\frac{19 * 4}{5 * 5}$

= $\frac{76}{25}$

=> $\frac{19}{5}$ * $\frac{4}{5}$ = $\frac{76}{25}$

**$3\tfrac{4}{5}$ = $\frac{19}{5}$**

Step 2: Multiply numerators together and denominators together

$\frac{19}{5}$ * $\frac{4}{5}$ = $\frac{19 * 4}{5 * 5}$

= $\frac{76}{25}$

=> $\frac{19}{5}$ * $\frac{4}{5}$ = $\frac{76}{25}$

**Question 2:**Solve $2\tfrac{2}{3}$ * $\frac{8}{5}$

**Solution:**

Step 1: Change mixed number to improper fraction

$2\tfrac{2}{3}$ = $\frac{8}{3}$

Step 2: Multiply numerators together and denominators together

$\frac{8}{3}$ * $\frac{8}{5}$ = $\frac{8 * 8}{3 * 5}$

= $\frac{64}{15}$

=> $2\tfrac{2}{3}$ * $\frac{8}{5}$ = $\frac{64}{15}$

$2\tfrac{2}{3}$ = $\frac{8}{3}$

Step 2: Multiply numerators together and denominators together

$\frac{8}{3}$ * $\frac{8}{5}$ = $\frac{8 * 8}{3 * 5}$

= $\frac{64}{15}$

=> $2\tfrac{2}{3}$ * $\frac{8}{5}$ = $\frac{64}{15}$

**Question 3:**Multiply $\frac{10}{3}$ and $\frac{4}{7}$

**Solution:**

Multiply numerators together and denominators together

$\frac{10}{3}$ * $\frac{4}{7}$ = $\frac{10 * 4}{3 * 7}$

= $\frac{40}{21}$

=> $\frac{10}{3}$ * $\frac{4}{7}$ = $\frac{40}{21}$

$\frac{10}{3}$ * $\frac{4}{7}$ = $\frac{10 * 4}{3 * 7}$

= $\frac{40}{21}$

=> $\frac{10}{3}$ * $\frac{4}{7}$ = $\frac{40}{21}$