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# Multiplication of fractions

## Multiplication of fraction and whole number.

Definition.
To multiply fraction by a whole number, it is necessary to multiply numerator by a whole number, and to leave without modifications a denominator. Simplify the fraction if needed.

### Examples of multiplication fraction and integer

Example 1.
Find the product of fraction and natural number:
 3 · 2 = 3 · 2 = 6 7 7 7

Example 2.
Find the product of fraction and natural number:
 1 · 4 = 4 = 2·2 = 2 2 2 2

## Multiplication of fractions.

Definition.

### Examples of multiplication of fractions

Example 3.
Find the product of two fractions:
 3 · 2 = 3 · 2 = 6 7 5 7 · 5 35

Example 4.
Find the product of two fractions:
 10 · 3 = 10 · 3 = 2 · 5 · 3 = 5 = 5 9 4 9 · 4 2 · 2 · 3 · 3 2 · 3 6

## Multiplication of mixed numbers.

Definition.

### Examples of multiplication of mixed numbers

Example 5.
Find the product of two mixed numbers:
 2 1 · 1 2 = 2 · 2 + 1 · 1 · 3 + 2 = 5 · 5 = 5 · 5 = 25 = 6 · 4 + 1 = 4 1 2 3 2 3 2 3 2 · 3 6 6 6

Example 6.
Find the product of mixed number and integer:
 4 1 · 6 = 4 · 3 + 1 · 6 = 13 · 6 = 26 3 3 3

Example 7.
Find the product of mixed number and fraction:
 2 1 · 3 = 2 · 7 + 1 · 3 = 15 · 3 = 15 · 3 = 3 · 3 = 9 = 7 + 2 = 1 2 7 5 7 5 7 5 7 · 5 7 7 7 7