## Multiplying fractions

### Multiplication fractions for a natural number

To multiply a fraction by a number, the numerator need to multiply the number and denominator remain unchanged.

### Example of multiplying fractions for a natural number

*Example 1: *Find the product of the fraction on an integer (multiply a fraction by a natural number): for

Answer:

### Multiplying fractions with different denominators

To *add two fractions with different denominators*, you need to:

- multiply the numerators and denominators of fractions;
- reduce the resulting fraction;

### Example multiplication of fractions with different denominators

*Example 2: Multiply two fractions with different denominators:* and

Answer:

### Multiplication of mixed numbers

To *multiply two mixed numbers*, you need to:

- convert mixed fractions to improper;
- multiply the numerators and denominators of fractions;
- reduce the resulting fraction;
- If you have received an improper fraction, you convert an improper fraction to a mixed.

### Examples of adding mixed numbers

*Example 3: Multiply the common fraction by a mixed number*: and

Answer:

*Example 4 Multiply mixed number by a natural number*: and

Answer:

*Example 5: Multiply mixed numbers*: and

Answer:

## Multiplying decimals

To *multiply two decimals, *you should:

- perform the multiplication, ignoring the commas
- separate with a comma as many figures on the right, how many of them after the decimal point in both factors together.

### Examples of multiplying decimals

*Example 1: Multiply fractions:* 13,2 and 0.2.

After completing the multiplication, ignoring the commas, we get: .

Separate decimal point right as many digits as is the decimal point in both factors together, that is two digits .

Consider other examples of multiplication of decimal numbers:

*Example 2: *

*Example 3: *

### Multiplying decimals and integers

The product of decimals and natural numbers is called a sum of terms, each of which is equal to the given decimal, and the number of summands is equal to this positive integer.

To*multiply a decimal fraction by a natural number,* you need to:

- multiply it by that number, ignoring the decimal point;
- in the resulting product to separate the decimal point as many digits to the right, how many of them separated by a comma in decimal fractions.

### Multiplying decimals by 10, 100, 1000, etc.

To*multiply a decimal fraction by 10,100,1000,etc.,* should:

- in this fraction it is necessary to move the decimal point that many digits to the right, how many zeros is in the multiplier after one.

*Example 4:*

If the result is fewer digits than necessary to separate with a comma, ahead write zero or several zeros.