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# Division of fraction.

## Division of fraction into natural number.

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

### Examples of dividing of fractions into integer

Example 1.
Find the quotient of the fraction into integer:
 3 : 2 = 3 = 3 7 7 · 2 14

Example 2.
Find the quotient of the fraction into integer:
 6 : 3 = 6 = 2 · 3 = 2 11 11 · 3 11 · 3 11

Definition.
To get the reciprocal of a fraction, just turn it upside down. In other words swap over the Numerator and Denominator.
 3 - reciprocal fraction 7 7 3

## Division of natural number into fraction.

Definition.
To divide natural number into fraction, it is necessary to multiply natural number by reciprocal of fraction.

### Examples of dividing of integer into fraction

Example 3.
Find the quotient of the integer into fraction:
 2: 7 = 2· 2 = 4 2 7 7

Example 4.
Find the quotient of the integer into fraction:
 2: 4 = 2· 5 = 2 · 5 = 2 · 5 = 5 = 2 · 2 + 1 = 2 1 5 4 4 2 · 2 2 2 2

## Division of fraction.

Definition.
To divide fractions, it is necessary to multiply first fraction by reciprocal of second fraction.

### Examples of dividing of two fractions

Example 5.
Find the quotient of the two fractions:
 3 : 4 = 3 · 5 = 3 · 5 = 15 7 5 7 4 7 · 4 28

Example 6.
Find the quotient of the two fractions:
 6 : 4 = 6 · 7 = 6 · 7 = 3 · 2 = 3 = 2 + 1 = 1 1 7 7 7 4 7 · 4 2 · 2 2 2 2

## Division of mixed numbers.

Definition.

### Examples of dividing of two mixed numbers

Example 7.
Find the quotient of the two mixed numbers:
 1 1 : 2 2 = 1 · 2 + 1 : 2 · 3 + 2 = 3 : 8 = 3 · 3 = 3 · 3 = 9 2 3 2 3 2 3 2 8 2 · 8 16

Example 8.
Find the quotient of the mixed number into fraction:
 2 1 : 3 = 2 · 7 + 1 : 3 = 15 · 5 = 15 · 5 = 25 = 3 4 7 5 7 5 7 3 7 · 3 7 7