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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
77 · 214

Example 2.
Find the quotient of the fraction into integer:
6 : 3 = 6 = 2 · 3 = 2
1111 · 311 · 311

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
73

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
277

Example 4.
Find the quotient of the integer into fraction:
2: 4 = 2· 5 = 2 · 5 = 2 · 5 = 5 = 2 · 2 + 1 = 21
5442 · 2222

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
75747 · 428

Example 6.
Find the quotient of the two fractions:
6 : 4 = 6 · 7 = 6 · 7 = 3 · 2 = 3 = 2 + 1 = 11
77747 · 42 · 2222
See also:


Division of mixed numbers.

Definition.

Examples of dividing of two mixed numbers

Example 7.
Find the quotient of the two mixed numbers:
11 : 22 = 1 · 2 + 1 : 2 · 3 + 2 = 3 : 8 = 3 · 3 = 3 · 3 = 9
232323282 · 816

Example 8.
Find the quotient of the mixed number into fraction:
21 : 3 = 2 · 7 + 1 : 3 = 15 · 5 = 15 · 5 = 25 = 34
7575737 · 377
See also:

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