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Addition and Subtraction of fractions.


Addition of fractions

Addition of fractions with equal denominators.

Definition.
To add two fractions with equal denominators, it is necessary to add their numerators, and to leave without modifications a denominator:
a + b = a + b
ccc

Examples of addition of fractions with the same denominators:

Example 1.
Find the sum of two fractions with equal denominator:
1 + 2 = 1 + 2 = 3
5555

Example 2.
Find the sum of two fractions with equal denominator:
3 + 2 = 3 + 2 = 5
7777

See also:


Addition of fractions.

Definition.
To add two fractions, it is necessary:

Examples of addition of fractions

Example 3.
Find the sum of two fractions:
1 + 1 = 1·2 + 1 = 2 + 1 = 2 + 1 = 3 = 3 = 1
363·2666663·22

Example 4.
Find the sum of two fractions:
29 + 44 = 29·3 + 44·2 = 87 + 88 = 87 + 88 = 
304530·345·2909090

 = 175 = 35·5 = 35 = 18 + 17 = 117
9018·5181818

See also:


Addition of mixed numbers

Definition.
To add two mixed numbers, it is necessary:

Examples of addition of mixed numbers

Example 5.
Find the sum of two mixed numbers:
2 + 11 = 2·2 + 11·3 = 4 + 13 = 1 + 4 + 3 = 
323·22·3666

 = 1 + 7 = 1 + 6 + 1 = 1 + 11 = 21
6666

Example 6.
Find the sum of two mixed numbers:
15 + 23 = 15·4 + 23·3 = 120 + 29 = 3 + 20 + 9 = 
686·48·3242424

 = 3 + 29 = 3 + 24 + 5 = 3 + 15 = 45
24242424

See also:



Subtraction of fractions

Subtraction of fractions with equal denominators.

Definition.
To receive a difference of fractions with equal denominatorsTo receive a difference of fractions with equal denominators, it is necessary to subtract their numerators , and to leave without modifications a denominator:
a - b = a - b
ccc

Examples of subtraction of fractions with the same denominators:

Example 7.
Find the difference between two fractions with the same denominators:
3 - 1 = 3 - 1 = 2
5555

Example 8.
Find the difference between two fractions with the same denominators:
8 - 5 = 8 - 5 = 3
41414141

See also:


Subtraction of fractions.

Definition.
To subtract two fractions, it is necessary:

Examples of subtraction of fractions

Example 9.
Find the difference between two fractions:
5 - 1 = 5 - 1·3 = 5 - 3 = 5 - 3 = 2 = 2 = 1
6262·366662·33

Example 10.
Find the difference between two fractions:
3 - 1 = 3·3 - 1·5 = 9 - 5 = 9 - 5 = 4 = 2·2 = 2
10610·36·53030303015·215

See also:


Subtraction of mixed numbers

Definition.
To subtract two mixed numbers, it is necessary:

Examples of subtraction of mixed numbers

Example 11.
Find the difference between two mixed numbers:
21 - 11 = 21·3 - 11·2 = (2 - 1) + 3 - 2 = 
232·33·266

 = 1 + 3 -2 = 1 + 1 = 11
666

Example 12.
Find the difference between two mixed numbers:
31 - 13 = 31·4 - 13·3 = 34 - 19 = 
686·48·32424

 = 224 + 4 - 19 = 1 + 28 - 9 = 1 + 19 = 119
2424242424

Example 13.
Find the difference between two mixed numbers:
11 - 32 = 11 - 32·2 = 11 - 34 = (1-3) + 1 - 4 = 
6363·2666

 = -2 - 3 = -2 - 3 = -2 - 1 = -21
62·322

See also:

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