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How to Solve Fractions

Learn to add, subtract, multiply, and divide fractions.

๐Ÿ“ Step by Step

  1. 1 To add or subtract fractions, first find a common denominator (least common multiple of denominators).
  2. 2 Convert each fraction by multiplying the numerator and denominator by the appropriate number to get the common denominator.
  3. 3 Add or subtract the numerators, keeping the common denominator.
  4. 4 Simplify the result if possible by dividing the numerator and denominator by their greatest common divisor.

Examples by Operation Type

โž• Adding Fractions

Example

3
10
+
11
13

Answer:

1 
19
130

Solution Steps

  1. 1
    Find common denominator (LCM): LCM(10, 13) = 130
  2. 2
    Convert fractions to common denominator: 3/10 = 39/130, 11/13 = 110/130
    3
    10
    +
    11
    13
  3. 3
    Add the numerators: 39/130 + 110/130 = 149/130
    39
    130
    +
    110
    130
    =
    149
    130
  4. 4
    Convert to mixed number: 1 19/130
    1 
    19
    130

โž– Subtracting Fractions

Example

7
15
-
2
19

Answer:

103
285

Solution Steps

  1. 1
    Find common denominator (LCM): LCM(15, 19) = 285
  2. 2
    Convert fractions to common denominator: 7/15 = 133/285, 2/19 = 30/285
    7
    15
    โˆ’
    2
    19
  3. 3
    Subtract the numerators: 133/285 - 30/285 = 103/285
    133
    285
    โˆ’
    30
    285
    =
    103
    285

โœ–๏ธ Multiplying Fractions

Example

5
6
ร—
2
5

Answer:

1
3

Solution Steps

  1. 1
    Write the fractions: 5/6 ร— 2/5
    5
    6
    ร—
    2
    5
  2. 2
    Multiply numerators and denominators: (5 ร— 2)/(6 ร— 5)
    (5 ร— 2)
    (6 ร— 5)
  3. 3
    Calculate the result: 10/30
    10
    30
  4. 4
    Simplify the result: 1/3
    1
    3

โž— Dividing Fractions

Example

3
6
รท
2
6

Answer:

1 
1
2

Solution Steps

  1. 1
    Write the fractions: 3/6 รท 2/6
    3
    6
    รท
    2
    6
  2. 2
    Change division to multiplication by reciprocal: 3/6 ร— 6/2
    3
    6
    ร—
    6
    2
  3. 3
    Multiply numerators and denominators: (3 ร— 6)/(6 ร— 2)
    (3 ร— 6)
    (6 ร— 2)
  4. 4
    Calculate the result: 18/12
    18
    12
  5. 5
    Convert to mixed number: 1 1/2
    1 
    1
    2

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