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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

2
15
+
2
3

Answer:

4
5

Solution Steps

  1. 1
    Find common denominator (LCM): LCM(15, 3) = 15
  2. 2
    Convert fractions to common denominator: 2/15 = 2/15, 2/3 = 10/15
    2
    15
    +
    2
    3
  3. 3
    Add the numerators: 2/15 + 10/15 = 12/15
    2
    15
    +
    10
    15
    =
    12
    15
  4. 4
    Simplify the result: 4/5
    4
    5

โž– Subtracting Fractions

Example

12
14
-
8
11

Answer:

10
77

Solution Steps

  1. 1
    Find common denominator (LCM): LCM(14, 11) = 154
  2. 2
    Convert fractions to common denominator: 12/14 = 132/154, 8/11 = 112/154
    12
    14
    โˆ’
    8
    11
  3. 3
    Subtract the numerators: 132/154 - 112/154 = 20/154
    132
    154
    โˆ’
    112
    154
    =
    20
    154
  4. 4
    Simplify the result: 10/77
    10
    77

โœ–๏ธ Multiplying Fractions

Example

4
12
ร—
2
5

Answer:

2
15

Solution Steps

  1. 1
    Write the fractions: 4/12 ร— 2/5
    4
    12
    ร—
    2
    5
  2. 2
    Multiply numerators and denominators: (4 ร— 2)/(12 ร— 5)
    (4 ร— 2)
    (12 ร— 5)
  3. 3
    Calculate the result: 8/60
    8
    60
  4. 4
    Simplify the result: 2/15
    2
    15

โž— Dividing Fractions

Example

1
3
รท
9
11

Answer:

11
27

Solution Steps

  1. 1
    Write the fractions: 1/3 รท 9/11
    1
    3
    รท
    9
    11
  2. 2
    Change division to multiplication by reciprocal: 1/3 ร— 11/9
    1
    3
    ร—
    11
    9
  3. 3
    Multiply numerators and denominators: (1 ร— 11)/(3 ร— 9)
    (1 ร— 11)
    (3 ร— 9)
  4. 4
    Calculate the result: 11/27
    11
    27

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