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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

25
26
+
9
13

Answer:

1 
17
26

Solution Steps

  1. 1
    Find common denominator (LCM): LCM(26, 13) = 26
  2. 2
    Convert fractions to common denominator: 25/26 = 25/26, 9/13 = 18/26
    25
    26
    +
    9
    13
  3. 3
    Add the numerators: 25/26 + 18/26 = 43/26
    25
    26
    +
    18
    26
    =
    43
    26
  4. 4
    Convert to mixed number: 1 17/26
    1 
    17
    26

โž– Subtracting Fractions

Example

15
16
-
9
15

Answer:

27
80

Solution Steps

  1. 1
    Find common denominator (LCM): LCM(16, 15) = 240
  2. 2
    Convert fractions to common denominator: 15/16 = 225/240, 9/15 = 144/240
    15
    16
    โˆ’
    9
    15
  3. 3
    Subtract the numerators: 225/240 - 144/240 = 81/240
    225
    240
    โˆ’
    144
    240
    =
    81
    240
  4. 4
    Simplify the result: 27/80
    27
    80

โœ–๏ธ Multiplying Fractions

Example

2
7
ร—
2
3

Answer:

4
21

Solution Steps

  1. 1
    Write the fractions: 2/7 ร— 2/3
    2
    7
    ร—
    2
    3
  2. 2
    Multiply numerators and denominators: (2 ร— 2)/(7 ร— 3)
    (2 ร— 2)
    (7 ร— 3)
  3. 3
    Calculate the result: 4/21
    4
    21

โž— Dividing Fractions

Example

4
11
รท
1
10

Answer:

3 
7
11

Solution Steps

  1. 1
    Write the fractions: 4/11 รท 1/10
    4
    11
    รท
    1
    10
  2. 2
    Change division to multiplication by reciprocal: 4/11 ร— 10/1
    4
    11
    ร—
    10
    1
  3. 3
    Multiply numerators and denominators: (4 ร— 10)/(11 ร— 1)
    (4 ร— 10)
    (11 ร— 1)
  4. 4
    Calculate the result: 40/11
    40
    11
  5. 5
    Convert to mixed number: 3 7/11
    3 
    7
    11

Practice Now!

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