Fractions

Adding Fractions Calculator

Add any two fractions with full step-by-step working. The calculator finds the lowest common denominator, converts both fractions, then adds the numerators — showing every step clearly.

First fraction
+Add
Second fraction
34\frac{3}{4}

= 0.75 (decimal)

Step-by-step working

  1. Find the lowest common denominator (LCD)

    LCD(2,4)=4\text{LCD}(2,\, 4) = 4

    The lowest common denominator of 2 and 4 is 4. Both fractions will be converted to this denominator.

  2. Convert the first fraction

    12=24\frac{1}{2} = \frac{2}{4}

    Multiply numerator and denominator of the first fraction by 2.

    Result:\frac{2}{4}
  3. Convert the second fraction

    14=14\frac{1}{4} = \frac{1}{4}

    Multiply numerator and denominator of the second fraction by 1.

    Result:\frac{1}{4}
  4. Add the numerators

    24+14=34\frac{2}{4} + \frac{1}{4} = \frac{3}{4}

    Add the numerators together. The denominator stays the same: 2 + 1 = 3.

    Result:\frac{3}{4}

The formula

ab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}
a,ca, cNumerators
b,db, dDenominators

Example substitution

12+13=36+26=56\frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}

LCD of 2 and 3 is 6. Convert both fractions, then add numerators.

Worked examples

1/4 + 1/4

  1. 1
    Same denominator: 4
  2. 2
    Add numerators: 1 + 1 = 2
  3. 3
    Result: 2/4 = 1/2
Answer: 1/2

1/3 + 1/6

  1. 1
    LCD(3,6): = 6
  2. 2
    Convert: 2/6 + 1/6
  3. 3
    Add: 3/6 = 1/2
Answer: 1/2

2/5 + 3/10

  1. 1
    LCD(5,10): = 10
  2. 2
    Convert: 4/10 + 3/10
  3. 3
    Add: 7/10
Answer: 7/10

Frequently asked questions

How do you add fractions with different denominators?+

Find the lowest common denominator (LCD), convert each fraction so it has the LCD as its denominator, add the numerators, then simplify.

How do you add fractions with the same denominator?+

When denominators are the same, simply add the numerators and keep the denominator. For example, 2/7 + 3/7 = 5/7.

How do you add mixed numbers?+

Convert each mixed number to an improper fraction, find the LCD, add the numerators, then convert the result back to a mixed number.

What is the lowest common denominator?+

The lowest common denominator (LCD) is the smallest number that both denominators divide into exactly. It equals the least common multiple (LCM) of the two denominators.

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