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Adding Fractions Calculator — common denominators, shown

Same denominators, different denominators, mixed numbers — the LCM step, both rewrites and the final simplification, all shown. Then the sum is checked backwards before you see it.

  • ✓100% free — no paywall, ever
  • ✓No sign-up, no app
  • ✓Every answer verified before you see it

In short

To add fractions, first give both fractions the same denominator — the least common multiple of the two denominators — then add the numerators and keep that denominator, simplifying at the end. VerifySolve shows the LCM, both rewrites and the simplification, then proves the sum by subtracting one addend from the answer and recovering the other.

Adding fractions, three cases

One rule covers all three: same denominator first, then add the tops. The cases differ only in how you get that shared denominator.

Same denominator

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

Different denominators

ab+cd=ad+bcbd\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}

Via the LCM (smallest numbers)

14+16=312+212=512\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}

Mixed numbers first

112+214=32+94=1541\tfrac{1}{2} + 2\tfrac{1}{4} = \frac{3}{2} + \frac{9}{4} = \frac{15}{4}

Worked examples — added, simplified, checked

From the easy case (same denominator) to mixed numbers. Every check is the backwards subtraction the live solver prints.

1/4 + 2/4

  1. 1.Same denominator (4) — add the numerators: 1 + 2 = 3

3/4

Verified backwards: 3/4 − 2/4 = 1/4 ✓.

1/3 + 1/6

  1. 1.LCM of 3 and 6 is 6
  2. 2.1/3 = 2/6; 1/6 stays 1/6
  3. 3.2/6 + 1/6 = 3/6
  4. 4.Simplify: 3/6 = 1/2

1/2

Verified backwards: 1/2 − 1/6 = 1/3 ✓.

2/5 + 3/7

  1. 1.LCM of 5 and 7 is 35 (no common factor)
  2. 2.2/5 = 14/35; 3/7 = 15/35
  3. 3.14/35 + 15/35 = 29/35

29/35

Verified backwards: 29/35 − 3/7 = 2/5 ✓. 29 is prime, so no simplifying is possible.

1 1/2 + 2 2/3

  1. 1.Convert: 1 1/2 = 3/2 and 2 2/3 = 8/3
  2. 2.Common denominator 6: 3/2 = 9/6 and 8/3 = 16/6
  3. 3.9/6 + 16/6 = 25/6

4 1/6

Verified backwards: 4 1/6 − 2 2/3 = 1 1/2 ✓.

Common mistakes — and how to dodge them

Adding the denominators

1/2 + 1/3 is not 2/5. The denominators are the sizes of the pieces — halves and thirds cannot be combined until both fractions are rewritten in pieces of one shared size. That rewrite is the whole skill, and the calculator shows it every time.

Multiplying denominators when the LCM is smaller

1/4 + 1/6 via 4 × 6 = 24 works (6/24 + 4/24 = 10/24 = 5/12) but the numbers balloon and the final simplification is easy to miss. The LCM (12) keeps everything small. Same answer, less room for slips.

Adding mixed numbers without converting

1 1/2 + 2 1/4 is tempting to do as “3 and a bit” — and the bit is where errors hide. Convert to improper fractions first (3/2 + 9/4), add cleanly, convert back. The calculator never skips the conversion step.

Adding Fractions Calculator — questions

How do you add fractions with different denominators?

Rewrite both fractions with one shared denominator — the least common multiple of the two denominators — then add the numerators and keep that denominator. 1/3 + 1/6 becomes 2/6 + 1/6 = 3/6 = 1/2. The calculator shows the LCM step and both rewrites.

What if the denominators are already the same?

Then you just add the numerators: 1/4 + 2/4 = 3/4. The denominator never changes in addition — it names the size of the pieces, and adding pieces of the same size only changes how many you have.

Can it add mixed numbers?

Yes. Mixed numbers are converted to improper fractions first (1 1/2 becomes 3/2), added normally, and the answer is converted back to a mixed number when it is top-heavy. Each conversion is its own visible step.

How is an addition answer verified?

By subtraction: the answer minus the second fraction must return the first fraction exactly. 5/6 − 1/3 = 1/2 proves that 1/2 + 1/3 = 5/6. The check is computed with exact fractions and printed under the steps.

Can the answer be negative?

Yes, when a negative fraction outweighs a positive one: 1/4 + (−1/2) = −1/4. The calculator handles signs through the same common-denominator steps, and the backwards check works identically.

Is the adding fractions calculator free?

Yes — free, no sign-up, no app, full steps and verification included.

Keep solving

Fraction Calculator →

The hub: all four operations in one box, plus simplifying.

Subtracting Fractions Calculator →

The same common-denominator method, with borrowing-free mixed subtraction.

Multiplying Fractions Calculator →

No common denominator needed — cancel first, then multiply straight across.

Dividing Fractions Calculator →

Keep, change, flip — the reciprocal step shown and verified.

Mixed Number Calculator →

Mixed ↔ improper conversion both ways, and mixed-number arithmetic.

Simplifying Fractions Calculator →

Reduce any fraction to lowest terms with the GCD step shown.

A note on honest use: VerifySolve is built for learning. Use the steps to understand the method, then close the tab and try one on your own — that is where the grade actually comes from. If your teacher or school has a policy on calculators, follow it.