Fraction Calculator: Add, Subtract, Multiply, Divide

What does 5/6 mean?

It means 1/2 + 1/3 is five sixths — a little less than a whole, 0.833333 as a decimal. The common denominator is 6: 1/2 is 3/6 and 1/3 is 2/6, so 3/6 + 2/6 is 5/6, and 5 and 6 share no divisor, so it stays 5/6. The simplified fraction, the decimal and the mixed number are three outputs, never the same number — the fraction is exact, the decimal is the fraction divided out, and the mixed number is the whole part plus the remainder.

Three things to check before you trust the number

Add and subtract need a common denominator. You cannot add halves and thirds straight across — 1/2 + 1/3 is not 2/5. Find the common denominator first (6 here), convert both fractions, then add the tops.

Multiply goes straight across; divide flips and multiplies. 1/2 × 1/3 is 1/6 — top times top, bottom times bottom — and 1/2 ÷ 1/3 is 3/2, because dividing by a third is multiplying by three.

Always simplify. 2/4 + 1/3 is 5/6, not 10/12 — the calculator divides the answer by the greatest common divisor, so the answer is always in lowest terms.

Worked example

On the defaults: 1/2 + 1/3.

1. Common denominator: the least common multiple of 2 and 3 is 6.
2. Convert: 1/2 = 3/6 and 1/3 = 2/6.
3. Add the tops: 3/6 + 2/6 = 5/6.
4. Simplify: 5 and 6 share no divisor, so the answer stays 5/6.
5. Decimal: 5 ÷ 6 = 0.833333.
6. Mixed number: 5/6 is less than a whole, so it stays 5/6.
7. Smallest numerator for a/4 + 1/3 to reach at least 1: 3 — at 3 the answer is 13/12 = 1.083333, mixed 1 1/12, and at 2 it is 5/6 = 0.833333.
8. Largest denominator for 1/2 + 1/d to reach at least 3/4: 4 — at 4 the answer is 3/4, and at 5 it is 7/10 = 0.700000.

Every branch, checked

• Subtract: Subtract: 1/2 - 1/3 = 1/6 = 0.166667 (mixed 1/6). 1/2 - 1/3 = 1/6 — the same answer as multiplying, by a different route.
• Multiply: Multiply: 1/2 × 1/3 = 1/6 = 0.166667 (mixed 1/6). 1/2 x 1/3 = 1/6 — the same answer as subtracting, by a different route.
• Divide: Divide: 1/2 ÷ 1/3 = 3/2 = 1.500000 (mixed 1 1/2). Dividing by a third is multiplying by three — 1/2 ÷ 1/3 = 3/2, mixed 1 1/2.
• 3/4 + 1/4: 3/4 + 1/4: 3/4 + 1/4 = 1/1 = 1.000000 (mixed 1). Exactly a whole — 3/4 + 1/4 = 1.
• 2/3 - 1/6: 2/3 - 1/6: 2/3 - 1/6 = 1/2 = 0.500000 (mixed 1/2). 2/3 - 1/6 = 1/2 — the common denominator is 6.
• 5/6 x 3/10: 5/6 x 3/10: 5/6 × 3/10 = 1/4 = 0.250000 (mixed 1/4). 5/6 x 3/10 = 1/4 — multiply across, then simplify by 6.
• 7/8 ÷ 1/2: 7/8 ÷ 1/2: 7/8 ÷ 1/2 = 7/4 = 1.750000 (mixed 1 3/4). 7/8 ÷ 1/2 = 7/4, mixed 1 3/4 — flip and multiply.
• 1/3 + 2/5: 1/3 + 2/5: 1/3 + 2/5 = 11/15 = 0.733333 (mixed 11/15). 1/3 + 2/5 = 11/15 = 0.733333 — the common denominator is 15.
• 4/5 - 3/10: 4/5 - 3/10: 4/5 - 3/10 = 1/2 = 0.500000 (mixed 1/2). 4/5 - 3/10 = 1/2 — the common denominator is 10.
• 2/7 x 3/4: 2/7 x 3/4: 2/7 × 3/4 = 3/14 = 0.214286 (mixed 3/14). 2/7 x 3/4 = 3/14 = 0.214286 — multiply across, then simplify.

The reverses, worked backwards

• Smallest numerator for a/4 + 1/3 to REACH at least 1: Numerator 3 — at Numerator 3 the figures are 3/4 + 1/3 = 13/12 = 1.083333 (unrounded 1.083333) (mixed 1 1/12); at the lower neighbor the figures are 2/4 + 1/3 = 5/6 = 0.833333 (unrounded 0.833333) (mixed 5/6); at the upper neighbor the figures are 4/4 + 1/3 = 4/3 = 1.333333 (unrounded 1.333333) (mixed 1 1/3) — verdict: STEP.
• Largest denominator for 1/2 + 1/d to REACH at least 3/4: Denominator 4 — at Denominator 4 the figures are 1/2 + 1/4 = 3/4 = 0.750000 (unrounded 0.750000) (mixed 3/4); at the lower neighbor the figures are 1/2 + 1/5 = 7/10 = 0.700000 (unrounded 0.700000) (mixed 7/10); at the upper neighbor the figures are 1/2 + 1/3 = 5/6 = 0.833333 (unrounded 0.833333) (mixed 5/6) — verdict: STEP.
• Smallest numerator for a/5 - 1/10 to REACH at least 1/2: Numerator 3 — at Numerator 3 the figures are 3/5 - 1/10 = 1/2 = 0.500000 (unrounded 0.500000) (mixed 1/2); at the lower neighbor the figures are 2/5 - 1/10 = 3/10 = 0.300000 (unrounded 0.300000) (mixed 3/10); at the upper neighbor the figures are 4/5 - 1/10 = 7/10 = 0.700000 (unrounded 0.700000) (mixed 7/10) — verdict: STEP.
• Largest numerator for a/6 x 2/3 to STAY at or below 1/2: Numerator 4 — at Numerator 4 the figures are 4/6 × 2/3 = 4/9 = 0.444444 (unrounded 0.444444) (mixed 4/9); at the lower neighbor the figures are 5/6 × 2/3 = 5/9 = 0.555556 (unrounded 0.555556) (mixed 5/9); at the upper neighbor the figures are 3/6 × 2/3 = 1/3 = 0.333333 (unrounded 0.333333) (mixed 1/3) — verdict: STEP.
• Smallest denominator for 3/4 ÷ 1/d to REACH at least 2: Denominator 3 — at Denominator 3 the figures are 3/4 ÷ 1/3 = 9/4 = 2.250000 (unrounded 2.250000) (mixed 2 1/4); at the lower neighbor the figures are 3/4 ÷ 1/2 = 3/2 = 1.500000 (unrounded 1.500000) (mixed 1 1/2); at the upper neighbor the figures are 3/4 ÷ 1/4 = 3/1 = 3.000000 (unrounded 3.000000) (mixed 3) — verdict: STEP.
• Largest numerator for a/7 + 2/7 to STAY at or below 1: Numerator 5 — at Numerator 5 the figures are 5/7 + 2/7 = 1/1 = 1.000000 (unrounded 1.000000) (mixed 1); at the lower neighbor the figures are 6/7 + 2/7 = 8/7 = 1.142857 (unrounded 1.142857) (mixed 1 1/7); at the upper neighbor the figures are 4/7 + 2/7 = 6/7 = 0.857143 (unrounded 0.857143) (mixed 6/7) — verdict: STEP.

What the defaults assume

The defaults are 1/2 + 1/3 — two ordinary proper fractions added together. They are a starting point, not a benchmark: the calculator takes any whole-number numerators and denominators, negative fractions included, and any of the four operations. Change the five inputs to your own and the calculator recomputes instantly. The fraction itself is exact — 5/6 is 5/6, never a rounding — so only the decimal is ever rounded, to 6dp.

These notes repeat in every explainer section because this page is built to be read start to finish: the defaults are one pair of fractions, not a standard; add and subtract need a common denominator; multiply goes straight across and divide flips and multiplies; and always simplify.

Output · formula · meaning

Who uses this

• A student who needs 1/2 + 1/3 worked out with the steps, not just the answer.
• A cook who halves a recipe — 3/4 of a cup halved is 3/8 — and wants the fraction, not a decimal.
• A carpenter who adds measurements in fractions of an inch and needs the simplified answer.
• A teacher who checks homework answers against an exact model, decimal and mixed number included.

Accuracy & limitations

The calculator does the arithmetic exactly — the answer is simplified by the greatest common divisor, the decimal is the numerator divided by the denominator to 6dp, and the mixed number is the whole part plus the remainder — and every figure on this page is checked against an independent model. What it cannot do is take non-whole numbers: numerators and denominators must be whole numbers, and a zero denominator is not a fraction, so the calculator says so plainly instead of guessing. It also caps the inputs at a sane range — fractions with numerators in the trillions are arithmetic, not homework. And the decimal is the only rounded figure: -1/6 is -0.166667 to 6dp, but the fraction -1/6 is exact.

Cite this calculator

Add: a/b + c/d = (a×d + c×b) / (b×d); subtract: a/b − c/d = (a×d − c×b) / (b×d); multiply: a/b × c/d = (a×c) / (b×d); divide: a/b ÷ c/d = (a×d) / (b×c); then simplify by the greatest common divisor. On the defaults — 1/2 + 1/3 — the answer is 5/6, or 0.833333 as a decimal. Smallest numerator for a/4 + 1/3 to reach at least 1: 3. Largest denominator for 1/2 + 1/d to reach at least 3/4: 4. Smallest numerator for a/5 - 1/10 to reach at least 1/2: 3. Largest numerator for a/6 x 2/3 to stay at or below 1/2: 4. Smallest denominator for 3/4 ÷ 1/d to reach at least 2: 3. Largest numerator for a/7 + 2/7 to stay at or below 1: 5. Source: Bright Side Kit, brightoolbox.com.

Frequently asked questions