VerifySolveSolve a problem

Fraction Calculator — free steps, verified answers

Add, subtract, multiply or divide any two fractions or mixed numbers. The working is shown the way a teacher would show it — and then the answer is checked by working backwards, in exact fractions, before you see it.

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

In short

A fraction calculator adds, subtracts, multiplies and divides fractions with the working shown: addition and subtraction first rewrite both fractions with a common denominator, multiplication cancels common factors before multiplying straight across, and division flips the second fraction and multiplies. VerifySolve checks every answer by working backwards with exact fractions, so a wrong step cannot hide.

The four fraction rules

Everything on this page is one of four moves. Learn which move your problem needs and the rest is arithmetic the calculator shows you.

Add / subtract

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

Multiply

ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Divide

ab÷cd=ab×dc=adbc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}

Mixed ↔ improper

WND=W×D+NDW\frac{N}{D} = \frac{W \times D + N}{D}

Worked examples — all four operations, checked

One of each operation, plus a mixed-number sum. Every check below is the same reverse-operation proof the live solver prints.

1/2 + 1/3

  1. 1.Common denominator: LCM of 2 and 3 is 6
  2. 2.1/2 = 3/6 and 1/3 = 2/6
  3. 3.3/6 + 2/6 = 5/6

5/6

Verified backwards: 5/6 − 1/3 = 1/2 ✓.

3/4 × 2/3

  1. 1.Cross-cancel: the 3s cancel, and 2 and 4 share 2
  2. 2.Becomes 1/2 × 1/1

1/2

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

5/6 ÷ 5/12

  1. 1.Flip the second fraction: 5/12 becomes 12/5
  2. 2.Cross-cancel: 5/6 × 12/5 becomes 1/1 × 2/1

2

Verified backwards: 2 × 5/12 = 5/6 ✓.

1 1/2 + 2 1/4

  1. 1.Convert: 1 1/2 = 3/2 and 2 1/4 = 9/4
  2. 2.Common denominator 4: 3/2 = 6/4
  3. 3.6/4 + 9/4 = 15/4

3 3/4

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

Common mistakes — and how to dodge them

Adding the denominators

1/2 + 1/3 is NOT 2/5. Denominators name the size of the pieces — halves and thirds are different sizes, so they cannot be added until both fractions are rewritten with one shared denominator. The calculator shows that rewrite every time.

Forgetting to flip when dividing

3/4 ÷ 2/5 is not 3/8. Division by a fraction means multiplying by its reciprocal: keep the first, change ÷ to ×, flip the second. Skip the flip and the answer is wrong by a mile — the backwards check would catch it, because 3/8 × 2/5 is not 3/4.

Cancelling across a + or − sign

Cancelling only works across multiplication. In 2/4 + 1/2 you cannot cancel the 2s — the fractions must share a denominator first. Cancel in 2/4 × 1/2 all you like; cancel in a sum and you have changed the problem.

Which fraction problem is it?

The calculator above handles every operation in one box. If you want a page that teaches one operation in depth — with its own examples, mistakes and practice — start from the operation you are stuck on.

Adding Fractions →

Same or different denominators, mixed numbers — the common-denominator method shown in full.

Subtracting Fractions →

Borrow-free subtraction via improper fractions, including answers that go negative.

Multiplying Fractions →

Cross-cancel first, then multiply straight across — no common denominator needed.

Dividing Fractions →

Keep, change, flip: the reciprocal step shown, then multiply and verify.

Mixed Numbers →

Convert mixed ↔ improper both ways, and calculate with mixed numbers directly.

Simplifying Fractions →

Reduce to lowest terms with the GCD step shown, and the multiply-back proof.

Fraction Calculator — questions

What can the fraction calculator do?

All four operations on two fractions, mixed numbers, whole numbers or decimals: add, subtract, multiply and divide. Type one fraction on its own and it simplifies it. Every answer comes with full steps and a backwards check that proves the result.

How are fraction answers verified?

By the reverse operation, computed with exact fractions. For addition, the answer minus the second fraction must return the first; for division, the answer times the divisor must return the dividend. The check is printed on the page — if it ever failed, you would see it.

Does it handle mixed numbers like 1 1/2?

Yes. Type mixed numbers with a space between the whole part and the fraction (1 1/2). The calculator converts them to improper fractions, does the operation, and converts the answer back — each conversion shown as its own step.

Can I type decimals or whole numbers?

Yes. Decimals are converted to exact fractions first (0.75 becomes 3/4 — no rounding anywhere), and whole numbers work as fractions with a denominator of 1, so 2 + 1/2 and 3 × 2/5 solve cleanly.

What about fractions inside fractions?

Not yet. A fraction stacked inside another fraction (a complex fraction) is outside this engine’s scope, and the solver says so honestly instead of guessing. Work out the top and bottom separately, then divide them here — that two-step route always works.

Is the fraction calculator free?

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

Keep solving

Adding Fractions Calculator →

Same or different denominators, mixed numbers — the common-denominator method shown in full.

Subtracting Fractions Calculator →

Borrow-free subtraction via improper fractions, including answers that go negative.

Multiplying Fractions Calculator →

Cross-cancel first, then multiply straight across — no common denominator needed.

Dividing Fractions Calculator →

Keep, change, flip: the reciprocal step shown, then multiply and verify.

Mixed Numbers Calculator →

Convert mixed ↔ improper both ways, and calculate with mixed numbers directly.

Simplifying Fractions Calculator →

Reduce to lowest terms with the GCD step shown, and the multiply-back proof.

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.