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Subtracting Fractions Calculator — borrow-free, every step shown

Different denominators, mixed numbers, answers that go negative — the LCM step, both rewrites and the simplification, all shown. Then the difference is checked by adding back.

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

In short

To subtract fractions, rewrite both with the same denominator — the least common multiple — then subtract the numerators and keep that denominator, simplifying at the end. Mixed numbers convert to improper fractions first, which removes borrowing entirely. VerifySolve then proves the difference by adding the subtracted fraction back and recovering the starting fraction.

Subtracting fractions, three cases

Subtraction mirrors addition exactly: one shared denominator, then subtract the tops. The only new idea is what a negative answer means.

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)

56−14=1012−312=712\frac{5}{6} - \frac{1}{4} = \frac{10}{12} - \frac{3}{12} = \frac{7}{12}

Mixed numbers first

214−112=94−32=342\tfrac{1}{4} - 1\tfrac{1}{2} = \frac{9}{4} - \frac{3}{2} = \frac{3}{4}

Worked examples — subtracted, simplified, checked

Including the two cases students find hardest: mixed numbers (no borrowing needed) and a difference that goes negative.

3/4 - 1/4

  1. 1.Same denominator (4) — subtract the numerators: 3 − 1 = 2
  2. 2.2/4 simplifies to 1/2

1/2

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

5/6 - 1/4

  1. 1.LCM of 6 and 4 is 12
  2. 2.5/6 = 10/12 and 1/4 = 3/12
  3. 3.10/12 − 3/12 = 7/12

7/12

Verified backwards: 7/12 + 1/4 = 5/6 ✓.

2 1/4 - 1 1/2

  1. 1.Convert: 2 1/4 = 9/4 and 1 1/2 = 3/2
  2. 2.Common denominator 4: 3/2 = 6/4
  3. 3.9/4 − 6/4 = 3/4

3/4

Verified backwards: 3/4 + 1 1/2 = 2 1/4 ✓. No borrowing anywhere.

1/3 - 1/2

  1. 1.LCM of 3 and 2 is 6
  2. 2.1/3 = 2/6 and 1/2 = 3/6
  3. 3.2/6 − 3/6 = −1/6

-1/6

Verified backwards: −1/6 + 1/2 = 1/3 ✓. A negative answer just means the second fraction was bigger.

Common mistakes — and how to dodge them

Subtracting the denominators

5/6 − 1/4 is not 4/2. The denominator is the piece size — it stays put while the numerators subtract, once both fractions share it. Subtracting denominators changes the size of the pieces mid-problem, which is how 5/6 − 1/4 “becomes” 2.

Subtracting in the wrong order

1/3 − 1/2 is −1/6, not 1/6. Subtraction is not commutative: flipping the order flips the sign. If your answer has the right size but the wrong sign, the order was swapped — the backwards check (answer + subtracted = start) exposes it immediately.

Borrowing across mixed numbers by hand

Borrowing 1 from the whole part, converting it, re-subtracting — three chances to slip. Converting both mixed numbers to improper fractions first is one clean subtraction. The calculator always takes the clean route, and shows it.

Subtracting Fractions Calculator — questions

How do you subtract fractions with different denominators?

The same way you add them: rewrite both fractions with one shared denominator (the least common multiple), subtract the numerators, keep the denominator, and simplify. 5/6 − 1/4 becomes 10/12 − 3/12 = 7/12.

What if the second fraction is bigger — can the answer be negative?

Yes, and the calculator shows it plainly: 1/3 − 1/2 = −1/6. A negative fraction just means the subtraction went past zero. The steps and the backwards check work exactly the same way.

Do I need to borrow when subtracting mixed numbers?

Not with this method. Converting both mixed numbers to improper fractions first (2 1/4 becomes 9/4) removes borrowing entirely — one subtraction, one simplification, one conversion back. The calculator shows every conversion.

How is a subtraction answer verified?

By adding back: the answer plus the fraction you subtracted must return the fraction you started with. 7/12 + 1/4 = 5/6 proves that 5/6 − 1/4 = 7/12. The check is computed with exact fractions and printed on the page.

Why does subtracting need a common denominator but multiplying does not?

Because subtraction (like addition) combines pieces, and pieces must be the same size to combine. Multiplication scales one fraction by another, which works directly on tops and bottoms. Different operations, different rules — the calculator names the rule each time.

Is the subtracting 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.

Adding Fractions Calculator →

The twin operation — same common-denominator method, numerators added.

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.