Mixed Number Calculator

Welcome to the Mixed Number Calculator

A mixed number is a whole number and a fraction written together, like 2 3/4 — two wholes and three quarters more. This mixed number calculator adds, subtracts, multiplies and divides mixed numbers, mixed fractions with different denominators, and plain whole numbers, and it shows the whole solution as numbered steps. The first step is always the one students find hardest to remember: turning each mixed number into an improper fraction. The last step turns the improper answer back into a mixed number in simplest form. The answer also appears as an improper fraction, a decimal, a percent and a point on the number line.

The calculator opens with 2 3/4 + 1 1/2 already filled in so you can see both conversions at work. Type your own whole numbers, numerators (the top numbers) and denominators (the bottom numbers) into the boxes, pick an operation, and the answer and the steps update as you type. Leave the whole-number box empty for a plain fraction, or leave the fraction boxes empty to enter a whole number on its own. Every calculation gets its own link in the “Share This Calculation” panel, so a problem can be saved or handed to a student exactly as it appears here.

Use the steps to check your homework rather than to skip it. Each section below explains one operation in the same order the calculator works it, with a fully worked example you can type in to compare.

How to Convert a Mixed Number to an Improper Fraction

Every operation on mixed numbers starts the same way, so learn this one cold. Multiply the whole number by the denominator (the bottom number), add the numerator (the top number), and write that total over the same denominator. The denominator never changes during the conversion — you are only counting how many pieces the wholes are worth.

Take 2 3/4. Each whole is 4 quarters, so 2 wholes are 2 × 4 = 8 quarters. Add the 3 quarters that were already there: 8 + 3 = 11. So 2 3/4 = 11/4. The calculator writes this as (2×4+3)/4 in its “Make improper” step so you can see where each number came from. A whole number with no fraction part, like 5, becomes 5/1 — any number over 1 is itself.

How to Convert an Improper Fraction to a Mixed Number

An improper fraction has a numerator bigger than its denominator, like 17/4. To turn it back into a mixed number, divide the numerator by the denominator: the quotient is the whole number and the remainder stays on top of the same denominator. For 17/4, 4 goes into 17 four times (4 × 4 = 16) with 1 left over, so 17/4 = 4 1/4. The calculator shows this in its “Make it proper” step as 16/4 + 1/4 → 4 1/4, splitting the wholes out of the total.

Two things to check at the end. First, if the fraction part can be reduced, reduce it — 6/8 should be written 3/4. The calculator reduces before it converts, so its mixed numbers are always in simplest form. Second, a negative answer gets one sign, written in front of the whole mixed number, never on the numerator and the whole separately.

Adding Mixed Numbers

To add mixed numbers, convert both to improper fractions, find a common denominator if the denominators differ, add the numerators, then convert the result back to a mixed number. You can also add the wholes and the fractions separately and carry when the fraction part goes over one, but the improper-fraction route has fewer places to slip, which is why the calculator uses it.

Try the example the calculator opens with, 2 3/4 + 1 1/2. Convert: 2 3/4 = 11/4 and 1 1/2 = 3/2. The denominators are 4 and 2, and the least common denominator is 4, so 3/2 becomes 6/4. Add the numerators: 11/4 + 6/4 = 17/4. Convert back: 17/4 = 4 1/4. The bar diagrams under each step show the two quantities being lined up on the same scale and combined.

How to Subtract Mixed Fractions

Subtracting mixed fractions trips people up when the second fraction part is larger than the first — 3 1/4 − 1 2/3, for instance, where 2/3 is bigger than 1/4. Working with wholes and parts separately means “borrowing” a whole and rewriting it as a fraction. Converting to improper fractions first avoids the borrowing altogether: the wholes are already folded into the numerators.

Work 3 1/4 − 1 2/3. Convert: 3 1/4 = 13/4 and 1 2/3 = 5/3. The least common denominator of 4 and 3 is 12, so 13/4 = 39/12 and 5/3 = 20/12. Subtract the numerators: 39/12 − 20/12 = 19/12. Convert back: 12 goes into 19 once with 7 left over, so the answer is 1 7/12. If you take a larger mixed number away from a smaller one, the numerator comes out negative and the answer is negative — the calculator shows a single minus sign in front of the result.

Multiplying Mixed Numbers

Never multiply the wholes together and the fractions together — 1 1/2 × 2 2/3 is not 2 2/6. Convert both mixed numbers to improper fractions, then multiply straight across: numerator times numerator over denominator times denominator. A common denominator is not needed for multiplication.

Work 1 1/2 × 2 2/3. Convert: 1 1/2 = 3/2 and 2 2/3 = 8/3. Before multiplying, cross-cancel: the 3 on top of the first fraction and the 3 on the bottom of the second share a factor of 3, and the 2 and the 8 share a factor of 2, so the problem shrinks to 1/1 × 4/1. Multiply straight across: 4/1 = 4. Without cross-cancelling you would get 24/6, which reduces to the same 4 — cross-cancelling just keeps the numbers small. The calculator marks each cancelled pair in its “Cross-cancel” step.

How to Divide Mixed Fractions

Dividing mixed fractions is multiplying with one extra move: keep the first fraction, change the division sign to multiplication, and flip the second fraction upside down (its reciprocal). Then multiply straight across and convert the answer back to a mixed number. As with multiplication, both mixed numbers must be improper fractions before you flip anything — flipping a mixed number directly gives the wrong answer.

Work 2 1/2 ÷ 1 1/4. Convert: 2 1/2 = 5/2 and 1 1/4 = 5/4. Keep, change, flip: 5/2 × 4/5. Cross-cancel the two 5s and the 2 with the 4 to get 1/1 × 2/1, then multiply: 2. That makes sense — one and a quarter fits into two and a half exactly twice. The calculator’s “Take the reciprocal and multiply” step shows the second fraction being turned over before the multiplication.

Fraction Calculator with Whole Numbers

Because a whole number is a fraction over 1, this tool also works as a fraction calculator with whole numbers. Type the whole number in the large box and leave its numerator and denominator boxes empty; the calculator treats 3 as 3/1 and says so in the first step. From there every operation works exactly as it does for two fractions.

Try 3 × 1/4: the calculator rewrites 3 as 3/1 and multiplies straight across to get 3/4. Or try 5 − 2/3: 5 becomes 5/1, the common denominator is 3, so 15/3 − 2/3 = 13/3, which converts back to 4 1/3. Combining a whole number with a fraction in the same box pair simply makes a mixed number, so 3 and 1/4 entered together is 3 1/4.

Further Reading on Mixed Numbers

• The visual fraction calculator handles the same four operations with a plain-fraction default and the full explanation of numerators, denominators and common denominators.
• The fraction chart shows halves through sixteenths side by side, which helps when picking a common denominator by eye.
• Mixed numbers at Wikipedia — the formal definition and the history of the notation.