What is a mixed fraction?

A whole number and a fraction written side by side, like 2 1/4, meaning two and a quarter. The same value written as a single fraction is 9/4, which is called an improper fraction because the top number is larger than the bottom one. They are two spellings of one quantity, and this page shows both for every answer so you can hand over whichever one was asked for.

How do I type a mixed number here?

Whole part, a space, then the fraction: 2 1/4. A minus sign goes at the front and applies to the whole quantity, so -1 3/4 is -7/4 and not minus one plus three quarters. A pasted glyph works too: 1½ is read as 1 1/2. If you would rather work in improper fractions, type 9/4 and nothing changes.

How do I multiply mixed numbers?

Convert each one to an improper fraction, then multiply the tops together and the bottoms together. 2 1/4 becomes 9/4 and 1 1/3 becomes 4/3, so the product is (9 × 4) over (4 × 3), which is 36/12, and dividing both by 12 gives 3. Multiplying the whole parts and the fractions separately is the common mistake here and gives 2 and a twelfth, which is nowhere near the answer.

How do I add mixed numbers?

Convert both, put them over a common denominator, then add the numerators. 1 1/2 + 2 3/4 becomes 3/2 + 11/4, which over 4 is 6/4 + 11/4, so 17/4, which is 4 1/4. Subtraction works the same way and does not care which number is bigger: 3 1/2 - 1 3/4 is 14/4 - 7/4, which is 7/4, or 1 3/4.

What happens when the answer is smaller than one?

There is no whole part to show, so the mixed form is just the fraction: 5/12 stays 5/12. The row under the stage says so rather than printing a bare 0 in front of it. When the answer lands exactly on a whole number, the fraction part disappears instead, so 36/12 is shown as 3.

Can I add three mixed fractions?

Select Add and Add a third number. 1 1/2 + 2 3/4 + 3 1/4 becomes 3/2 + 11/4 + 13/4 = 30/4 = 15/2 = 7 1/2. Each step uses exact fractions, and the working shows the intermediate answer.

How do I convert mixed numbers and improper fractions?

Choose Add and leave the second number at zero. For 2 1/4, calculate (2 × 4 + 1)/4 = 9/4. In the other direction, 17/4 has four wholes and a remainder of 1, giving 4 1/4. Negative mixed numbers retain the sign of the entire quantity: -1 3/4 = -7/4.

How do I divide mixed numbers?

Convert them to improper fractions and multiply by the reciprocal of the divisor. 1 1/2 ÷ 2 1/4 = 3/2 ÷ 9/4 = 3/2 × 4/9 = 12/18 = 2/3. A zero divisor is rejected with the field named.

Is a mixture fraction the same as a mixed number?

A mixed number is a whole part plus a fractional part, which this page calculates. In combustion or chemistry, mixture fraction describes a physical composition and needs a separate model, measurements and units. That scientific calculation is not implemented here.

Mixed Fraction Calculator

A calculator for mixed numbers, the kind written as a whole part and a fraction: 2 1/4, 1 3/4, 3 1/2. Type one in each box, pick the operation, and the answer comes back as a mixed number and as an improper fraction together, with the decimal beside them. The page opens on 2 1/4 × 1 1/3, which is 9/4 × 4/3, then 36/12, and exactly 3. Every mixed number is converted to an improper fraction first and the working says so line by line, because that conversion is the step where the arithmetic is usually lost. Add a third number for three mixed terms under one selected operation; for example, 1 1/2 + 2 3/4 + 3 1/4 = 7 1/2. Adding zero converts a mixed number to an improper fraction or an improper fraction back to its mixed form. This page uses mixed numbers in arithmetic; it does not calculate chemical or combustion mixture fractions.

2 1/4 × 1 1/3336/12 before simplifying · 3 as a fraction · 3 as a decimal · 300%

Operation

First

Second

Show

Each box takes a fraction like 3/4, a mixed number like 1 3/4, a whole number like 7 or a decimal like 0.75 or a percentage like 25%, and the answer comes back in every form at once. First box: a mixed number, like 2 1/4. Second box: a mixed number, like 1 1/3.

Simplifiedreduced from 36/12
3
As a mixed numbera whole number, with nothing left over
3
As a decimalit stops, so this is the whole value
3
As a percentagethe same value out of a hundred
300%

The working

The same steps you would write on paper, and only the ones these two numbers actually needed.

2 1/4 is 9/4.
1 1/3 is 4/3.
Multiply across: (9 × 4) over (4 × 3) = 36/12.
Divide both by 12: 36/12 = 3.

Worked cases

Each one is computed by the same code that answers your own numbers, every time this page loads.

Decimal in0.375 as a fraction
3/8 · 0.375 as a decimal
Mixed numbers2 1/4 by 1 1/3
3 · 36/12 before simplifying, 3 as a decimal
Whole number5/8 of 24
15 · 120/8 before simplifying, 15 as a decimal

Exact rational arithmetic, then the conversions. Exact fraction arithmetic and comparisons. Decimal previews show a repeating cycle when it is found within 240 displayed digits; longer expansions are cut short and marked. Each numeric entry is limited to 200 characters. The exact fraction remains available. The numerator and the denominator stay whole numbers from start to finish, the answer is reduced once by the greatest common divisor, and where a decimal is too long for the page it is cut short rather than rounded, so every digit on screen is a real digit of the value at that place.

Common questions

What is a mixed fraction?: A whole number and a fraction written side by side, like 2 1/4, meaning two and a quarter. The same value written as a single fraction is 9/4, which is called an improper fraction because the top number is larger than the bottom one. They are two spellings of one quantity, and this page shows both for every answer so you can hand over whichever one was asked for.
How do I type a mixed number here?: Whole part, a space, then the fraction: 2 1/4. A minus sign goes at the front and applies to the whole quantity, so -1 3/4 is -7/4 and not minus one plus three quarters. A pasted glyph works too: 1½ is read as 1 1/2. If you would rather work in improper fractions, type 9/4 and nothing changes.
How do I multiply mixed numbers?: Convert each one to an improper fraction, then multiply the tops together and the bottoms together. 2 1/4 becomes 9/4 and 1 1/3 becomes 4/3, so the product is (9 × 4) over (4 × 3), which is 36/12, and dividing both by 12 gives 3. Multiplying the whole parts and the fractions separately is the common mistake here and gives 2 and a twelfth, which is nowhere near the answer.
How do I add mixed numbers?: Convert both, put them over a common denominator, then add the numerators. 1 1/2 + 2 3/4 becomes 3/2 + 11/4, which over 4 is 6/4 + 11/4, so 17/4, which is 4 1/4. Subtraction works the same way and does not care which number is bigger: 3 1/2 - 1 3/4 is 14/4 - 7/4, which is 7/4, or 1 3/4.
What happens when the answer is smaller than one?: There is no whole part to show, so the mixed form is just the fraction: 5/12 stays 5/12. The row under the stage says so rather than printing a bare 0 in front of it. When the answer lands exactly on a whole number, the fraction part disappears instead, so 36/12 is shown as 3.
Can I add three mixed fractions?: Select Add and Add a third number. 1 1/2 + 2 3/4 + 3 1/4 becomes 3/2 + 11/4 + 13/4 = 30/4 = 15/2 = 7 1/2. Each step uses exact fractions, and the working shows the intermediate answer.
How do I convert mixed numbers and improper fractions?: Choose Add and leave the second number at zero. For 2 1/4, calculate (2 × 4 + 1)/4 = 9/4. In the other direction, 17/4 has four wholes and a remainder of 1, giving 4 1/4. Negative mixed numbers retain the sign of the entire quantity: -1 3/4 = -7/4.
How do I divide mixed numbers?: Convert them to improper fractions and multiply by the reciprocal of the divisor. 1 1/2 ÷ 2 1/4 = 3/2 ÷ 9/4 = 3/2 × 4/9 = 12/18 = 2/3. A zero divisor is rejected with the field named.
Is a mixture fraction the same as a mixed number?: A mixed number is a whole part plus a fractional part, which this page calculates. In combustion or chemistry, mixture fraction describes a physical composition and needs a separate model, measurements and units. That scientific calculation is not implemented here.

Exact fraction arithmetic and comparisons. Decimal previews show a repeating cycle when it is found within 240 displayed digits; longer expansions are cut short and marked. Each numeric entry is limited to 200 characters. The exact fraction remains available.