Add, subtract, multiply and divide mixed numbers — and convert between mixed numbers and improper fractions — with full working.
To calculate with mixed numbers, first turn each one into an improper fraction using whole × denominator + numerator. Then add, subtract, multiply or divide as normal fractions, and convert the answer back to a mixed number in simplest form. For example, 1½ + 2⅓ becomes 3/2 + 7/3 = 23/6 = 3⅚. This calculator shows every step.
Whole numbers only. Leave the Whole box blank for a simple fraction like 3/4. Put a minus sign on the Whole box (or the Numerator if there is no whole part) for a negative value.
Choose Calculate to work with two mixed numbers, or Convert to switch a single value between forms.
2, Numerator 3, Denominator 4. Leave the Whole box blank for a plain fraction such as 3/4, and enter 4 with numerator 0 and denominator 1 for a whole number.Press Calculate or the Enter key. Use Copy result for the answer, or Share link to copy a web address that reopens the page with your numbers already filled in.
What the letters mean. In a fraction a/b, a is the numerator (how many parts you have) and b is the denominator (how many equal parts make one whole). When two fractions have different denominators, multiplying by bd gives them a common denominator so the parts are the same size and can be counted together.
Why converting first works. A mixed number is really an addition in disguise: 2¾ means 2 + ¾. Turning it into 11/4 gives a single fraction, so the ordinary fraction rules apply with no separate whole number to keep track of. That is why this method never goes wrong, even when subtraction crosses below zero.
When to use each form. Improper fractions are easier to calculate with; mixed numbers are easier to picture and to read. Most teachers expect working shown in improper fractions and the final answer given as a mixed number in simplest form — which is exactly what this calculator produces.
(whole × den) + num e.g. 2¾ = (2×4)+3 = 11/4num ÷ den, remainder over den e.g. 11/4 = 2 r3 = 2¾common denominator firsttops × tops, bottoms × bottomsflip the second fraction, then multiplydivide top and bottom by the GCF
| Mixed number | Improper fraction | Decimal |
|---|---|---|
| 1 1/2 | 3/2 | 1.5 |
| 1 1/4 | 5/4 | 1.25 |
| 1 3/4 | 7/4 | 1.75 |
| 2 1/2 | 5/2 | 2.5 |
| 2 1/3 | 7/3 | 2.333… |
| 2 3/4 | 11/4 | 2.75 |
| 3 1/3 | 10/3 | 3.333… |
| 3 5/6 | 23/6 | 3.8333… |
| 4 1/8 | 33/8 | 4.125 |
| 5 3/4 | 23/4 | 5.75 |
| Feature | Mixed number | Improper fraction |
|---|---|---|
| Looks like | 2 3/4 | 11/4 |
| Easy to picture | Yes — you can see it is almost 3 | Harder to judge at a glance |
| Easy to calculate with | No — the whole part gets in the way | Yes — ordinary fraction rules apply |
| Used in | Recipes, measurements, everyday speech | Algebra, working out, exam method |
| Best for | Reading the final answer | Doing the middle steps |
Every fraction is a division, and every mixed number is an addition. Writing 2¾ as 11/4 does not change the value — it just rewrites 2 + ¾ with a single denominator, because 2 is the same as 8/4. Once both numbers are single fractions, the standard rules apply: a common denominator makes the parts the same size so they can be counted, multiplying scales one fraction by another, and dividing by a fraction is the same as multiplying by its reciprocal. Simplifying at the end divides the top and bottom by the same number, which never changes the value either.
1) 13/4 2) 4½ 3) 3 4) 1½ 5) 3
1) 4 7/20 2) −1 1/6 3) 3 4) 3 5) −1½
Cooking. Recipes are written in mixed numbers — 1½ cups, 2¾ teaspoons — so scaling a batch up or down means multiplying mixed numbers.
Construction and woodworking. Imperial measurements use mixed numbers constantly: a board 8½ feet long, a bolt 1⅝ inches. Cutting lists are mixed-number subtraction.
Education. Mixed numbers appear from upper primary through to secondary school, and converting between forms is a standard exam skill.
Engineering and trades. Drill sizes, pipe diameters and material thicknesses are often fractional, and totals must be added precisely rather than rounded.
Sport and time. Race distances and training splits are frequently expressed as mixed numbers, such as running 3½ laps or resting 1¼ minutes.
What is a mixed number?
A mixed number is a whole number written together with a proper fraction, such as 2 3/4. It means the whole number plus the fraction, so 2 3/4 is 2 + 3/4.
How do you add mixed numbers?
Convert each mixed number to an improper fraction, give them a common denominator, add the numerators, then convert the answer back to a mixed number in simplest form. So 1 1/2 + 2 1/3 = 3/2 + 7/3 = 23/6 = 3 5/6.
How do you subtract mixed numbers?
Convert both to improper fractions, use a common denominator, then subtract the numerators. Working this way handles answers that fall below zero without any extra borrowing steps.
How do you multiply mixed numbers?
Convert both to improper fractions, multiply the numerators together and the denominators together, then simplify. So 1 1/2 x 2 1/3 = 3/2 x 7/3 = 21/6 = 3 1/2.
How do you divide mixed numbers?
Convert both to improper fractions, flip the second fraction, then multiply. So 1 1/2 divided by 2 1/3 = 3/2 x 3/7 = 9/14.
How do you convert a mixed number to an improper fraction?
Multiply the whole number by the denominator and add the numerator, keeping the same denominator. For 2 3/4 that is 2 x 4 + 3 = 11, giving 11/4.
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The whole-number part of the answer becomes the whole number and the remainder becomes the new numerator. So 11/4 is 11 divided by 4 = 2 remainder 3, giving 2 3/4.
What is the difference between a mixed number and an improper fraction?
They are two ways of writing the same value. A mixed number such as 2 3/4 is easier to picture, while the improper fraction 11/4 is easier to calculate with.
Can a mixed number be negative?
Yes. The minus sign applies to the whole mixed number, so -1 1/2 means -(1 + 1/2), which is -3/2. It does not mean -1 plus 1/2.
How do you write a mixed number in simplest form?
Simplify the fraction part by dividing the numerator and denominator by their greatest common factor, and carry any extra whole from an improper fraction part into the whole number. So 2 4/8 becomes 2 1/2.
How do you convert a mixed number to a decimal?
Divide the numerator by the denominator and add the whole number. For 2 3/4, 3 divided by 4 = 0.75, so the decimal is 2.75. This calculator shows the decimal alongside every answer.
How do you convert a decimal to a mixed number?
Keep the whole part, write the decimal part over its place value, then simplify. So 2.75 becomes 2 and 75/100, which reduces to 2 3/4.
Why convert to improper fractions before calculating?
A mixed number is really a whole number plus a fraction, which makes two parts to track. Converting to a single improper fraction means the ordinary fraction rules work every time, including when a subtraction crosses below zero.
Does this calculator show the working?
Yes. Every answer lists the conversion to improper fractions, the common denominator or reciprocal step, the arithmetic, and the final simplification, so it can be used for learning as well as checking.
Can you add a whole number and a mixed number?
Yes. Treat the whole number as a fraction over 1 by entering it with numerator 0 and denominator 1. For example, 3 + 2 1/4 becomes 3/1 + 9/4 = 21/4 = 5 1/4. You can also simply add the whole numbers and keep the fraction part unchanged.
Is this Mixed Number Calculator free?
Yes. It is free with no sign-up, works on any device, and runs in your browser so your entries stay private.