About the Mixed Number Calculator
This mixed number calculator does arithmetic with numbers like 2 3/4 and 1 1/2. Enter each mixed number as a whole part, numerator and denominator, choose an operation, and it returns the answer as a simplified mixed number, an improper fraction and a decimal, together with the steps used.
It is handy for homework checking, scaling recipes (1 1/2 cups × 2 1/3), woodworking and construction measurements in inches, and anyone who needs to convert a mixed number to an improper fraction or back. To enter a plain fraction set the whole number to 0; to enter a whole number set the numerator to 0.
Negative mixed numbers are written with the minus sign on the whole part, so −1 3/4 means −(1 + 3/4) = −7/4. If the whole part is 0, put the minus sign on the numerator instead.
How to use the mixed number calculator
- 1Enter the whole number, numerator and denominator of the first mixed number.
- 2Choose add, subtract, multiply or divide.
- 3Enter the second mixed number the same way (use 0 for the whole part of a plain fraction).
- 4Read the simplified mixed-number answer, improper fraction and decimal.
- 5Check the notes for the working steps.
Formula and method
Each mixed number is first converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator. The operation is then done on the improper fractions: addition and subtraction use a common denominator, multiplication multiplies numerators and denominators, and division multiplies by the reciprocal of the second fraction.
The result is reduced by dividing numerator and denominator by their greatest common divisor, then converted back to a mixed number by dividing the numerator by the denominator: the quotient is the whole part and the remainder becomes the new numerator.
- w
- Whole-number part of the mixed number
- n / d
- Numerator and denominator of the fractional part
- a/b, c/d
- The two numbers written as improper fractions
Worked examples
1 1/2 + 2 3/4
Convert to improper fractions: 1 1/2 = 3/2 and 2 3/4 = 11/4. With a common denominator, 6/4 + 11/4 = 17/4, which is 4 remainder 1, so the answer is 4 1/4.
3 1/3 − 1 5/6
3 1/3 = 10/3 = 20/6 and 1 5/6 = 11/6. Subtracting gives 9/6, which simplifies to 3/2 = 1 1/2.
Recipe scaling: 2 2/5 × 1 1/4
2 2/5 = 12/5 and 1 1/4 = 5/4. Multiplying gives 60/20, which simplifies to exactly 3.
4 1/2 ÷ 1 1/2
4 1/2 = 9/2 and 1 1/2 = 3/2. Dividing means multiplying by the reciprocal: 9/2 × 2/3 = 18/6 = 3.
Negative: −1 3/4 + 5/8
−1 3/4 = −7/4 = −14/8. Adding 5/8 gives −9/8, which is −1 1/8 as a mixed number.
Frequently asked questions
How do I convert a mixed number to an improper fraction?+
Multiply the whole number by the denominator and add the numerator; keep the same denominator. For example, 3 2/5 = (3 × 5 + 2)/5 = 17/5.
How do I convert an improper fraction to a mixed number?+
Divide the numerator by the denominator. The quotient is the whole number and the remainder is the new numerator over the same denominator. For example, 17/5 = 3 remainder 2, so 3 2/5.
Can I add the whole numbers and fractions separately?+
Yes, for addition: add the whole parts, add the fractions, then carry any whole number the fractions make. For subtraction you may need to borrow, and for multiplication and division you must convert to improper fractions first.
Why do I need to convert before multiplying mixed numbers?+
Multiplying the whole parts and the fractions separately gives the wrong answer because it skips the cross terms. 1 1/2 × 1 1/2 is 9/4 = 2 1/4, not 1 1/4.
How do I enter a plain fraction or whole number?+
For a fraction like 3/8, set the whole part to 0. For a whole number like 5, set the numerator to 0 and leave any non-zero denominator.