Mixed numbers — a whole number plus a fraction, like 2 1/3 — show up in recipes, measurements and lumber sizes. They are easy to read but awkward to calculate with directly. This calculator converts them to improper fractions, performs the operation, simplifies, and converts back, and for addition and subtraction it also shows the whole-and-fraction method many classes teach.
How to use the mixed numbers calculator
- Enter the first mixed number: whole part on the left, fraction on the right. Leave the whole box empty for a simple fraction.
- Choose the operation: add, subtract, multiply or divide.
- Enter the second mixed number.
- The tape shows the answer as a mixed number, an improper fraction, a decimal and a percent; the steps show every conversion.
Method 1: convert to improper fractions (works for every operation)
- Convert each mixed number: w n/d = (w × d + n)/d.
- Add or subtract over a common denominator, multiply straight across, or multiply by the reciprocal to divide.
- Simplify and convert the improper result back to a mixed number by dividing the numerator by the denominator.
Method 2: whole parts and fraction parts (addition and subtraction)
Add or subtract the whole numbers, then the fractions over a common denominator. If an addition gives a fraction of 1 or more, carry the extra whole. If a subtraction needs a bigger top fraction, regroup by borrowing 1 whole.
Worked examples
Addition: 2 1/3 + 1 3/4. Improper fractions: 7/3 + 7/4 = 28/12 + 21/12 = 49/12 = 4 1/12. Whole-part method: 2 + 1 = 3; 4/12 + 9/12 = 13/12 = 1 1/12; 3 + 1 1/12 = 4 1/12.
Subtraction with regrouping: 5 1/4 − 2 2/3. In twelfths: 5 3/12 − 2 8/12. Since 3/12 is less than 8/12, borrow 1: 4 15/12 − 2 8/12 = 2 7/12. Check with improper fractions: 21/4 − 8/3 = 63/12 − 32/12 = 31/12 = 2 7/12.
Multiplication: 2 1/3 × 1 3/4. 7/3 × 7/4 = 49/12 = 4 1/12.
Mixed numbers in measurements
Tape measures and recipes use mixed numbers because they are easy to read. Some everyday cases:
| Task | Calculation | Answer |
|---|---|---|
| Two boards, 23 5/16 in and 7 3/8 in | 23 5/16 + 7 3/8 | 30 11/16 in |
| Cut 2 3/4 ft off a 6 ft board | 6 − 2 3/4 | 3 1/4 ft |
| Double a recipe calling for 1 2/3 cups | 1 2/3 × 2 | 3 1/3 cups |
| Split 4 1/2 lb into 3 equal parts | 4 1/2 ÷ 3 | 1 1/2 lb |
For lengths given in feet and inches, the feet and inches calculator handles the 12-inch carries. To practice just the conversions, use the mixed number to improper fraction and improper fraction to mixed number calculators.
Common mistakes
- Multiplying parts separately. 2 1/2 × 2 1/2 = 5/2 × 5/2 = 25/4 = 6 1/4, not 4 1/4.
- Forgetting to regroup. In 5 1/4 − 2 2/3, subtracting the smaller fraction from the larger gives the wrong answer.
- Leaving an improper fraction part. An answer like 3 13/12 should be written 4 1/12.
Frequently asked questions
How do you add mixed numbers?
Either convert both to improper fractions and add, or add the whole numbers and the fractions separately and carry if the fraction part reaches 1. For 2 1/3 + 1 3/4, the wholes give 3 and the fractions give 13/12 = 1 1/12, so the answer is 4 1/12.
How do you subtract mixed numbers when the first fraction is smaller?
Regroup: borrow 1 from the whole number and add it to the fraction as a full set of pieces. In 5 1/4 − 2 2/3, write the fractions as twelfths, then rewrite 5 3/12 as 4 15/12. Now 4 15/12 − 2 8/12 = 2 7/12.
Can I multiply mixed numbers by multiplying the whole parts and the fractions?
No. That skips the cross terms. 2 1/2 × 2 1/2 is 6 1/4, not 4 1/4. Always convert to improper fractions before multiplying or dividing.
How do I enter a negative mixed number?
Type the minus sign on the whole number, for example −2 in the whole box and 1/2 in the fraction boxes for −2 1/2. The sign applies to the entire mixed number.