Mixed Numbers

7 min read · Updated September 26, 2026 · by the SolveCalcPro editorial team

A mixed number combines a whole number and a fraction, such as 3 2/5. It is the everyday way to write amounts like “two and a half cups”. For calculation, mixed numbers are usually converted to improper fractions first. This guide shows both conversions and all four operations.

Mixed number to improper fraction

Multiply the whole number by the denominator and add the numerator. 3 2/5 = (3 × 5 + 2)/5 = 17/5.

Improper fraction to mixed number

Divide the numerator by the denominator. 23 ÷ 6 = 3 remainder 5, so 23/6 = 3 5/6.

Adding and subtracting

Add: 2 3/4 + 1 5/6. Use a common denominator of 12: 2 9/12 + 1 10/12 = 3 19/12 = 4 7/12.

Subtract: 5 1/3 − 2 3/4. Write with denominator 12: 5 4/12 − 2 9/12. Borrow 1 from the 5: 4 16/12 − 2 9/12 = 2 7/12.

Multiplying and dividing

Convert to improper fractions first. 1 1/2 × 2 2/3 = 3/2 × 8/3 = 24/6 = 4. And 3 1/2 ÷ 1 3/4 = 7/2 ÷ 7/4 = 7/2 × 4/7 = 2.

Check with an estimate

Round each number to check reasonableness: 2 3/4 + 1 5/6 is about 3 + 2 = 5, and 4 7/12 is close to 4.6, so it is sensible. Confirm exact answers with the fraction calculator.