What is a Mixed Number Calculator?
A mixed number is a whole number combined with a proper fraction. The whole number part represents complete units, and the fraction part represents a portion of one additional unit. For example, 2¾ contains the whole number 2 and the proper fraction ¾.
Mixed numbers express values that fall between two consecutive integers. The value 2¾ sits between 2 and 3 on a number line. Every mixed number has 3 components: a whole number, a numerator (top number of the fraction), and a denominator (bottom number of the fraction).
Proper Fraction
¾ Numerator < Denominator
Improper Fraction
11/4 Numerator ≥ Denominator
Mixed Number
2¾ Whole + Proper Fraction
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Key Point: A mixed number and an improper fraction represent the same value. The mixed number 2¾ equals the improper fraction 11/4. Mixed numbers are easier to read, while improper fractions are easier to calculate with.
Interactive Number Line — Drag the dot
Conversion Chart
This reference table shows 22 common improper fractions with their mixed number and decimal equivalents. Convert any improper fraction to a mixed number, or use the calculator at the top of this page for instant results.
| Improper Fraction | Mixed Number | Decimal |
|---|
| 9/8 | 1 1⁄8 | 1.13 |
| 26/21 | 1 5⁄21 | 1.24 |
| 5/4 | 1¼ | 1.25 |
| 27/20 | 1 7⁄20 | 1.35 |
| 3/2 | 1½ | 1.50 |
| 13/8 | 1 5⁄8 | 1.63 |
| 5/3 | 1⅔ | 1.67 |
| 7/4 | 1¾ | 1.75 |
| 15/8 | 1 7⁄8 | 1.88 |
| 21/9 | 2⅓ | 2.33 |
| 12/5 | 2 2⁄5 | 2.40 |
| 5/2 | 2½ | 2.50 |
| 11/4 | 2¾ | 2.75 |
| 50/18 | 2 7⁄9 | 2.78 |
| 19/6 | 3 1⁄6 | 3.17 |
| 16/5 | 3 1⁄5 | 3.20 |
| 7/2 | 3½ | 3.50 |
| 15/4 | 3¾ | 3.75 |
| 21/4 | 5¼ | 5.25 |
| 20/3 | 6⅔ | 6.67 |
| 15/2 | 7½ | 7.50 |
| 37/3 | 12⅓ | 12.33 |
Performing Arithmetic Operations on Mixed Numbers
Mixed number arithmetic requires converting to improper fractions first. There are 4 operations: addition, subtraction, multiplication, and division. Each operation follows the same starting step — convert mixed numbers to improper fractions — but the calculation method differs.
Adding Mixed Numbers
To add mixed numbers, convert both to improper fractions, find a common denominator, add the numerators, then simplify.
Equation
Example
Add 1 2⁄6 and 2 1⁄4
Convert: 1 2⁄6 = 8/6 and 2 1⁄4 = 9/4
Apply formula: (8 × 4 + 9 × 6) / (6 × 4) = (32 + 54) / 24 = 86/24
Simplify: GCF(86, 24) = 2, so 86/24 = 43/12 = 3 7⁄12
Subtracting Mixed Numbers
To subtract mixed numbers, convert both to improper fractions, find a common denominator, subtract the numerators, then simplify.
Equation
Example
Subtract 2 1⁄4 from 1 2⁄6
Convert: 1 2⁄6 = 8/6 and 2 1⁄4 = 9/4
Apply formula: (8 × 4 − 9 × 6) / (6 × 4) = (32 − 54) / 24 = −22/24
Simplify: GCF(22, 24) = 2, so −22/24 = −11/12
Multiplying Mixed Numbers
To multiply mixed numbers, convert both to improper fractions, multiply numerators together, multiply denominators together, then simplify.
Equation
Example
Multiply 1 2⁄6 by 2 1⁄4
Convert: 1 2⁄6 = 8/6 and 2 1⁄4 = 9/4
Multiply: (8 × 9) / (6 × 4) = 72/24
Simplify: 72/24 = 3/1 = 3
Dividing Mixed Numbers
To divide mixed numbers, convert both to improper fractions, flip the second fraction (reciprocal), then multiply and simplify.
Equation
Example
Divide 1 2⁄6 by 2 1⁄4
Convert: 1 2⁄6 = 8/6 and 2 1⁄4 = 9/4
Flip and multiply: (8 × 4) / (6 × 9) = 32/54
Simplify: GCF(32, 54) = 2, so 32/54 = 16/27
Common Use Cases for a Mixed Number Calculator
A mixed number calculator serves 3 primary use cases:
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Cooking and Baking
Recipes use mixed numbers for ingredient measurements. A mixed number calculator converts 2½ cups to decimals or scales recipes by multiplying fractions.
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Construction and Carpentry
Measurements in construction use fractions of inches and feet. Adding 3¼ inches to 5⅞ inches requires precise mixed number addition.
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Math Homework and Exams
Students use a mixed number calculator to verify manual calculations and understand each step of the solution process.
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Data and Measurements
Scientific measurements and statistical data often produce mixed number results that require conversion between improper fractions and decimals.