Mixed Numbers Calculator

Use mixed numbers, fractions, integers or decimals

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Accepts: 1 3/4 · −2 3/8 · 5/6 · −3 · 1.5


Math Guide

Mixed Numbers

Everything you need to understand, calculate, and master mixed numbers — from what they are to how to add, subtract, multiply, and divide them.

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What is a Mixed Number?

Imagine you ordered two pizzas and ate one full pizza plus three slices of the second. You didn't eat a whole second pizza — you ate a part of it. That's a mixed number in real life: a whole number living side by side with a fraction.

2
whole
+
34
fraction
=
234
mixed number
The whole part
2
A regular integer. It counts how many complete units you have — full pizzas, whole hours, entire miles.
The fraction part
34
Always less than 1. It represents the leftover bit that didn't fill a whole unit — like 3 out of 4 slices.
The improper twin
114
Every mixed number has an equivalent improper fraction (numerator ≥ denominator). Same value, different clothing.

The key insight: 2¾ and 11⁄4 are the exact same quantity. To convert, multiply the whole number by the denominator and add the numerator: 2 × 4 + 3 = 11. This trick is the secret behind every mixed-number calculation.

How Can the Mixed Numbers Calculator Help?

Working with mixed numbers by hand means converting, finding common denominators, simplifying — a chain of steps where one slip ruins everything. The calculator handles all of that silently, while also showing you why each step happens.

Instant answers
Get results for any combination of mixed numbers, fractions, integers, or decimals in one click.
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Step-by-step breakdown
Every calculation is shown in full — LCD, conversion, simplification — so you can learn the method, not just the answer.
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All four operations
Add, subtract, multiply, and divide. Handles negatives, improper fractions, and whole numbers without complaint.
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Auto-simplified results
Answers come fully reduced, with the mixed number and improper fraction form shown side by side.
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Flexible input
Type 1 3/4, -2 3/8, 5/6, -3, or 1.5 — whatever form you have, the calculator understands it.
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Great for learning
Students can use it to check homework, verify their working, or study the exact technique for each operation.

How to Work with Mixed Numbers

The golden rule for every operation: convert mixed numbers to improper fractions first. Once they're improper fractions, the arithmetic becomes straightforward. Then convert back and simplify at the end.

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Adding Mixed Numbers

To add mixed numbers, convert them to improper fractions, find a common denominator, add the numerators, then simplify.

Formula
abc+def=(ac+b)c+(df+e)f
Example — 1¾ + 2⅝
1
Convert to improper fractions
1¾ = 74  ·  2⅝ = 218
2
Find LCD (LCD of 4 and 8 = 8)
74 = 148
3
Add numerators
14 + 218 = 358
4
Convert back & simplify
358 = 4⅜
Subtracting Mixed Numbers

Subtraction follows the same path as addition — convert to improper fractions, align denominators, then subtract the numerators.

Formula
(ac+b)c(df+e)f=(ac+b)·f − (df+e)·cc·f
Example — 3½ − 1¼
1
Convert to improper fractions
3½ = 72  ·  1¼ = 54
2
LCD of 2 and 4 = 4; rewrite
72 = 144
3
Subtract numerators
14 − 54 = 94
4
Convert back
94 =
×
Multiplying Mixed Numbers

Multiplication is actually the easiest operation — no common denominator needed. Convert, multiply top-by-top and bottom-by-bottom, then simplify.

Formula
pq×rs=p × rq × s
Example — 2⅓ × 1½
1
Convert to improper fractions
2⅓ = 73  ·  1½ = 32
2
Multiply numerators & denominators
7 × 33 × 2 = 216
3
Simplify (GCF = 3)
216 = 72
4
Convert back
72 =
÷
Dividing Mixed Numbers

Division has one extra trick: flip the second fraction (take its reciprocal), then multiply. That's the whole secret — "keep, change, flip."

Formula — Keep · Change · Flip
pq÷rs=pq×sr=p × sq × r
Example — 3¾ ÷ 1½
1
Convert to improper fractions
3¾ = 154  ·  1½ = 32
2
Keep first, flip second → multiply
154 × 23 = 3012
3
Simplify (GCF = 6)
3012 = 52
4
Convert back
52 =