혼합 숫자 계산자

단계별 솔루션을 통해 대분수를 즉시 더하고, 빼고, 곱하고, 나눕니다.

계산기

살다
분수 A
+
분수 B
결과
0
0
0
가분수 0/1
소수값 0.00

What is a Mixed Numeral 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

📝
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

Mixed Numeral Formula

The Mixed Number formula converts between mixed numbers and improper fractions. This conversion is the first step in every mixed number calculation.

Mixed → Improper

(Whole × Denominator) + Numerator Denominator

2¾ → (2 × 4 + 3) / 4 = 11/4

Improper → Mixed

Quotient Remainder Denominator

11/4 → 11 ÷ 4 = 2 R 3 → 2¾

Try It — Convert a Mixed Number

Whole
Num
Den
→
Improper
11/4
(2 × 4) + 3 = 11

Conversion Chart

This reference table shows 22 common improper fractions with their mixed number and decimal equivalents. Use the Mixed Numeral Formula above to convert any improper fraction to a mixed number, or use the calculator at the top of this page for instant results.

Improper FractionMixed NumberDecimal
9/81 1⁄81.13
26/211 5⁄211.24
5/41¼1.25
27/201 7⁄201.35
3/21½1.50
13/81 5⁄81.63
5/31⅔1.67
7/41¾1.75
15/81 7⁄81.88
21/92⅓2.33
12/52 2⁄52.40
5/22½2.50
11/42¾2.75
50/182 7⁄92.78
19/63 1⁄63.17
16/53 1⁄53.20
7/23½3.50
15/43¾3.75
21/45¼5.25
20/36⅔6.67
15/27½7.50
37/312⅓12.33

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

ab + cd = (a × d) + (b × c)b × d

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

ab − cd = (a × d) − (b × c)b × d

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

ab × cd = a × cb × d

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

ab ÷ cd = a × db × c

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:

🍳

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.

📐

Construction and Carpentry

Measurements in construction use fractions of inches and feet. Adding 3¼ inches to 5⅞ inches requires precise mixed number addition.

📚

Math Homework and Exams

Students use a mixed number calculator to verify manual calculations and understand each step of the solution process.

📊

Data and Measurements

Scientific measurements and statistical data often produce mixed number results that require conversion between improper fractions and decimals.

Simplifying Fractions

To simplify a fraction, divide both the numerator and denominator by their greatest common factor (GCF). The GCF is the largest number that divides evenly into both values.

Not simplified 3 4⁄8
→
Simplest form 3½

To simplify a mixed number fraction, follow these 4 steps:

  1. Take the fraction part (e.g., 4⁄8).
  2. Find the GCF of the numerator and denominator → GCF(4, 8) = 4.
  3. Divide both by the GCF: 4 ÷ 4 = 1, 8 ÷ 4 = 2 → 1⁄2.
  4. Recombine with the whole number → 3½.

A fraction is fully simplified when the GCF of numerator and denominator equals 1. The Mixed Number Calculator at the top of this page simplifies every result automatically.

Try It — Simplify a Fraction

/ →
2/3
GCF(24, 36) = 12 → 24÷12 / 36÷12
자주 묻는 질문

자주 묻는 질문

대분수 계산에 대한 일반적인 질문입니다.

대분수는 2 3/4처럼 정수와 진분수를 결합한 것입니다. 1보다 큰 값을 나타냅니다.
각 대분수를 가분수로 변환하고, 공통 분모를 찾고, 분자를 더한 다음, 필요한 경우 단순화하고 다시 대분수로 변환합니다.
첫 번째 분수 부분이 더 작은 경우 정수에서 1을 빌리십시오. 분수 부분에 분모/분모로 1을 더한 다음 정상적으로 뺍니다.
두 대분수를 가분수로 변환하고 분자와 분모를 곱한 다음 최종 분수를 단순화합니다.