How do you add mixed numbers?

To add mixed numbers: 1) Convert each to an improper fraction (multiply whole by denominator, add numerator), 2) Find the LCD of both denominators, 3) Convert both fractions to equivalent fractions with the LCD, 4) Add the numerators, 5) Simplify and convert back to a mixed number.

How do you subtract mixed numbers?

Subtracting mixed numbers works the same as addition: convert to improper fractions, find the LCD, subtract the numerators, then simplify. Example: 3½ - 1¾ = 7/2 - 7/4 = 14/4 - 7/4 = 7/4 = 1¾.

How do you multiply mixed numbers?

To multiply mixed numbers: convert each to an improper fraction, then multiply numerator × numerator and denominator × denominator. Example: 2½ × 1⅓ = 5/2 × 4/3 = 20/6 = 10/3 = 3⅓.

How do you divide mixed numbers?

To divide mixed numbers: convert to improper fractions, then flip the second fraction (find its reciprocal) and multiply. Example: 2½ ÷ 1¼ = 5/2 ÷ 5/4 = 5/2 × 4/5 = 20/10 = 2.

How do you convert a mixed number to an improper fraction?

Multiply the whole number by the denominator, then add the numerator. This becomes the new numerator over the same denominator. Example: 3¾ = (3×4+3)/4 = 15/4.

How do you convert an improper fraction to a mixed number?

Divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same. Example: 17/5 = 3 remainder 2 = 3⅖.

How do you simplify a mixed number?

Simplify the fractional part by dividing the numerator and denominator by their Greatest Common Divisor (GCD). Example: 2 6/8 simplifies to 2¾ because GCD(6,8)=2, so 6/8 = 3/4.

Mixed Number Calculator

Our Mixed Number Calculator makes working with mixed numbers simple and intuitive. Whether you're adding 2¾ + 1½, multiplying 3⅓ × 2¼, or converting between mixed numbers and improper fractions, this calculator handles it all with detailed step-by-step explanations. Perfect for students, teachers, and anyone working with fractions in cooking, carpentry, or everyday math.

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calendar_today Updated: April 2026

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New

Operation

First Mixed Number

Whole

Fraction

2¾ (11/4)

Second Mixed Number

Whole

Fraction

1⅔ (5/3)

Result

4 5/12

Mixed Number

53/12

Improper Fraction

4.4167

Decimal

format_list_numbered Step-by-Step Solution

1 Convert to improper fractions: 2 3/4 → 11/4, 1 2/3 → 5/3

2 LCD(4, 3) = 12

3 33/12 + 20/12 = 53/12

4 As mixed number: 4 5/12

2 3/4 + 1 2/3 = 4 5/12

Input Values

Operation

add Add (+)

remove Subtract (−)

close Multiply (×)

more_horiz Divide (÷)

First Number - Whole

First Number - Numerator

First Number - Denominator

Second Number - Whole

Second Number - Numerator

Second Number - Denominator

tips_and_updates Tips

• To add mixed numbers: convert to improper fractions first, then find the LCD (Least Common Denominator)
• For multiplication: just convert to improper fractions and multiply straight across
• For division: flip the second mixed number and multiply (Keep-Change-Flip rule)
• Always simplify your answer by dividing numerator and denominator by their GCD
• A negative mixed number like -2¾ means -(2 + ¾) = -11/4 as an improper fraction
• Check your work: convert the result to decimal to verify it makes sense

How to Use This Calculator

Select Operation

Choose add, subtract, multiply, or divide

Enter First Mixed Number

Input the whole number, numerator, and denominator for the first number

Enter Second Mixed Number

Input the whole number, numerator, and denominator for the second number

View Result

See the answer as a mixed number, improper fraction, and decimal with step-by-step solution

The Formula

A mixed number combines a whole number and a proper fraction. To add/subtract mixed numbers: convert to improper fractions (W×D+N)/D, find LCD, perform operation, then simplify. To multiply: convert to improper fractions and multiply numerators and denominators. To divide: convert and multiply by the reciprocal.

Mixed Number = Whole + Numerator/Denominator

lightbulb Variables Explained

W Whole number part (e.g., 2 in 2¾)
N Numerator of fraction part (e.g., 3 in 2¾)
D Denominator of fraction part (e.g., 4 in 2¾)
I Improper fraction = W×D + N over D

tips_and_updates Pro Tips

To add mixed numbers: convert to improper fractions first, then find the LCD (Least Common Denominator)

For multiplication: just convert to improper fractions and multiply straight across

For division: flip the second mixed number and multiply (Keep-Change-Flip rule)

Always simplify your answer by dividing numerator and denominator by their GCD

A negative mixed number like -2¾ means -(2 + ¾) = -11/4 as an improper fraction

Check your work: convert the result to decimal to verify it makes sense

Working with Mixed Numbers and Improper Fractions

Mixed numbers — whole numbers combined with proper fractions like 3¾ or 2⅓ — appear constantly in everyday life: cooking recipes call for 1½ cups of flour, lumber comes in 2×4 boards that are actually 1½ by 3½ inches, and construction measurements are routinely expressed as mixed fractions. Performing arithmetic with mixed numbers requires converting them to improper fractions first, then applying standard fraction operations. To convert 3¾ to an improper fraction, multiply the whole number by the denominator (3 times 4 equals 12), add the numerator (12 plus 3 equals 15), and place over the original denominator: 15/4. For addition and subtraction, you need a common denominator; for multiplication, simply multiply numerators and denominators directly; for division, multiply by the reciprocal. The final step — converting the result back to a mixed number and simplifying — requires finding the greatest common divisor (GCD) of numerator and denominator. While these steps are straightforward, they involve enough intermediate calculations that errors are common, especially with unlike denominators. A 2023 National Assessment found that fraction arithmetic remains one of the most challenging areas for middle school students, with only 41% of eighth graders demonstrating proficiency in operations with fractions.

What is a Mixed Number?

A mixed number combines a whole number with a proper fraction, like 2¾ or 5⅓. Mixed numbers appear frequently in everyday life — cooking recipes, measurements in carpentry, and distance calculations often use them.

How to Calculate with Mixed Numbers

The key to mixed number arithmetic is converting to improper fractions first. Once converted, you can apply standard fraction operations, then convert the result back to a mixed number for a clean answer.

Frequently Asked Questions

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Mixed Number Calculator

tips_and_updates Tips

How to Use This Calculator

Select Operation

Enter First Mixed Number

Enter Second Mixed Number

View Result

The Formula

lightbulb Variables Explained

tips_and_updates Pro Tips

Working with Mixed Numbers and Improper Fractions

What is a Mixed Number?

How to Calculate with Mixed Numbers

Frequently Asked Questions

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