Mixed Number Calculator

Q: How do you calculate with mixed numbers?

Convert each mixed number to an improper fraction, perform the operation, reduce the result, and convert it back to a mixed number if needed.

Q: What is an improper fraction?

An improper fraction has a numerator greater than or equal to its denominator. It can represent the same value as a mixed number.

Q: Can the mixed number calculator use negative values?

Yes. Enter a negative whole number or numerator to calculate with a negative mixed number.

Calculate with two mixed numbers by converting them to improper fractions, completing the chosen operation, and simplifying the result.

Mixed Number Calculator

Decimal 6.25

How it works

Formula and steps

The formula shows how the mixed number calculator turns your inputs into the result. Use it to check the calculation, then follow the example steps to see each part of the math.

Formula & steps

Mixed number to improper fraction formula

w \frac{a}{b} = \frac{w b + a}{b}

Convert each mixed number before performing the selected fraction operation.

w= Whole-number part

a= Numerator

b= Denominator

1Enter the whole number, numerator, and denominator for both mixed numbers.
2Convert each mixed number to an improper fraction.
3Add, subtract, multiply, or divide the improper fractions.
4Reduce the result and convert it back to a mixed number when appropriate.

Worked examples

Example 1

2 \frac{1}{2} + 3 \frac{3}{4}

1
Convert to improper fractions
$2 \frac{1}{2} = \frac{5}{2}, 3 \frac{3}{4} = \frac{15}{4}$
2
Use a common denominator
$\frac{5}{2} = \frac{10}{4}$
3
Add the fractions
$\frac{10}{4} + \frac{15}{4} = \frac{25}{4}$
4
Convert to a mixed number
$\frac{25}{4} = 6 \frac{1}{4}$

Example 2

4 \frac{1}{3} \div 1 \frac{1}{2}

1
Convert to improper fractions
$4 \frac{1}{3} = \frac{13}{3}, 1 \frac{1}{2} = \frac{3}{2}$
2
Flip the second fraction
$\frac{3}{2} \to \frac{2}{3}$
3
Multiply across
$\frac{13}{3} \times \frac{2}{3} = \frac{26}{9}$
4
Convert to a mixed number
$\frac{26}{9} = 2 \frac{8}{9}$

Common uses

Adding mixed numbers
Subtracting mixed fractions
Multiplying mixed numbers
Dividing mixed numbers

Common mistakes

Operating on the whole numbers and fractional parts separately.
Forgetting to convert both mixed numbers to improper fractions first.
Applying a negative sign only to the whole-number part.

Fraction guide

How to calculate mixed numbers

Mixed numbers combine a whole number and a proper fraction. Converting them to improper fractions makes all four arithmetic operations consistent.

Convert to improper fractions

Multiply the whole number by the denominator, add the numerator, and place that total over the original denominator.

Calculate and convert back

Perform the selected fraction operation, simplify, then divide the numerator by the denominator to write an improper result as a mixed number.

Negative mixed numbers

A negative sign applies to the entire mixed number. The calculator preserves that sign during conversion and calculation.

FAQ

How do you calculate with mixed numbers?

What is an improper fraction?

Can the mixed number calculator use negative values?

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