Mixed Numbers Calculator

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Mixed Numbers Calculator

Use mixed numbers, fractions,
integers or decimals

Answer:

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Calculator Use

Do math calculations with mixed numbers (mixed fractions) including fractions, integers, mixed numbers and improper fractions. The Mixed Numbers Calculator can add, subtract, multiply and divide mixed numbers and fractions.

What is a Mixed Number?

A mixed number is a positive or negative integer and a proper fraction, together. An integer is a whole number without a decimal, and a proper fraction is a fraction where the top number is smaller than the bottom number.

What Can the Mixed Numbers Calculator Do?

This online calculator does simple math operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is a reduced fraction and a mixed number if it exists.

Enter mixed numbers, whole numbers or fractions in the following formats:

Mixed numbers: Enter as 1 1/2 which is one and one half or 25 3/32 which is twenty five and three thirty seconds. Use one space between the whole number and fraction, and use a forward slash to input fractions.
Whole numbers and positive or negative integers
Fractions: Enter as 3/4 which is three fourths or 3/100 which is three one hundredths

Add Mixed Numbers using the Adding Fractions Formula

Convert each mixed number to an improper fraction:
Multiply the whole number by the denominator, then add the numerator. Place that result over the denominator.
Use the formula for adding fractions:
a/b + c/d = (ad + bc) / bd
Reduce fractions and simplify if possible

Equation to Add Fractions

\( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \times d) + (b \times c)}{b \times d} \)

Example

Add 1 2/6 and 2 1/4

\( 1 \dfrac{2}{6} + 2 \dfrac{1}{4} = \dfrac{8}{6} + \dfrac{9}{4} \)

\( = \dfrac{(8 \times 4) + (9 \times 6)}{6 \times 4} \)

\( = \dfrac{32 + 54}{24} = \dfrac{86}{24} = \dfrac{43}{12} \)

\( = 3 \dfrac{7}{12} \)

1 2/6 + 2 1/4 = 8/6 + 9/4 = (8*4 + 9*6) / 6*4 = 86 / 24

So we get 86/24 which simplifies to 3 7/12

Subtract Mixed Numbers using the Subtracting Fractions Formula

Convert each mixed number to an improper fraction:
Multiply the whole number by the denominator, then add the numerator. Place that result over the denominator.
Use formula for subtracting fractions: a/b - c/d = (ad - bc) / bd
Reduce fractions and simplify if possible

Equation to Subtract Fractions

\( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{(a \times d) - (b \times c)}{b \times d} \)

Example

Subtract 2 1/4 from 1 2/6

1 2/6 - 2 1/4 = 8/6 - 9/4 = (8*4 - 9*6) / 6*4 = -22 / 24

Reduce the fraction to get -11/12

Multiply Mixed Numbers using the Multiplying Fractions Formula

Convert each mixed number to an improper fraction:
Multiply the whole number by the denominator, then add the numerator. Place that result over the denominator.
Use the formula for multiplying fractions: a/b * c/d = ac / bd
Reduce fractions and simplify if possible

Equation to Multiply Fractions

\( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d} \)

Example

Multiply 1 2/6 by 2 1/4

1 2/6 * 2 1/4 = 8/6 * 9/4 = 8*9 / 6*4 = 72 / 24

Reduce the fraction to get 3/1 and simplify to 3

Divide Mixed Numbers using the Dividing Fractions Formula

Convert each mixed number to an improper fraction:
Multiply the whole number by the denominator, then add the numerator. Place that result over the denominator.
Use the formula for dividing fractions: a/b ÷ c/d = ad / bc
Reduce fractions and simplify if possible

Equation to Divide Fractions

\( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a \times d}{b \times c} \)

Example

Divide 1 2/6 by 2 1/4

1 2/6 ÷ 2 1/4 = 8/6 ÷ 9/4 = 8*4 / 9*6 = 32 / 54

Reduce the fraction to get 16/27

Related Calculators

To do math on simple proper or improper fractions use the CalculatorSoup® Fractions Calculator. This calculator simplifies improper fraction answers into mixed numbers.

If you want to simplify an individual fraction into lowest terms use our Simplify Fractions Calculator.

To learn how to factor numbers to find the greatest common factor (GCF) see the Greatest Common Factor Calculator.

If you are simplifying large fractions by hand you can use the Long Division with Remainders Calculator to find whole number and remainder values.