Calculator Use
Do math calculations with mixed numbers (mixed fractions) performing operations on fractions, whole numbers, integers, mixed numbers, mixed fractions and improper fractions. The Mixed Numbers Calculator can add, subtract, multiply and divide mixed numbers and fractions.
Mixed Numbers Calculator (also referred to as Mixed Fractions):
This online calculator handles simple operations on whole numbers, integers, mixed numbers, fractions and improper fractions by adding, subtracting, dividing or multiplying. The answer is provided in 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. Keep exactly one space between the whole number and fraction and use a forward slash to input fractions. You can enter up to 3 digits in length for each whole number, numerator or denominator (123 456/789).
- Whole numbers: Up to 3 digits in length.
- Fractions: Enter as 3/4 which is three fourths or 3/100 which is three one hundredths. You can enter up to 3 digits in length for each the numerators and denominators (e.g., 456/789).
Adding Mixed Numbers using the Adding Fractions Formula
- Convert the mixed numbers to improper fractions
- Use the
algebraic formula for addition of fractions:
a/b + c/d = (ad + bc) / bd - Reduce fractions and simplify if possible
Adding Fractions Formula
\( \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{(a \times d) + (b \times c)}{b \times d} \)
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 and simplify to 3 7/12
Subtracting Mixed Numbers using the Subtracting Fractions Formula
- Convert the mixed numbers to improper fractions
- Use the algebraic formula for subtraction of fractions: a/b - c/d = (ad - bc) / bd
- Reduce fractions and simplify if possible
Subtracting Fractions Formula
\( \dfrac{a}{b} - \dfrac{c}{d} = \dfrac{(a \times d) - (b \times c)}{b \times d} \)
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
Multiplying Mixed Numbers using the Multiplying Fractions Formula
- Convert the mixed numbers to improper fractions
- Use the algebraic formula for multiplying of fractions: a/b * c/d = ac / bd
- Reduce fractions and simplify if possible
Multiplying Fractions Formula
\( \dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d} \)
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
Dividing Mixed Numbers using the Dividing Fractions Formula
- Convert the mixed numbers to improper fractions
- Use the algebraic formula for division of fractions: a/b ÷ c/d = ad / bc
- Reduce fractions and simplify if possible
Dividing Fractions Formula
\( \dfrac{a}{b} \div \dfrac{c}{d} = \dfrac{a \times d}{b \times c} \)
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 perform math operations on simple proper or improper fractions use our 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.
For an explanation of 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.
How Do You Add Mixed Fractions with Different Denominators by Converting to Improper Fractions?
Note:
Adding mixed fractions? You could first convert each to an improper fraction. If they don't have common denominators, then find a common denominator and use it to rewrite each fraction. Then, add the fractions together and simplify. In this tutorial, take a look at adding together mixed fractions with unlike denominators!
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Background Tutorials
Converting Decimals and Fractions
How Do You Turn a Mixed Fraction Into an Improper Fraction?
Working with mixed fractions in equations can be tough, but things get easier if you convert them into improper fractions first. Once you learn this skill, you'll find yourself using it all the time, so take look at how to convert a mixed fraction to an improper fraction.
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How Do You Turn an Improper Fraction Into a Mixed Fraction?
In math, it's often important to change a fraction from one type to another. It can help you work with the fraction in an equation or help make more sense of an answer. This tutorial shows you how to convert an improper fraction to a mixed fraction.
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Adding Fractions
How Do You Add Fractions with the Same Denominator?
While adding fractions can be hard, adding fractions with the same denominator is just as easy as adding numbers. That's why when you add fractions you first get all of them to have the same denominator, and then add them up. In this tutorial you get to see just how easy it is to add up fractions once they have the same denominator!
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Least Common Denominator
Mixed Numbers and Improper Fractions
What's a Mixed Number?
Fractions come in all sorts of flavors, and in this tutorial you'll learn how to recognize mixed numbers.
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Further Exploration
Subtracting Fractions