Mixed Number Calculator

Whatever you need to do with mixed numbers, either add, divide, multiply or simplify them, don’t hesitate because our Mixed Number Calculator has all of that in assets. You will learn how to use the calculator, how to get a mixed number and how math operations work with them. Clearly, it is a must to have all-in-one tool for every math geek dealing with fractions on daily basis.

However, this is not the only calculator we have built related to fractions, so take a look at the list below of additional posts used with the terms of fractions:

• Fraction Exponent Calculator
• Multiplicative Inverse Calculator
• Fraction Calculator

Mixed Number

What is a mixed number?

According to the mixed number definition, it is a composition of a whole number and a fractional part. Generally, it represents a number between any two whole numbers. 

Each mixed number has three parts: a whole number, including numerator and denominator, which form proper fractions as an internal part of any mixed number. For those who are not familiar with the term “mixed number”, in some places, you can another term used – mixed fractions.

Mixed number example:

For example, 2 \frac{2}{3} is a mixed number in which:

• 2 is the whole number part
• and \frac{2}{3} is the fractional part

Conversions

You will never be given fractions as mixed numbers. Therefore, sometimes we convert mixed numbers to other possible forms, such as improper fractions, decimal, percent, and more.

This section will show and teach you how to convert a mixed number to:

• improper fractions and vice versa
• a decimal and vice versa
• a percent

Note: You can make those conversions in a simpler way using our mixed number converter (calculator).

Mixed Number to Improper Fraction

How to turn an improper fraction into a mixed number?

If we are given a mixed number 3 \frac{1}{2}, and you want to turn it into an improper fraction (getting rid of the whole number), you need to:

• First, you need to multiply the whole number by the fraction’s denominator: 3 \times 2 = 6
• Take the result you get from the addition and add it to the dividend: 6 + 1 = 7
• The number you get from this calculation is the new numerator of the fraction: \frac{7}{4}

Improper Fraction to Mixed Number

But, what happens in the opposite scenario. What if you have an improper fraction, and you need to figure out how to get a mixed number from it for some reason. So, how can you do it?

• Let’s assume you are given a fraction: \frac{8}{3}
• First, instead of multiplying, you need to do the opposite. Take the dividend and divide it by the denominator of the improper fraction: 8 / 3 = 2 with a remainder of 2
• The whole number you get from the division is the value that will represent a whole number in a mixed fraction. But, what shall we do with a remainder?
• Take the remainder and use it as a new numerator in the fraction. In addition, the denominator remains the same, and you don’t need to change it: 2 \frac{2}{3}
• As a result, now we have a mixed number 2 \frac{2}{3}

There are various other possible conversions between mixed numbers (fractions) and other forms of writing numbers.

Therefore, instead of covering all of those aspects here, for more conversions related to fractions, you should check out these:

• Fractions to Percent Calculator – is a calculator used to convert a fractional expression to a percent. Additionally, it supports both directions: fractions to percent and percent to fractions (including mixed number to percent conversion).
• Fractions to Decimal Calculator – is a calculator for converting a simple or mixed number to decimal (or vice versa, decimal to mixed number)

Math Operations with Mixed Numbers

What operations can we apply for mixed numbers? Well, mixed numbers are nothing more than a specific type of fractions; therefore, all the math operations you do with fractions can also be used in the terms of mixed numbers. As a result, you can:

• add
• subtract
• divide
• and multiply mixed numbers.

We will cover each of them one by one in the next few sections.

Addition

When adding mixed number fractions, you can choose from two methods:

1. Adding whole numbers and fractions separately
2. Converting mixed numbers to improper fractions

Let’s explore more about them and see where they differ in the calculation. However, whichever method you choose, you will get the same result eventually.

Method: Adding whole numbers and the fractional part separately

Suppose we have two mixed numbers: 3 \frac{1}{2} and 5 \frac{2}{3}, and we are told to add them.

1. First, you need to add their whole numbers: 3 + 5 = 8
2. After you solve their whole numbers, you need to add their fractional parts: \frac{1}{2} and \frac{2}{3}
3. \frac{1}{2} and \frac{2}{3} don’t have the same denominator. Therefore, we need to find their least common multiple = 6.
4. Now, after you find it, add them: \frac{1}{2} + \frac{2}{3} = \frac{7}{6}
5. Finally, we get a new mixed fraction 8 \frac{7}{6} = 9 \frac{1}{6}

Method: Adding whole numbers and the fractional part separately

We will use the same mixed numbers as in the previous method.

1. Convert both mixed numbers into their equivalent improper fractions: 3 \frac{1}{2} = \frac{7}{2} and 5 \frac{2}{3} = \frac{17}{3}
2. Add them: \frac{7}{2} + \frac{17}{3} = \frac{55}{6}
3. Now, write the improper fraction as a mixed number, and you will get: 9 \frac{1}{6}

While here, you should also check this Addition Calculator.

Subtraction

Subtracting mixed numbers follows the same approach as when we add mixed numbers. Therefore, there is nothing much to explain, because we showed everything you need to know in the previous section. However, let’s go through a quick example below:

Let’s imagine you have two mixed numbers: 5 \frac{1}{2} and 3 \frac{2}{4}. How to subtract them?

1. Convert them into improper fractions first: 5 \frac{1}{2} = \frac{11}{2} and 3 \frac{2}{4} = \frac{14}{4}
2. Subtract the two fractions: \frac{11}{2} – \frac{14}{4} = \frac{8}{4} = 2
3. Therefore, we get only a whole number, and there is no the fractional part

Multiplication

When multiplying two mixed numbers, we use the same “to improper fractions” conversion approach.

Let’s choose two mixed numbers: 2 \frac{1}{3} and 1 \frac{2}{5}.

1. First, convert both mixed numbers to improper fractions: 2 \frac{1}{3} = \frac{1}{3} and 1 \frac{2}{5} = \frac{7}{5}
2. Now, multiply the first numerator by the numerator of the second mixed number. Then do the same for denominators: \frac{7}{3} \times \frac{7}{5} = \frac{49}{15}
3. Finally, let’s change the improper fraction into a mixed fraction: \frac{49}{15} = 3 \frac{4}{15}

Division

Dividing mixed numbers work the same way with only one extra step. You will need to find the reciprocal of the second improper fraction before calculating between them. Let’s see how it’s done:

Divide two mixed numbers: 2 \frac{1}{2} and 3 \frac{1}{3}

1. Convert them into improper fractions:2 \frac{1}{2} = \frac{5}{2} and 3 \frac{1}{3} = \frac{10}{3}
2. Calculate the multiplicative inverse of the second fraction: \frac{10}{3} = \frac{3}{10}
3. Multiply their numerators and denominators, respectively: \frac{5}{2} \times \frac{3}{10} = \frac{15}{20}

Note: You can easily access and use all of these operations in our calculator. Simply, select one of the from the list in the calculator, enter the parameters and wait for the calculator to complete the calculation.

Mixed Number Calculator – How to Use

Whatever you’ve read or seen so far is how we approach the mixed numbers, converting them and using math operations with them. But have you ever wondered about an easier and quicker way to deal with fractions, specifically mixed numbers – maybe with some kind of calculator?

You can do all of that and even more using our Mixed Number Calculator. Importantly, we built this calculator as an all-in-one tool to have in your pocket and use it to calculate anything you need about mixed numbers. Therefore, it doesn’t matter whether you need to add, subtract, divide, or simplify mixed numbers because our calculator got your back.

How to use our calculator? Follow the steps below:

• Open the calculator and select one of the provided options depending on what you want to do with mixed numbers (add, subtract, simplify, and more)
• Depending on what you choose in the calculator, you will be given a certain number of parameters that you can enter. For example, if you choose “multiply mixed number”, you will need to specify a whole number, numerator, and denominator for both fractions
• Once you have all the required parameters specified, the calculator will calculate and return the result
• Our calculator does not only return the result but the whole process of calculation. You can check it below the parameters in the calculator

Mixed Number Calculator – Example

Follow the steps above and utilize the Mixed Number Calculator in the example below.

Scenario: For example, let’s assume you have a mixed number 3 \frac{2}{4} (a whole number + fractional part), but you can further simplify it. So, how can you achieve that with our calculator?

Steps to follow:

1. Select “simplify a mixed number” from the list in the calculator
2. Enter the dividend, divisor, and whole number in the parameter fields of the calculator
3. Mixed Number Calculator will simplify your mixed number and return the mixed number in simplest form: 3 \frac{2}{4} = 3 \frac{1}{2}

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