Mixed Numbers Calculator

A mixed number calculator is a tool used for performing all basic math operations on mixed numbers. These operations include Addition, Subtractions, Multiplication, and Division.

How to use this mixed fractions calculator?

To perform arithmetic operations on two mixed fractions, follow the steps below:

• Input the "mixed fraction 1" and "mixed fraction 2".
• Select the operator (+, -, ÷, *).
• Hit the "calculate" button to get the result.
• Press the "reset" button to recalculate the value.
• Click on “show more” to see a detailed step-by-step process.

After pressing the calculate button, this mixed fractions calculator will provide you with results in mixed numbers with steps.

What are mixed numbers (fractions)?

The mixed number definition is; “When a proper fraction is combined with a whole number”. Mixed numbers are another way to write improper fractions.

Usually, it is done to avoid using a decimal value. A mixed number has three components;

• Denominator
• Numerator
• Whole Number

Mathematical Operations on mixed numbers:

You need to convert mixed numbers to improper fractions before performing operations. The manual processes for each operation are as follows:

1. Adding Mixed Numbers:

After converting mixed numbers into improper fractions,

Use the formula a/b + c/d = (ad + bc) / bd.

After this, simplify.

Example:

Add the mixed number fractions 3 7/10, 1 2/9.

Solution:

Step 1: Convert to an improper fraction.

37/10 + 11/9

Step 2: Put the values in the algebraic formula.

a/b + c/d = (ad + cb) / bd

= [(37)(9) + (11)(10)] / (10)(9)
= 443 / 90
= 4.922

For adding mixed numbers you can use the calculator above instead.

2. Subtracting Mixed Numbers:

After converting mixed numbers into an improper form, use the same formula as used to add mixed numbers just change the operation to minus (-) i.e a/b - c/d = (ad - bc) / bd.

Let’s try to use the same numbers for this example.

Example:

Subtract the mixed number fractions  3 7/10, 1 2/9.

Solution:

Step 1: Convert to an improper fraction.

= 37/10 - 11/9

Step 2: Put the values in the algebraic formula.

a/b - c/d = (ad - cb) / bd

= [(37)(9) - (11)(10)] / (10)(9)
= 213 / 90
= 2.3778

3. Multiplying mixed numbers:

It is relatively easy to multiply and subtract the mixed numbers. After converting, multiply the numerator of the 1st improper fraction with the numerator of the 2nd improper fraction.

Then, Multiply the denominator of the 1st improper fraction by the denominator of the 2nd improper fraction.

Example:

Multiply 2 6/7 by 4 1/7.

Solution:

Step 1: Transform into an improper fraction.

= 20/7 * 29/7

Step 2: Multiply the numerators.

= 20 x 29
= 580

Step 3: Multiply the denominators.

= 7 x 7
= 49

Step 4: Put back as an improper form of fraction and solve.

= 580 /49
= 11.836

4. Dividing mixed numbers:

The only difference in this operation is that you will need to invert the 2nd fraction. After converting, multiply the numerator of the 1st fraction with the numerator of the 2nd fraction. 

Then, Multiply the denominator of the 1st fraction by the denominator of the 2nd fraction.

Example:

Divide 2 6/7 by 4 1/7

Solution:

Step 1: First make the fraction improper

= (20/7) / (29/7)

Step 2: Invert the second fraction.

= (20/7) / (7/29)

Step 3: Multiply the numerators.

= 20 x 7
= 140

Step 4: Multiply the denominators.

= 7 x 29
= 203

Step 5: Put back as a fraction and solve.

= 140 /203
= 0.689