Adding Subtracting Mixed Numbers Calculator That Shows Its Work

Add/Subtract Mixed Numbers Calculator Sign

This calculator will add one mixed number to another, or subtract one mixed number from another -- regardless if the two mixed numbers have the same or different denominators -- and give the resulting fraction in simplest form.

Plus, unlike some other online mixed number calculators, this calculator will show its work and give a detailed step-by-step explanation as to how it arrived at the result.

Also, be sure to check out my other online math calculators for help with fractions and mixed numbers:


Read more ...

Also on this page:

Add/Subtract Mixed Numbers Calculator

Add and subtract mixed numbers and simplify the result.

Learn More

Selected Data Record:

A Data Record is a set of calculator entries that are stored in your web browser's Local Storage. If a Data Record is currently selected in the "Data" tab, this line will list the name you gave to that data record. If no data record is selected, or you have no entries stored for this calculator, the line will display "None".

DataData recordData recordSelected data record: None
Augend/Minuend

Augend/Minuend:

If the augend (addition) or minuend (subtraction) is a whole number only, leave the numerator and denominator blank. If the augend/minuend is a mixed number, enter a positive integer for the whole number, the numerator, and denominator. If the augend/minuend is a fraction only, leave the whole number field blank.

#
#
Addend/Subtrahend

Addend/Subtrahend:

If the addend (addition) or subtrahend (subtraction) is a whole number only, leave the numerator and denominator blank. If the addend/subtrahend is a mixed number, enter a positive integer for the whole number, the numerator, and denominator. If the addend/subtrahend is a fraction only, leave the whole number field blank.

#
#
Result:Result:Sum or difference:Sum or difference:

Result:

This is the result of adding or subtracting the mixed numbers. After performing the selected operation, the adding and subtracting mixed numbers calculator will show its work and give a detailed explanation of each step it took to arrive at this result.

All Step Explanations

If you would like to save the current entries to the secure online database, tap or click on the Data tab, select "New Data Record", give the data record a name, then tap or click the Save button. To save changes to previously saved entries, simply tap the Save button. Please select and "Clear" any data records you no longer need.

Related Calculators

algebra calculator

Help and Tools

Learn

How to add and subtract mixed numbers.

The only difference between adding or subtracting mixed numbers and adding or subtraction fractions, is that before you begin to add or subtract you must first convert the mixed numbers to improper fractions.

How to convert Mixed Numbers Into Fractions

To convert a mixed number to an improper fraction, you first multiply the denominator of the fractional portion by the whole number and then add that product to the numerator. That result then becomes the numerator (top) of the improper fraction, while the denominator (bottom) remains unchanged.

Converting a Mixed Number to an Improper Fraction

 21=3 x 2 + 1=7 
333

Once you have converted the mixed numbers to improper fractions, you simply add or subtract the fractions as usual.

Tutorial: How to Add Mixed Numbers

Step #1:

Convert the mixed number in the augend (2 2/3) into a fraction. To convert the mixed number, multiply the denominator (3) by the whole number (2) and then add the numerator (2). This gives you a top number of 8 (3 × 2 + 2) while the bottom number (3) stays the same.

 22=3 x 2 + 2=8 
333

Step #2:

Convert the mixed number in the addend (3 1/2) into a fraction. To convert the mixed number, multiply the denominator (2) by the whole number (3) and then add the numerator (1). This gives you a top number of 7 (2 × 3 + 1) while the bottom number (2) stays the same.

 31=2 x 3 + 1=7 
222

Step #3:

Since 8/3 and 7/2 have different denominators, you need to find the Least Common Multiple (LCM) of the denominators and then multiply the top and bottom of each fraction by the number of times the denominator goes into the LCM.

According to my calculations, the LCM of the two denominators is 6. Therefore, since 3 goes into 6 a total of 2 times, you would multiply the top and bottom of the first fraction by 2. And since 2 goes into 6 a total of 3 times, you would multiply the top and bottom of the second fraction by 3.

=8x 2+7x 3
3x 22x 3

Step #4:

Now that the denominators are the same, you simply add the numerators (16 + 21) while keeping the denominator (6) the same -- giving you a result of 37/6.

=16+21=37
666

Step #5:

Since 37 and 6 have no common factors, the result cannot be reduced.

=37
6

Step #6:

Since the numerator is greater than the denominator, the fraction 37/6 is an improper fraction. To convert the improper fraction to a mixed number, you divide the numerator (37) by the denominator (6). Since 6 goes into 37 a total of 6 times, with a remainder of 1, the mixed number would be 6 1/6.

=61
6

To subtract one mixed number from the other, you repeat all of the same steps above, but instead of adding the numerators (top) in Step #4 you subtract the second numerator from the first while still keeping the denominators (bottom) the same.

Happy adding and subtracting!

Adjust Calculator Width:

Move the slider to left and right to adjust the calculator width. Note that the Help and Tools panel will be hidden when the calculator is too wide to fit both on the screen. Moving the slider to the left will bring the instructions and tools panel back into view.

Also note that some calculators will reformat to accommodate the screen size as you make the calculator wider or narrower. If the calculator is narrow, columns of entry rows will be converted to a vertical entry form, whereas a wider calculator will display columns of entry rows, and the entry fields will be smaller in size ... since they will not need to be "thumb friendly".

Show/Hide Popup Keypads:

Select Show or Hide to show or hide the popup keypad icons located next to numeric entry fields. These are generally only needed for mobile devices that don't have decimal points in their numeric keypads. So if you are on a desktop, you may find the calculator to be more user-friendly and less cluttered without them.

Stick/Unstick Tools:

Select Stick or Unstick to stick or unstick the help and tools panel. Selecting "Stick" will keep the panel in view while scrolling the calculator vertically. If you find that annoying, select "Unstick" to keep the panel in a stationary position.

If the tools panel becomes "Unstuck" on its own, try clicking "Unstick" and then "Stick" to re-stick the panel.