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.
| 2 | 1 | = | 3 x 2 + 1 | = | 7 | ||
| 3 | 3 | 3 |
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
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.
| 2 | 2 | = | 3 x 2 + 2 | = | 8 | ||
| 3 | 3 | 3 |
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.
| 3 | 1 | = | 2 x 3 + 1 | = | 7 | ||
| 2 | 2 | 2 |
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 2 | 2x 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 |
| 6 | 6 | 6 |
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.
| = | 6 | 1 |
| 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!