Two Techniques for Adding Mixed Fractions
A mixed fraction (or mixed number) is made up of both a whole number and a fraction. For example, 1 2/3 is a mixed fraction in which 1 is the whole number and 2/3 is the fraction. Adding mixed fractions can be done in two ways. The first technique requires you to convert the mixed fractions into improper fractions, or fractions in which the top number is larger than the bottom number, add the two improper fractions together, and then convert the result back into a mixed fraction. The second technique requires you to add together first the whole numbers, then the fractions, and then simplify the resulting mixed fraction.
The First Technique - Adding Improper Fractions
The first technique involves five steps:
- Convert the two mixed fractions into improper fractions. For example, in the problem “2 1/2 + 1 3/4,” you would convert 2 1/2 to 5/2 and 1 3/4 to 7/4. The problem would now read 5/2 + 7/4.
- Find the LCD (lowest common denominator) of the two improper fractions. In this case, it would be 4.
- Convert the two fractions so that they each have the LCD as the denominator. This would leave us with 10/4 + 7/4.
- Add the two fractions together. In our example, 10/4 + 7/4 = 17/4
- Convert the resulting fraction into a mixed fraction: 17/4 = 4 1/4
The Second Technique - Adding Parts
The second technique involves five steps as well. In this case, you would add the fraction parts and the whole number parts separately. The trick here is to remember to carry over from the fraction part to the whole number part, as needed.
- Find the LCD of the two mixed fractions. Using the same example as above, the LCD would be 4.
- Convert the two fraction parts of the mixed fractions so that they each have the LCD as the denominator. This would leave us with 2 2/4 + 1 3/4.
- Add the two fraction parts together: 2/4 + 3/4 = 5/4.
- If the resulting fraction is improper, carry over to the whole number part of the equation. In this case, 5/4 = 1 1/4, so the equation would now read 2 + 1 + 1 (carried over) + 1/4. (If the resulting fraction is not improper, skip this step.)
- Add the whole numbers, plus any carried over whole numbers. This would leave us with 4 1/4.
Note that both of the techniques for adding mixed fractions got the same answer. Either of these techniques will work, but you may find it easier at the beginning to use the first technique. Once you become more comfortable with mixed fractions, you may find it easier to use the second technique.
You can find practice sheets on adding mixed numbers at each of the following links:
Math Is Fun. “Adding and Subtracting Mixed Fractions.” https://www.mathsisfun.com/numbers/fractions-mixed-addition.html
Math.com. “Adding and Subtracting Mixed Numbers.” https://www.math.com/school/subject1/lessons/S1U4L6GL.html#sm4
This post is part of the series: Math Study Guides
Confused in math class? These math study guides span various topics, from square roots to improper fractions.