Adding and subtracting mixed numbers
Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
What a learner can do afterwards
- Calculate 2 3/5 + 1 4/5 and express as a mixed number
- Subtract 3 1/4 from 5 3/4
- Solve 4 2/6 − 1 5/6 by regrouping the whole number
The lesson
You already know what mixed numbers are and how to add simple fractions. Adding and subtracting mixed numbers works the same way, but now there is one more step. Add or subtract the whole numbers first. Then add or subtract the fraction parts.
Try 2 and 3/5 + 1 and 4/5. Add the whole numbers: 2 + 1 = 3. Add the fraction parts: 3/5 + 4/5 = 7/5. Since 7/5 is more than one whole, turn it into 1 whole and 2/5. Add that whole to 3, and the answer is 4 and 2/5.
Now try 5 and 3/4 − 3 and 1/4. Subtract the whole numbers: 5 − 3 = 2. Subtract the fraction parts: 3/4 − 1/4 = 2/4. The answer is 2 and 2/4.
When the fraction part you are subtracting is bigger, borrow one whole first. In 4 and 2/6 − 1 and 5/6, borrow a whole from the 4 and change it into 6/6. Now you have 3 and 8/6. Subtract: 3 − 1 = 2, and 8/6 − 5/6 = 3/6. The answer is 2 and 3/6.
Add or subtract the whole numbers and the fraction parts, and regroup or borrow a whole when the fractions don't fit.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.