Worked example 1
Add 2 1/3 + 1 1/2.
First convert to improper fractions so the mixed numbers are easier to combine: 2 1/3 = 7/3 and 1 1/2 = 3/2. LCD =6. 7/3 = 14/6 and 3/2 = 9/6. Sum = 23/6 = 3 5/6.
Answer: 3 5/6
Grade 6 Math · Topic 12
Adding and Subtracting Mixed Numbers
A mixed number like 2 1/3 is a whole number plus a fraction. To add or subtract, you can either (a) keep the whole and fraction parts separate, or (b) convert to improper fractions first. Either way works — pick the cleaner path.
Lesson alignment: Prerequisite review · 5.NF.A.1–2 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Add and subtract mixed numbers
The strips show whole units and equal-sized fractional parts. Regroup one whole when needed.
Think first: Will you need to regroup a whole before combining or subtracting the fractional parts?
Ready? Reveal the model and try your prediction
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Follow the worked examples
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 2
Subtract 5 1/4 - 2 2/3.
First convert to a form that is easier to calculate: 21/4 - 8/3. LCD = 12: 63/12 - 32/12 = 31/12 = 2 7/12.
Answer: 2 7/12
Try a few on your own
Work these on paper first. Open “Check” when you are ready to compare your answer.
- 1 1/2 + 2 1/3 =
Check
3 5/6
- 3 1/4 + 1 1/2 =
Check
4 3/4
- 4 2/3 + 1 1/6 =
Check
5 5/6
- 2 3/4 + 3 1/8 =
Check
5 7/8
- 5 1/2 - 2 1/4 =
Check
3 1/4
- 6 1/3 - 1 1/2 =
Check
4 5/6
- 4 5/6 - 2 1/3 =
Check
2 1/2
- 7 1/4 - 3 2/3 =
Check
3 7/12
Try this situation 1
A board is 5 3/4 feet long. Another board is 3 1/2 feet long. What is their combined length?
Show a worked solution
Answer: 9 1/4 feet.
Start by writing the calculation clearly: 5 3/4 + 3 1/2. LCD =4: 5 3/4 + 3 2/4 = 8 5/4 = 9 1/4.
Try this situation 2
A pitcher holds 4 1/2 liters of juice. After serving, 1 3/4 liters are left. How much was served?
Show a worked solution
Answer: 2 3/4 liters.
Start by writing the calculation clearly: 4 1/2 - 1 3/4. Convert: 9/2 - 7/4 = 18/4 - 7/4 = 11/4 = 2 3/4.
Fresh questions · saved on this device
Practice this skill
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Question 1 of 50 correct so far
Session complete
Check what you learned
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Practice and finish
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
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More Grade 6 resources
Use these free materials if you want another explanation, extra paper practice, or a broader review.