Solve: 1/3 + 2/3 + 2¾ Mixed Number and Fraction Addition

Mixed Number Addition with Like Fractions

13+23+234= \frac{1}{3}+\frac{2}{3}+2\frac{3}{4}=

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Step-by-step video solution

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00:05 Let's solve this problem together.
00:08 First, we gather all the factors. This is an important step!
00:13 And that, is how we find the solution to the question.

Step-by-step written solution

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1

Understand the problem

13+23+234= \frac{1}{3}+\frac{2}{3}+2\frac{3}{4}=

2

Step-by-step solution

According to the rules of the order of operations in arithmetic, we solve the exercise from left to right.

Let's note that:

13+23=33=1 \frac{1}{3}+\frac{2}{3}=\frac{3}{3}=1

We should obtain the following exercise:

1+234=334 1+2\frac{3}{4}=3\frac{3}{4}

3

Final Answer

334 3\frac{3}{4}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add fractions with same denominators by adding numerators
  • Technique: Combine 13+23=33=1 \frac{1}{3}+\frac{2}{3}=\frac{3}{3}=1 first
  • Check: Final result 334 3\frac{3}{4} equals whole number plus proper fraction ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators along with numerators
    Don't add 13+23=36 \frac{1}{3}+\frac{2}{3}=\frac{3}{6} by adding both top and bottom = wrong fraction! This creates an incorrect denominator. Always keep the same denominator when adding like fractions.

Practice Quiz

Test your knowledge with interactive questions

\( 1:\frac{3}{4}= \)

FAQ

Everything you need to know about this question

Why don't I need a common denominator for all three terms?

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Great observation! You only need common denominators when adding fractions. Since 234 2\frac{3}{4} is a mixed number, you can add it to whole numbers directly after combining the like fractions first.

Should I convert the mixed number to an improper fraction?

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Not necessary here! It's actually easier to work with mixed numbers in this problem. First add the like fractions to get 1, then add 1+234=334 1 + 2\frac{3}{4} = 3\frac{3}{4} .

What if I get confused about the order of operations?

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Remember: addition has the same priority level, so you work from left to right. Group the like fractions first: (13+23)+234 (\frac{1}{3}+\frac{2}{3}) + 2\frac{3}{4} .

How do I add a whole number to a mixed number?

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Simply add the whole number parts together! 1+234 1 + 2\frac{3}{4} means (1+2)+34=334 (1 + 2) + \frac{3}{4} = 3\frac{3}{4} . The fraction part stays the same.

What if my fraction part becomes improper after adding?

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If your fraction becomes improper (like 54 \frac{5}{4} ), convert it! 54=114 \frac{5}{4} = 1\frac{1}{4} , then add that 1 to your whole number part.

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