Solve Mixed Number Addition: 7 + 2⅓ Step-by-Step

Mixed Number Addition with Whole Numbers

7+213= 7+2\frac{1}{3}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 First, let's break down each mixed fraction into its whole number and fraction
00:12 Let's calculate the sum of the whole numbers 3
00:18 Now let's add the fraction to the sum of the numbers
00:22 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

7+213= 7+2\frac{1}{3}=

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Separate the mixed number into whole and fractional parts.
  • Step 2: Add the whole numbers separately from the fractional part.
  • Step 3: Combine the results for the final sum.

Now, let's work through each step:

Step 1: The mixed number 2132\frac{1}{3} consists of the whole number 2 and the fraction 13\frac{1}{3}.

Step 2: Add the whole numbers: 7+2=97 + 2 = 9.

Step 3: Since the fraction 13\frac{1}{3} has no other fractional parts to add, we simply keep it as is and attach it to the 9.

Therefore, the overall sum is 9139\frac{1}{3}.

After comparing our solution to the possible answer choices, the correct choice is 9139\frac{1}{3}.

3

Final Answer

913 9\frac{1}{3}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add whole numbers separately from the fractional part
  • Technique: Combine 7 + 2 = 9, then attach 13 \frac{1}{3}
  • Check: Verify 913=9+13=7+213 9\frac{1}{3} = 9 + \frac{1}{3} = 7 + 2\frac{1}{3}

Common Mistakes

Avoid these frequent errors
  • Converting everything to improper fractions unnecessarily
    Don't convert 7 to 213 \frac{21}{3} and then add 73 \frac{7}{3} = makes simple problems complicated! This creates unnecessary work and more chances for errors. Always add whole numbers first, then attach any remaining fractions.

Practice Quiz

Test your knowledge with interactive questions

\( 2\frac{2}{5}+2\frac{2}{5}= \)

FAQ

Everything you need to know about this question

Do I need to convert the whole number 7 to a fraction?

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No! When adding a whole number to a mixed number, just add the whole parts together first. Converting 7 to 213 \frac{21}{3} makes the problem harder than it needs to be.

What if the fractional part was bigger, like 2⅔?

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The same method works! Add the whole numbers: 7 + 2 = 9. Then keep the fraction: 923 9\frac{2}{3} . Only convert to improper fractions when you need to add or subtract fractional parts.

How do I know when to convert to improper fractions?

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Convert to improper fractions only when you need to add or subtract fractional parts. For example, 213+123 2\frac{1}{3} + 1\frac{2}{3} requires converting because 13+23=1 \frac{1}{3} + \frac{2}{3} = 1 .

Can I just add 7 + 2 + ⅓ in any order?

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Yes! Addition is commutative, so you can rearrange. But it's clearest to group whole numbers together: (7 + 2) + 13 \frac{1}{3} = 913 9\frac{1}{3} .

Why isn't the answer just 9?

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Because 213 2\frac{1}{3} means 2 AND 13 \frac{1}{3} more! You can't ignore the fractional part. Think of it as 2.33... + 7 = 9.33... = 913 9\frac{1}{3} .

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