Solve for the Missing Addend: 3⅔ + ? = 6

Missing Addend Problems with Mixed Numbers

323+?=6 3\frac{2}{3}+?=6

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the unknown
00:03 Arrange the equation so the unknown is on one side
00:22 Convert mixed fraction to fraction
00:50 Convert whole number to proper fraction
01:04 Subtract with common denominator
01:15 Now convert to mixed fraction
01:21 Break down 7 into 6 plus 1
01:24 Break down into proper fraction and remainder
01:32 Convert proper fraction to whole number and add to mixed fraction
01:40 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

323+?=6 3\frac{2}{3}+?=6

2

Step-by-step solution

To solve 323+?=63\frac{2}{3} + ? = 6, we need to determine what number, when added to the mixed fraction 3233\frac{2}{3}, results in 6.

Follow these steps:

  • Convert the mixed number to an improper fraction:
    323=3+23=3×3+23=9+23=1133\frac{2}{3} = 3 + \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}.
  • Determine the number needed to reach 6:
    We rewrite the equation as 61136 - \frac{11}{3}.
  • Convert 6 to a fraction with a denominator of 3:
    6=6×33=1836 = \frac{6 \times 3}{3} = \frac{18}{3}.
  • Subtract the improper fraction from 6:
    183113=18113=73\frac{18}{3} - \frac{11}{3} = \frac{18 - 11}{3} = \frac{7}{3}.
  • Convert the result back to a mixed number:
    73=213\frac{7}{3} = 2 \frac{1}{3} since 7÷3=27 \div 3 = 2 remainder 11.

Therefore, the missing number is 2132\frac{1}{3}.

The correct answer from the given choices is Option 3: 2132\frac{1}{3}.

3

Final Answer

213 2\frac{1}{3}

Key Points to Remember

Essential concepts to master this topic
  • Subtraction Method: Solve ? by calculating 6 - 3⅔
  • Technique: Convert to improper fractions: 183113=73 \frac{18}{3} - \frac{11}{3} = \frac{7}{3}
  • Check: Verify that 323+213=6 3\frac{2}{3} + 2\frac{1}{3} = 6

Common Mistakes

Avoid these frequent errors
  • Adding instead of subtracting to find the missing addend
    Don't add 3⅔ + 6 = 9⅔! This gives you a completely wrong number that's bigger than the target. Always subtract the known addend from the total: 6 - 3⅔.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why do I subtract 3⅔ from 6 instead of adding?

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Think of it like this: What + 3⅔ = 6? To find the missing piece, you take the whole (6) and remove the part you already have (3⅔). This is why we calculate 6 - 3⅔.

Do I have to convert mixed numbers to improper fractions?

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It's the most reliable method! While you could work with mixed numbers directly, converting to improper fractions like 113 \frac{11}{3} makes the subtraction cleaner and reduces errors.

How do I subtract when the fractions have the same denominator?

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When denominators match, just subtract the numerators: 183113=18113=73 \frac{18}{3} - \frac{11}{3} = \frac{18-11}{3} = \frac{7}{3} . Keep the denominator the same!

What if I get confused converting back to a mixed number?

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Divide the numerator by the denominator: 73 \frac{7}{3} means 7 ÷ 3 = 2 remainder 1, so the answer is 213 2\frac{1}{3} .

How can I check if my answer is correct?

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Add your answer to the known addend: 213+323 2\frac{1}{3} + 3\frac{2}{3} . The whole numbers add to 5, and 13+23=1 \frac{1}{3} + \frac{2}{3} = 1 , giving you 6. Perfect!

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