Solve Mixed Number Addition: 6⅔ + 1⅔

Mixed Number Addition with Same Denominators

626+126= 6\frac{2}{6}+1\frac{2}{6}=

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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
00:14 We'll use the commutative property and arrange the exercise in a convenient way to solve
00:18 Let's calculate the sum of the whole numbers
00:29 Let's add using the common denominator
00:37 This is the sum of the fractions, now let's add it to the sum of the numbers
00:41 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

626+126= 6\frac{2}{6}+1\frac{2}{6}=

2

Step-by-step solution

To solve this problem, we will add the mixed numbers 626 6\frac{2}{6} and 126 1\frac{2}{6} by following these steps:

  • Step 1: Add the integer parts: 6+1=7 6 + 1 = 7 .
  • Step 2: Add the fractional parts: 26+26=46\frac{2}{6} + \frac{2}{6} = \frac{4}{6}.
  • Step 3: Combine the results to express the sum: 7+46 7 + \frac{4}{6} .

Now, let's work through each step:
Step 1: Adding the whole numbers, we get 7 7 .
Step 2: Since both fractions have a common denominator of 6, we add the numerators: 2+2=4 2 + 2 = 4 , thus giving us the fraction 46\frac{4}{6}.
Step 3: The combined sum of the whole number and the fraction is 746 7\frac{4}{6} .

Hence, the solution to the problem is 746 7\frac{4}{6} .

3

Final Answer

746 7\frac{4}{6}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add whole numbers and fractions separately when denominators match
  • Technique: Add numerators: 26+26=46 \frac{2}{6} + \frac{2}{6} = \frac{4}{6}
  • Check: Verify by converting to improper fractions: 406+86=486 \frac{40}{6} + \frac{8}{6} = \frac{48}{6}

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of keeping them the same
    Don't add 6 + 6 = 12 to get 412 \frac{4}{12} ! This creates a completely different fraction value and gives wrong answers. Always keep the denominator unchanged when adding fractions with the same denominator.

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

Why don't I add the denominators together?

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The denominator tells us the size of the pieces. When adding 26+26 \frac{2}{6} + \frac{2}{6} , you're adding 2 sixths plus 2 sixths = 4 sixths, not changing the piece size!

Should I simplify the fraction 46 \frac{4}{6} ?

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You can simplify 46 \frac{4}{6} to 23 \frac{2}{3} , but since the problem gives fractions in sixths, the answer 746 7\frac{4}{6} is perfectly correct as written.

What if the fractional parts add up to more than 1?

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If your fraction sum is improper (numerator ≥ denominator), convert the extra whole number and add it to your whole number sum. For example: 556+246=796=836 5\frac{5}{6} + 2\frac{4}{6} = 7\frac{9}{6} = 8\frac{3}{6}

Can I add mixed numbers a different way?

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Yes! You can convert both to improper fractions first: 626=386 6\frac{2}{6} = \frac{38}{6} and 126=86 1\frac{2}{6} = \frac{8}{6} , then add to get 466=746 \frac{46}{6} = 7\frac{4}{6} .

How do I check if my answer is right?

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Convert your answer to decimal form and check: 746=7.67 7\frac{4}{6} = 7.67 . Also check that 626+126=6.33+1.33=7.67 6\frac{2}{6} + 1\frac{2}{6} = 6.33 + 1.33 = 7.67

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