Solve Mixed Number Addition: 2 + 3/7 + 4/7

Fraction Addition with Whole Numbers

2+37+47= 2+\frac{3}{7}+\frac{4}{7}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 We will use the commutative law and solve this operation first
00:09 We will add fractions with the same denominator by adding numerators
00:13 We will convert from fraction to whole number
00:16 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

2+37+47= 2+\frac{3}{7}+\frac{4}{7}=

2

Step-by-step solution

First, we will find the sum of the fractions:

37+47=3+47=77=1 \frac{3}{7}+\frac{4}{7}=\frac{3+4}{7}=\frac{7}{7}=1

Now we get the exercise:

2+1=3 2+1=3

3

Final Answer

3 3

Key Points to Remember

Essential concepts to master this topic
  • Same Denominators: Add numerators directly when denominators match perfectly
  • Technique: Convert improper fractions like 77 \frac{7}{7} to whole numbers (1)
  • Check: Verify 37+47=1 \frac{3}{7} + \frac{4}{7} = 1 then add whole number ✓

Common Mistakes

Avoid these frequent errors
  • Adding denominators along with numerators
    Don't add 3/7 + 4/7 = 7/14! This creates a wrong fraction that doesn't equal the parts you're combining. Always keep the same denominator and only add the numerators: 3/7 + 4/7 = (3+4)/7 = 7/7.

Practice Quiz

Test your knowledge with interactive questions

\( 13+5+5= \) ?

FAQ

Everything you need to know about this question

Why don't I add the denominators together?

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The denominator tells you what size pieces you're working with. Since both fractions use sevenths, you're adding pieces of the same size. Adding denominators would change the piece size, which doesn't make sense!

How do I know when 7/7 equals 1?

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When the numerator and denominator are equal, the fraction equals 1 whole unit. Think of it as 7 pieces out of 7 total pieces - that's the complete whole!

Can I add the whole number first instead?

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You can, but it's usually easier to add the fractions first. This way you can see if they make a whole number, then combine everything at the end.

What if my fraction parts don't make a whole number?

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No problem! Just add the whole number to whatever fraction you get. For example: 2+57=257 2 + \frac{5}{7} = 2\frac{5}{7} (a mixed number).

Do I need to find a common denominator here?

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Not in this problem! Both fractions already have the same denominator (7). You only need to find a common denominator when the denominators are different.

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