Solve Mixed Number Addition: 2⅖ + 2⅖

Mixed Number Addition with Same Denominators

225+225= 2\frac{2}{5}+2\frac{2}{5}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Break down mixed numbers into whole numbers and remainders
00:19 Arrange the exercise in a convenient way to solve
00:25 Sum up the whole numbers
00:32 Add with common denominator
00:40 Convert to mixed fraction
00:43 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

225+225= 2\frac{2}{5}+2\frac{2}{5}=

2

Step-by-step solution

To solve the problem 225+225 2\frac{2}{5} + 2\frac{2}{5} , follow these steps:

  • Step 1: Add the whole numbers together. We have 2+2=42 + 2 = 4.
  • Step 2: Add the fractional parts together. Since both fractions have the same denominator, simply add the numerators: 25+25=45\frac{2}{5} + \frac{2}{5} = \frac{4}{5}.
  • Step 3: Combine the results from Step 1 and Step 2. The sum of the whole numbers and fraction parts is 4+45=4454 + \frac{4}{5} = 4\frac{4}{5}.

Thus, the sum of 225 2\frac{2}{5} and 225 2\frac{2}{5} is 445\mathbf{4\frac{4}{5}}.

The answer corresponds to choice 4.

3

Final Answer

445 4\frac{4}{5}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add whole numbers separately, then add fractional parts separately
  • Technique: For 25+25 \frac{2}{5} + \frac{2}{5} , add numerators: 2 + 2 = 4
  • Check: Verify 445 4\frac{4}{5} by converting: 245+245=485=445 \frac{24}{5} + \frac{24}{5} = \frac{48}{5} = 4\frac{4}{5}

Common Mistakes

Avoid these frequent errors
  • Adding whole numbers and fractions incorrectly
    Don't add 2 + 2 + 2 + 5 + 2 + 5 = 18! This treats each part as separate numbers instead of mixed numbers. Always keep whole numbers and fractions separate: add 2 + 2 = 4 for wholes, then 25+25=45 \frac{2}{5} + \frac{2}{5} = \frac{4}{5} for 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

Why don't I need to find a common denominator?

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Great observation! Since both fractions already have the same denominator (5), you can add the numerators directly: 2 + 2 = 4. You only need to find common denominators when fractions have different denominators.

Should I convert to improper fractions first?

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You can, but it's not necessary! Adding mixed numbers directly is often faster and easier. However, converting 225=125 2\frac{2}{5} = \frac{12}{5} then adding 125+125=245=445 \frac{12}{5} + \frac{12}{5} = \frac{24}{5} = 4\frac{4}{5} works too.

What if my fraction part needs to be simplified?

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Always check if your final fraction can be reduced to lowest terms! In this problem, 45 \frac{4}{5} is already simplified since 4 and 5 share no common factors except 1.

How do I know if I need to carry over from the fraction?

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If your fraction part equals or exceeds 1 whole (like 65 \frac{6}{5} ), convert it! 65=115 \frac{6}{5} = 1\frac{1}{5} , so add that 1 to your whole number part. In this problem, 45 \frac{4}{5} is less than 1, so no carrying needed.

Can I use a different method to solve this?

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Absolutely! You could convert both to decimals: 2.4+2.4=4.8=445 2.4 + 2.4 = 4.8 = 4\frac{4}{5} . Or use improper fractions: 125+125=245 \frac{12}{5} + \frac{12}{5} = \frac{24}{5} . Choose the method that feels most comfortable!

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