Solve: Adding Mixed Numbers 13 3/10 + 2 1/2

Mixed Number Addition with Different Denominators

13310+212= 13\frac{3}{10}+2\frac{1}{2}=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:04 First, convert mixed fractions to fractions
00:50 Multiply to find the common denominator
01:10 Add using the common denominator
01:20 Now convert to a mixed fraction
01:26 Break down 158 into 150 plus 8
01:33 Break down the fraction into whole number and remainder
01:40 Break down the fraction into whole number and remainder
01:46 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

13310+212= 13\frac{3}{10}+2\frac{1}{2}=

2

Step-by-step solution

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

  • Step 1: Identify the integer and fractional parts of each mixed number.
  • Step 2: Find a common denominator for the fractional parts.
  • Step 3: Add the fractional parts.
  • Step 4: Add the integer parts.
  • Step 5: Combine the results from Steps 3 and 4.

Now, let's work through each step:

Step 1: Identify the integer and fractional parts:
1331013\frac{3}{10} has an integer part of 13 and a fractional part of 310\frac{3}{10}.
2122\frac{1}{2} has an integer part of 2 and a fractional part of 12\frac{1}{2}.

Step 2: Find a common denominator for 310\frac{3}{10} and 12\frac{1}{2}.
The denominators are 10 and 2, with the common denominator being 10. Convert 12\frac{1}{2} to an equivalent fraction with this common denominator: 12=510\frac{1}{2} = \frac{5}{10}.

Step 3: Add the fractional parts:
310+510=810\frac{3}{10} + \frac{5}{10} = \frac{8}{10}.

Step 4: Add the integer parts:
13+2=1513 + 2 = 15.

Step 5: Combine the integer sum and fractional sum:
The result is 1581015\frac{8}{10}.

Therefore, the solution to the problem is 1581015\frac{8}{10}.

3

Final Answer

15810 15\frac{8}{10}

Key Points to Remember

Essential concepts to master this topic
  • Rule: Convert fractions to common denominators before adding
  • Technique: Change 12 \frac{1}{2} to 510 \frac{5}{10} when adding to tenths
  • Check: Verify: 13 + 2 = 15 and 310+510=810 \frac{3}{10} + \frac{5}{10} = \frac{8}{10}

Common Mistakes

Avoid these frequent errors
  • Adding denominators instead of finding common denominators
    Don't add 310+12 \frac{3}{10} + \frac{1}{2} as 412 \frac{4}{12} by adding 3+1 and 10+2! This creates a meaningless fraction. Always convert to the same denominator first, then add only the numerators.

Practice Quiz

Test your knowledge with interactive questions

\( 1:\frac{3}{4}= \)

FAQ

Everything you need to know about this question

How do I know which denominator to use as the common denominator?

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Use the Least Common Multiple (LCM) of the denominators. For 10 and 2, since 10 is already divisible by 2, the LCM is 10. This makes converting easier!

Do I need to simplify 15810 15\frac{8}{10} ?

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You can simplify 810 \frac{8}{10} to 45 \frac{4}{5} , but the answer is correct either way. Check if your teacher prefers simplified fractions or if the answer choices give you a hint!

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

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That's called an improper fraction! Convert it to a mixed number and add the whole number part to your integer sum. For example, if fractions add to 1310 \frac{13}{10} , that's 1310 1\frac{3}{10} .

Can I convert everything to improper fractions instead?

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Yes! Convert both mixed numbers to improper fractions: 13310+52 \frac{133}{10} + \frac{5}{2} . Find common denominators and add. Some students find this method easier than separating whole and fractional parts.

Why can't I just add the whole numbers and fractions separately?

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You can add them separately - that's exactly what we did! Add integers: 13 + 2 = 15. Add fractions: 310+12=810 \frac{3}{10} + \frac{1}{2} = \frac{8}{10} . Then combine for the final answer.

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