Solve Decimal Addition: 12.75 + 3.35 Step-by-Step

Decimal Addition with Carrying Operations

12.75+3.35= 12.75+3.35=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's solve this math problem together.
00:08 We'll use vertical addition to find the answer. Ready?
00:13 Make sure to line up the decimal points neatly, okay?
00:19 Fill in any missing digits with a zero.
00:24 Start by adding the smallest digits first. Easy!
00:31 Add and place the number. Remember to carry over one.
00:35 For this next step, don't forget to add the one you carried.
00:44 Keep calculating. Add and remember, carry one more.
00:51 Place your answer and continue adding the next digits.
00:58 Keep going. Add, place, and you're almost there!
01:10 And that's how we solve the problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

12.75+3.35= 12.75+3.35=

2

Step-by-step solution

To solve this problem, we'll add the numbers 12.75 and 3.35 by aligning them by their decimal points:

12.75+3.35 \begin{array}{c} 12.75 \\ + \underline{3.35} \\ \end{array}

Step-by-step:

  • Hundredths Place: Add 5 and 5 to get 10. Write down 0 and carry over 1 to the tenths place.
  • Tenths Place: Add 7 and 3, plus the carry-over 1, to get 11. Write down 1 and carry over 1 to the units place.
  • Units Place: Add 2 and the carry-over 1 to get 3. Write down 3.
  • Tens Place: Add 1 (from 12) with nothing to carry over to get 1. Write down 1.

The sum is 16.10\mathbf{16.10}. However, since trailing zeroes after the decimal point in a non-fractional number can be omitted without affecting its value, the final answer is given as 16.1\mathbf{16.1}.

Therefore, the solution to the problem is 16.1 16.1 .

3

Final Answer

16.1

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up decimal points vertically before adding digits
  • Technique: Add column by column: 5+5=10, write 0 carry 1
  • Check: Count decimal places: both numbers have 2, answer has 1 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't just write down 10 when adding 5+5 in hundredths place = wrong answer 15.110! This ignores place value rules and creates extra digits. Always carry the 1 to the next column and write only the units digit.

Practice Quiz

Test your knowledge with interactive questions

\( \text{0.6+0}.5= \)

+=

FAQ

Everything you need to know about this question

Why do I need to line up the decimal points?

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Lining up decimal points ensures you're adding digits in the same place value. Without alignment, you might add tenths to hundredths, which gives completely wrong results!

What does it mean to 'carry over' a number?

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When adding digits gives you 10 or more, write down the ones digit and add the tens digit to the next column. For example: 7+3+1=11, so write 1 and carry 1.

Can I drop the zero at the end of 16.10?

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Yes! Trailing zeros after the decimal point don't change the value. 16.10=16.1 16.10 = 16.1 , so both answers are mathematically equivalent.

How do I know when to stop adding zeros?

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You don't need to add zeros! Just make sure both numbers have the same number of decimal places by imagining zeros if needed: 12.75 + 3.35 (both have 2 places).

What if I forget to carry and get the wrong answer?

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Always double-check by estimating first: 12.75 + 3.35 should be close to 13 + 3 = 16. If your answer is far off, you likely missed a carry operation.

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