Solve Vertical Addition: 77 + 8 Step by Step

Vertical Addition with Carrying

77+  8776 \begin{aligned} &77 \\ +& \\ &~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Each time consider combining 2 digits, and then place
00:06 Let's start by combining ones with ones
00:09 Place the ones, add the tens to the tens column
00:12 Remember to carry 1 up
00:15 Place 0 where there is no digit
00:18 Add tens with tens, remember to add 1
00:21 Place the solution in the tens
00:24 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

77+  8776 \begin{aligned} &77 \\ +& \\ &~~8 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Add the ones digits: 7+87 + 8.
  • Step 2: Determine any carry-over from the addition.
  • Step 3: Add the tens digits, incorporating any carry-over.

Now, let's work through each step:

Step 1: Add the ones digits:
7+8=15 7 + 8 = 15
Since the sum (15) is greater than 9, we write down the 5 in the ones place and carry over the 1 to the tens place.

Step 2: Add the tens digits with the carried-over 1:
1 (carry)+7=8 1 \text{ (carry)} + 7 = 8

Therefore, the result of adding 77 and 8 is:
85 \boxed{85}

The correct choice from the given options is 85.

3

Final Answer

85

Key Points to Remember

Essential concepts to master this topic
  • Rule: Add column by column, starting from the ones place
  • Technique: When sum exceeds 9, write ones digit and carry tens digit left: 7+8=15 7 + 8 = 15 , write 5 carry 1
  • Check: Verify by adding horizontally: 77+8=85 77 + 8 = 85 matches vertical result ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't write down the full sum like 15 in the ones place = impossible single digit! This creates numbers that don't exist. Always write the ones digit (5) and carry the tens digit (1) to the next column.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &90 \\ +& \\ &~~9\\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

What does it mean to 'carry over' in addition?

+

When adding digits gives a sum greater than 9, you write the ones digit in that column and carry the tens digit to the next column left. For example, 7+8=15 7 + 8 = 15 means write 5 and carry 1.

Why can't I just write 15 in the ones place?

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Each column can only hold one digit! Writing 15 would mean putting two digits in one place, which breaks our number system. That's why we separate it: 5 stays, 1 moves left.

Do I always start adding from the right?

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Yes! Always start from the ones place (rightmost column) and work left. This ensures you handle any carrying correctly as you move through each column.

What if there's no tens digit to add the carry to?

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If you're carrying to an empty column (like carrying to hundreds place when adding two 2-digit numbers), just write the carry digit in that new column. It becomes part of your final answer!

How can I check if my vertical addition is correct?

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Try adding the numbers horizontally instead: 77+8=85 77 + 8 = 85 . If you get the same answer both ways, you did it right!

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