Solve Vertical Addition: 175 + 5 Step-by-Step

Q: Why do I need to line up the numbers vertically?

Vertical alignment ensures you're adding like place values together - ones with ones, tens with tens, etc. This prevents mixing up different place values and getting wrong answers.

Q: What does carrying mean in addition?

When a column adds up to 10 or more, you write the ones digit and carry the tens digit to the next column. For example, 5 + 5 = 10, so write 0 and carry 1.

Q: Do I always start adding from the right?

Yes! Always start from the ones place (rightmost column) and work left. This way, any carrying flows naturally to the next higher place value.

Q: What if one number has fewer digits?

Just imagine invisible zeros in the empty spots! In this problem, 5 is really 005, so you're adding 175 + 005 = 180.

Q: How can I check my vertical addition answer?

Try these methods: Add the numbers in reverse order (5 + 175)Use counting up: start at 175 and count 5 moreEstimate: 175 + 5 should be close to 180

Vertical Addition with Place Value Alignment

$\begin{aligned} &175 \\ +& \\ &~~~~5 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:07 We'll calculate the sum of two digits each time.

00:11 First, add the ones digits together.

00:16 Put the ones digit in the ones place, carry over to the tens.

00:22 Any missing digits should be zero.

00:25 Now, let's add the tens digits, don't forget to add one.

00:31 Again, zeros for any missing digits.

00:35 Finally, add the hundreds digits.

00:39 And that's how we find the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &175 \\ +& \\ &~~~~5 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll go through the following steps:

Step 1: Arrange the numbers vertically with digits aligned by place value.
Step 2: Start adding from the rightmost column (ones place).
Step 3: Move to the next column to the left if necessary.
Step 4: Record the result above the underscore line.

Now, let's add the numbers:

$\begin{aligned} & 175 \\ + &~~~5 \\ \underline{\phantom{180}} \\ \end{aligned}$

Step 1: Add the ones place digits: $5 + 5 = 10$

Write 0 in the ones place and carry over 1 to the tens place.

Step 2: Add the tens place digits, including the carry: $7 + 0 + 1 = 8$

Write 8 in the tens place. There's no carryover to the hundreds place in this case.

Step 3: Add the hundreds place digits: $1 + 0 = 1$

Write 1 in the hundreds place.

Thus, the sum of 175 and 5 is 180.

Therefore, the solution to the problem is $180$ .

Final Answer

180

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers with ones, tens, hundreds columns properly lined up
Technique: Add column by column from right to left: 5 + 5 = 10
Check: Count up from 175: 176, 177, 178, 179, 180 ✓

Common Mistakes

Avoid these frequent errors

Not aligning digits by place value
Don't just stack numbers randomly without considering place value = wrong columns added together! This mixes ones with tens or hundreds, giving completely wrong answers. Always align digits vertically by their place value positions.

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

Why do I need to line up the numbers vertically?

Vertical alignment ensures you're adding like place values together - ones with ones, tens with tens, etc. This prevents mixing up different place values and getting wrong answers.

What does carrying mean in addition?

When a column adds up to 10 or more, you write the ones digit and carry the tens digit to the next column. For example, 5 + 5 = 10, so write 0 and carry 1.

Do I always start adding from the right?

Yes! Always start from the ones place (rightmost column) and work left. This way, any carrying flows naturally to the next higher place value.

What if one number has fewer digits?

Just imagine invisible zeros in the empty spots! In this problem, 5 is really 005, so you're adding 175 + 005 = 180.

How can I check my vertical addition answer?

Try these methods:

Add the numbers in reverse order (5 + 175)
Use counting up: start at 175 and count 5 more
Estimate: 175 + 5 should be close to 180

What if I forget to carry a number?

You'll get the wrong answer! Always double-check each column. If any column sum is 10 or greater, you must carry the extra digit to the next column.

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