Solve Vertical Addition: 75 + 10 Step by Step

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

Place value alignment is crucial! Each column represents a different place value (units, tens, hundreds). If you don't align them properly, you're adding the wrong digits together.

Q: What if one number has fewer digits than the other?

No problem! Just imagine invisible zeros in the empty spots. For example, 10 is really 10, so when you stack it under 75, the units column has 5 + 0.

Q: Do I always start adding from the right?

Yes, always! Start with the units column (rightmost), then move left to tens, hundreds, and so on. This helps you handle any carrying that might be needed.

Vertical Addition with Two-Digit Numbers

$\begin{aligned} &75 \\ +& \\ &10 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 we'll calculate the sum of 2 digits, and then we'll place

00:06 We'll start by adding ones with ones

00:09 We'll place in the correct position

00:12 We'll add tens with tens

00:15 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$\begin{aligned} &75 \\ +& \\ &10 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we'll use vertical addition. Let's follow these steps to ensure accuracy:

Step 1: Align the two numbers vertically by their place values. The given numbers are 75 and 10. Write 75 on top and 10 below it, making sure that the digits are aligned in the correct columns:

\begin{array}{c} 75 \\ +10 \\ \underline{\phantom{776}} \end{array}

Step 2: Add the digits in the units column (the rightmost column). This means adding 5 (from 75) and 0 (from 10):
$5 + 0 = 5$
Step 3: Move to the tens column (the next column on the left). Add 7 (from 75) and 1 (from 10):
$7 + 1 = 8$
Step 4: Combine the results from each column to form the sum. Since there are no carries, the direct sum of the columns is:
$\begin{array}{c} 75 \\ +10 \\ \underline{85} \end{array}$ The resulting sum is 85.

Therefore, the solution to the problem is $85$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers so place values line up correctly
Technique: Add column by column: 5 + 0 = 5, then 7 + 1 = 8
Check: Verify 75 + 10 = 85 by counting up from 75 ✓

Common Mistakes

Avoid these frequent errors

Misaligning place values when stacking numbers
Don't line up numbers by their left edges like 75 and 10 = wrong columns! This puts the 1 from 10 in the units place instead of tens place, giving 76 instead of 85. Always align numbers by their rightmost digits (units place).

Practice Quiz

Test your knowledge with interactive questions

$\begin{aligned} &83 \\ +& \\ &~~6 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

FAQ

Everything you need to know about this question

Why do I need to line up the numbers in columns?

Place value alignment is crucial! Each column represents a different place value (units, tens, hundreds). If you don't align them properly, you're adding the wrong digits together.

What if one number has fewer digits than the other?

No problem! Just imagine invisible zeros in the empty spots. For example, 10 is really 10, so when you stack it under 75, the units column has 5 + 0.

Do I always start adding from the right?

Yes, always! Start with the units column (rightmost), then move left to tens, hundreds, and so on. This helps you handle any carrying that might be needed.

How can I double-check my answer quickly?

Try adding in a different order! Instead of 75 + 10, try 10 + 75. You should get the same answer: $85$ . You can also count up: 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85!

What happens when I need to carry over?

In this problem there's no carrying needed, but when a column adds to 10 or more, write the units digit and carry the tens digit to the next column. Practice makes perfect!

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