Solve Vertical Addition: 73 + 18 Step-by-Step

Q: Why do I need to carry over when adding 3 + 8?

When digits add up to 10 or more, you get more than one digit! The rightmost digit stays in that column, but the leftmost digit moves to the next column. Think of it like exchanging 10 ones for 1 ten.

Q: How do I know if my vertical addition is correct?

Try adding horizontally as a check: 73 + 18. Break it down: 70 + 10 = 80, then 3 + 8 = 11, so 80 + 11 = 91. Both methods should give the same answer!

Vertical Addition with Two-Digit Carrying

$\begin{aligned} &73\\ +& \\ &18 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 calculate the sum of 2 digits, and then substitute

00:06 Let's start by adding ones with ones

00:09 Place the ones in ones position, and add 1 to tens

00:12 Add tens with tens, remember to add 1 to the calculation

00:17 Place in tens

00:20 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

$\begin{aligned} &73\\ +& \\ &18 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

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

Step 1: Align the numbers by place value, ensuring the units and tens are in the correct columns.
Step 2: Add the digits in the units column (3 and 8).
Step 3: Address any carryover from the units addition, which affects the tens column calculation.
Step 4: Add the digits in the tens column (7 and 1), including any carry.

Now, let's work through each step:

Step 1: The problem provides the vertical alignment:
$\begin{array}{c} 73 \\ +18 \\ \end{array}$
We confirm that the units and tens digits are properly aligned.

Step 2: Add the units digits (3 and 8):
$3 + 8 = 11$
Place the 1 in the units position and carry over 1 to the tens position.

Step 3: Add the tens digits along with the carryover:
$7 + 1 + 1 = 9$
Write the 9 in the tens position for the sum.

The resulting sum of the numbers vertically added is:
$\begin{array}{cc} & 91 \\ \end{array}$
Therefore, the solution to the problem is $91$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value, units under units
Technique: Add units first: 3 + 8 = 11, write 1 carry 1
Check: Verify 73 + 18 = 91 by adding horizontally ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when units sum exceeds 9
Don't write 11 in the units place when 3 + 8 = 11 = wrong answer 711! The 1 in the tens place gets ignored and creates impossibly large sums. Always write the units digit (1) 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

Why do I need to carry over when adding 3 + 8?

When digits add up to 10 or more, you get more than one digit! The rightmost digit stays in that column, but the leftmost digit moves to the next column. Think of it like exchanging 10 ones for 1 ten.

What if I forget to add the carried number?

You'll get the wrong answer! In this problem, forgetting the carried 1 would give you 81 instead of 91. Always remember: tens column = 7 + 1 + 1 (carried) = 9.

Can I add from left to right instead?

It's much harder! You'd need to mentally keep track of carries. Always start from the rightmost column (units) and work left. This way, you handle carries one at a time.

How do I know if my vertical addition is correct?

Try adding horizontally as a check: 73 + 18. Break it down: 70 + 10 = 80, then 3 + 8 = 11, so 80 + 11 = 91. Both methods should give the same answer!

What happens if both digits in a column are large, like 9 + 9?

You'd get 9 + 9 = 18, so write 8 in that column and carry 1 to the next column. The same rule applies: write the units digit, carry the tens digit!

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