Solve Vertical Addition: 1547 + 7656 Step-by-Step

Q: What does 'carry over' mean exactly?

When two digits add up to 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. For example: $ 7 + 6 = 13 $ means write 3, carry 1.

Q: Why do we start adding from the right side?

We start from the units place (rightmost) because any carrying affects the column to the left. If we started from the left, we'd have to go back and fix our work when we carry!

Q: What if I forget to add the carried number?

Your final answer will be wrong! Always remember to add the carried digit to your next column. It helps to write small carry numbers above each column as reminders.

Q: How can I check if my addition is correct?

Try adding the numbers in a different order, or use subtraction to check: $ 9203 - 1547 = 7656 $. If you get back one of your original numbers, your addition is correct!

Q: What if the numbers have different amounts of digits?

No problem! Just imagine invisible zeros in front of the shorter number. For example, treat 1547 as 01547 when adding to 7656, so all columns line up properly.

Q: Is there a faster way to do this?

The column method is actually the most reliable way for multi-digit addition! While mental math tricks exist, showing your work step-by-step prevents errors and helps you learn the place value system.

Multi-Digit Addition with Carrying

$\begin{aligned} &1547 \\ +& \\ &7656 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 consider combining 2 digits, and then we place

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

00:09 Place the ones, add 1 to the tens

00:13 Multiply tens with tens, remember to add 1 to the calculation

00:17 Place tens in tens, add 1 to hundreds

00:22 Multiply hundreds with hundreds, remember to add 1

00:27 Place hundreds in hundreds, and add 1 to thousands

00:34 Multiply thousands with thousands, remember to add 1

00:37 Place in thousands

00:40 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

$\begin{aligned} &1547 \\ +& \\ &7656 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

Let's solve the problem by completing an addition of the numbers vertically.

Write the numbers vertically, aligning them by their place values:
$\begin{array}{c@{}c@{}c@{}c@{}c} & 1 & 5 & 4 & 7 \\ + & & 7 & 6 & 5 & 6 \\ \end{array}$
Add the digits starting from the rightmost (units place):

Units Place: $7 + 6 = 13$ . Write 3 and carry over 1 to the tens place.
Tens Place: $4 + 5 = 9$ , plus 1 from the carry-over equals 10. Write 0 and carry over 1 to the hundreds place.
Hundreds Place: $5 + 6 = 11$ , plus 1 from the carry-over equals 12. Write 2 and carry over 1 to the thousands place.
Thousands Place: $1 + 7 = 8$ , plus 1 from the carry-over equals 9. Write 9.

The final addition gives us:
$\begin{array}{c} 9 \quad 2 \quad 0 \quad 3 \\ \end{array}$

Thus, the sum of 1547 and 7656 is $\boxed{9203}$ .

Final Answer

9203

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers with same place values in columns
Technique: Start from units place: 7 + 6 = 13, write 3 carry 1
Check: Verify each column sum matches final answer digits ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't just write the full sum like 13 in the units place = wrong answer! This ignores place value rules and creates incorrect digits. Always write the ones digit and carry the tens digit to the next column.

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

What does 'carry over' mean exactly?

When two digits add up to 10 or more, you write the ones digit in that column and carry the tens digit to the next column left. For example: $7 + 6 = 13$ means write 3, carry 1.

Why do we start adding from the right side?

We start from the units place (rightmost) because any carrying affects the column to the left. If we started from the left, we'd have to go back and fix our work when we carry!

What if I forget to add the carried number?

Your final answer will be wrong! Always remember to add the carried digit to your next column. It helps to write small carry numbers above each column as reminders.

How can I check if my addition is correct?

Try adding the numbers in a different order, or use subtraction to check: $9203 - 1547 = 7656$ . If you get back one of your original numbers, your addition is correct!

What if the numbers have different amounts of digits?

No problem! Just imagine invisible zeros in front of the shorter number. For example, treat 1547 as 01547 when adding to 7656, so all columns line up properly.

Is there a faster way to do this?

The column method is actually the most reliable way for multi-digit addition! While mental math tricks exist, showing your work step-by-step prevents errors and helps you learn the place value system.

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