Solve Four-Digit Addition: 5421 + 1657 Using Column Method

Q: What does it mean to 'carry' in addition?

When two digits add up to 10 or more, you write down the ones digit and carry the tens digit to the next column. It's like exchanging 10 ones for 1 ten!

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

We add from right to left because carrying flows from smaller place values to larger ones. Starting from units → tens → hundreds → thousands follows the natural flow of our number system.

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

Always remember to add the carried digit to your column sum! In this problem, 5 + 1 + 1(carry) = 7. Missing the carry gives you 6 instead of the correct 7.

Column Addition with Four-Digit Carrying

$\begin{aligned} &5421 \\ +& \\ &1657 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 adding 2 digits, and then substitute

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

00:09 Substitute the ones

00:12 Add tens with tens, substitute in tens

00:15 Add hundreds with hundreds

00:19 Substitute hundreds in hundreds, and add 1 to thousands

00:22 Add thousands with thousands, remember to add 1

00:25 Substitute in thousands

00:28 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

$\begin{aligned} &5421 \\ +& \\ &1657 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve the problem of adding 5421 and 1657 using vertical addition, we will proceed through the following steps:

Step 1: Align the numbers vertically according to their place values:

$\begin{aligned} &5421 \\ + &1657 \\ \end{aligned}$

Step 2: Begin addition from the rightmost digit (units place):

Units place: $1 + 7 = 8$ . Write 8 in the units place.
Tens place: $2 + 5 = 7$ . Write 7 in the tens place.
Hundreds place: $4 + 6 = 10$ . Write 0 in the hundreds place and carry over 1 to the thousands place.
Thousands place: $5 + 1 = 6$ , plus the carried over 1 gives $6 + 1 = 7$ . Write 7 in the thousands place.

Step 3: Write down the final result underneath the drawn line:

$\begin{aligned} &\underline{7078} \end{aligned}$

Therefore, the sum of 5421 and 1657 is $\textbf{7078}$ .

Final Answer

7078

Key Points to Remember

Essential concepts to master this topic

Alignment: Stack numbers by place value with units under units
Carrying: When 4 + 6 = 10, write 0 and carry 1
Check: Add from right to left: 8, 7, 0+carry, 7 = 7078 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 10 in the hundreds place when 4 + 6 = 10 = wrong answer 70108! This ignores place value rules and creates extra digits. Always write the units digit and carry the tens digit to the next column.

Practice Quiz

Test your knowledge with interactive questions

$\begin{aligned} &12 \\ +& \\ &~~2 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

FAQ

Everything you need to know about this question

What does it mean to 'carry' in addition?

When two digits add up to 10 or more, you write down the ones digit and carry the tens digit to the next column. It's like exchanging 10 ones for 1 ten!

Why do I start adding from the right side?

We add from right to left because carrying flows from smaller place values to larger ones. Starting from units → tens → hundreds → thousands follows the natural flow of our number system.

What if I forget to add the carried number?

Always remember to add the carried digit to your column sum! In this problem, 5 + 1 + 1(carry) = 7. Missing the carry gives you 6 instead of the correct 7.

How can I check if my addition is correct?

Try these methods: 1) Add the numbers in reverse order, 2) Use a calculator to verify, or 3) Estimate by rounding (5400 + 1700 ≈ 7100, close to 7078!).

What happens if there's carrying in multiple columns?

Handle each column separately! Carry flows from right to left, so finish each column completely before moving to the next. Never skip a column - every place value matters.

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