Calculate the Sum: 728 + 56 in Vertical Format

Q: What does 'carry over' mean exactly?

Carrying over means when two digits add up to 10 or more, you write down the ones digit and add the tens digit to the next column. Like $ 8 + 6 = 14 $, so write 4 and carry the 1.

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

We start from the ones place (rightmost) because any carrying affects the next column to the left. If we started from the left, we'd miss the carried amounts!

Q: What if there are no digits to add in a column?

If one number is shorter, treat missing digits as zero. For example, 56 has no hundreds digit, so it's like 056. The hundreds place becomes $ 7 + 0 = 7 $.

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

Use subtraction to check! Take your answer and subtract one of the original numbers. You should get the other original number. Like $ 784 - 56 = 728 $ ✓

Q: What if I need to carry from multiple columns?

Handle each carry one at a time moving left. Each carried digit only affects the very next column. Don't try to carry multiple places at once!

Vertical Addition with Carrying

$\begin{aligned} &728 \\ +& \\ &~~56 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 calculate the sum of 2 digits, and then we substitute

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

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

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

00:19 Place in the tens position

00:22 Place 0 in the missing digits

00:25 Add hundreds with hundreds, place in hundreds position

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

$\begin{aligned} &728 \\ +& \\ &~~56 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we need to add the numbers 728 and 56 using vertical addition. Let's break this down step by step:

Step 1: Add the ones place digits. Here, we add $8 + 6 = 14$ . The digit 4 remains in the ones place, and we carry over the 1 to the tens place.
Step 2: Add the tens place. Now, add the tens digits, taking into account the carry-over: $2 + 5 + 1 = 8$ . Write 8 in the tens place.
Step 3: Add the hundreds place. Since there are no more digits to add to the hundreds place and no carry over, we keep the hundreds digit as is: $7$ .

Thus, the sum of 728 and 56 is $784$ .

Therefore, the correct answer is choice 2: 784.

Final Answer

784

Key Points to Remember

Essential concepts to master this topic

Rule: Add column by column from right to left
Technique: When sum exceeds 9, write ones digit and carry tens
Check: Verify $784 - 56 = 728$ using subtraction ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when digits sum to 10 or more
Don't write 14 in the ones place when adding 8 + 6 = wrong answer like 72814! This creates impossible multi-digit place values. Always write the ones digit (4) 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

What does 'carry over' mean exactly?

Carrying over means when two digits add up to 10 or more, you write down the ones digit and add the tens digit to the next column. Like $8 + 6 = 14$ , so write 4 and carry the 1.

Why do we start adding from the right side?

We start from the ones place (rightmost) because any carrying affects the next column to the left. If we started from the left, we'd miss the carried amounts!

What if there are no digits to add in a column?

If one number is shorter, treat missing digits as zero. For example, 56 has no hundreds digit, so it's like 056. The hundreds place becomes $7 + 0 = 7$ .

How can I check if my addition is correct?

Use subtraction to check! Take your answer and subtract one of the original numbers. You should get the other original number. Like $784 - 56 = 728$ ✓

What if I need to carry from multiple columns?

Handle each carry one at a time moving left. Each carried digit only affects the very next column. Don't try to carry multiple places at once!

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