Calculate the Sum: 78156 + 19763 Using Vertical Addition

Q: What does it mean to 'carry' a digit?

When two digits add up to 10 or more, you write the ones digit and carry the tens digit to the next column. For example, $5 + 6 = 11$, so write 1 and carry 1.

Q: Why do we start from the right side?

We start from the ones place because carrying moves from right to left. If we started from the left, we couldn't handle carries properly!

Q: What if I get confused about which digit to carry?

Always carry the tens digit only. If $8 + 9 = 17$, write down 7 and carry the 1. The carried digit is always smaller!

Addition with Column-by-Column Carrying

$\begin{aligned} &78156\\ +& \\ &19763 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

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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 consider combining 2 digits, and then we'll place

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

00:09 Place the ones

00:12 Combine tens with tens

00:15 Place tens in tens, and add 1 to hundreds

00:18 Combine hundreds with hundreds, and place in hundreds

00:26 Combine thousands with thousands

00:30 Place thousands in thousands, and add 1 to tens of thousands

00:36 Combine tens of thousands with tens of thousands, add 1 to calculation

00:40 Place in tens of thousands

00:44 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

$\begin{aligned} &78156\\ +& \\ &19763 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

Step-by-step solution

To solve this problem, we will perform vertical addition of the two numbers:

We have: $\begin{array}{c@{}c@{}c@{}c@{}c@{}c} & & & & & \\ & 7 & 8 & 1 & 5 & 6 \\ + & 1 & 9 & 7 & 6 & 3 \\ \hline \end{array}$

Let's add the numbers column by column from right to left:

Units place: $6 + 3 = 9$ . Write 9.
Tens place: $5 + 6 = 11$ . Write 1 and carry over 1 to the hundreds place.
Hundreds place: $1 + 7 + 1 \, (\text{carried}) = 9$ . Write 9.
Thousands place: $8 + 9 = 17$ . Write 7 and carry over 1 to the ten-thousands place.
Ten-thousands place: $7 + 1 + 1 \, (\text{carried}) = 9$ . Write 9.

Thus, the sum is $\boxed{97919}$ .

The solution to the problem is $97919$ , which matches choice :

97919

Final Answer

97919

Key Points to Remember

Essential concepts to master this topic

Rule: Always start from rightmost column and work left
Technique: When sum exceeds 9, write ones digit and carry tens
Check: Add numbers horizontally: 78156 + 19763 = 97919 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to add carried digits to the next column
Don't write down the carried digit without adding it to the next column's sum = wrong answer every time! This creates errors that compound through remaining columns. Always add the carried digit to the sum of the next column before writing your answer.

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' a digit?

When two digits add up to 10 or more, you write the ones digit and carry the tens digit to the next column. For example, $5 + 6 = 11$ , so write 1 and carry 1.

Why do we start from the right side?

We start from the ones place because carrying moves from right to left. If we started from the left, we couldn't handle carries properly!

What if I get confused about which digit to carry?

Always carry the tens digit only. If $8 + 9 = 17$ , write down 7 and carry the 1. The carried digit is always smaller!

How can I check if my answer is correct?

Try adding the numbers in a different order or use a calculator to verify. You can also estimate: $78000 + 20000 = 98000$ , so 97919 makes sense!

What if there's nothing to add in a column?

If one number is shorter, treat the missing digits as 0. For example, adding 156 + 78 means the hundreds place is $1 + 0 = 1$ .

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