Solve Vertical Addition: 978 + 53 Step-by-Step

Q: What does 'carrying over' mean in addition?

When you add digits and get a sum of 10 or more, you write the ones digit in that column and carry the tens digit to the next column on the left. For example, 8 + 3 = 11, so write 1 and carry 1.

Q: Why do I need to align the numbers properly?

Place value alignment ensures you're adding units to units, tens to tens, and hundreds to hundreds. If numbers aren't aligned, you'll add the wrong digits together and get an incorrect answer.

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

When one number is shorter (like 53 vs 978), treat the missing digits as zeros. So in the hundreds place, you're adding 9 + 0 + any carryover.

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

Use horizontal addition to verify: $ 978 + 53 = 1031 $. You can also try adding in reverse order: $ 53 + 978 = 1031 $. Both should give the same result!

Q: What happens when I have multiple carryovers?

Handle each carryover one column at a time. In this problem: units gives carryover 1, tens (7+5+1) gives carryover 1, hundreds (9+1) gives carryover 1 to thousands place.

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, add 1 to the tens

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

00:20 Place tens in tens, add 1 to hundreds

00:23 Place 0 in the missing digits

00:27 Combine hundreds with hundreds, remember to add 1

00:32 Place the hundreds in hundreds, add 1 to thousands

00:35 Place 0 in the missing digits

00:38 Combine thousands with thousands, and place in thousands

00:41 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

$\begin{aligned} &978 \\ +& \\ &~~53 \\ &\underline{\phantom{776}} & \\ \end{aligned}$

2

Step-by-step solution

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

Step 1: Align the numbers 978 and 53 by their place value, where 53 is written below 978, making sure that the rightmost digits are in the same column. This means placing 978 over 53.

Align the numbers:
$\begin{array}{c} 978 \\ + \\ \underline{~53} \\ \end{array}$

Step 2: Add the units place. Add 8 (from 978) and 3 (from 53). The sum is 8 + 3 = 11. Write 1 in the units place of the answer and carry over 1 to the tens place.
Step 3: Add the tens place. Add 7 (from 978) and 5 (from 53), also add the carryover of 1 from the previous step. The sum is 7 + 5 + 1 = 13. Write 3 in the tens place of the answer and carry over 1 to the hundreds place.
Step 4: Add the hundreds place. Add 9 (from 978) and the carryover 1 (from the tens calculation). The sum is 9 + 1 = 10. Write 0 in the hundreds place of the answer and carry over 1 to the thousands place.
Step 5: Since we have a carryover for the thousands place, write 1.

Thus, the complete sum is $1031$ .

The solution to the problem is $1031$ , which matches choice 2.

3

Final Answer

1031

Key Points to Remember

Essential concepts to master this topic

Alignment: Line up numbers by place value from right to left
Carrying: When sum exceeds 9, write ones digit and carry tens
Check: Verify 978 + 53 = 1031 by adding left-to-right ✓

Common Mistakes

Avoid these frequent errors

Forgetting to carry over when sum exceeds 9
Don't write 11 in the units column when 8 + 3 = 11! This creates a two-digit number in a single place value position. Always write the ones 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

What does 'carrying over' mean in addition?

+

When you add digits and get a sum of 10 or more, you write the ones digit in that column and carry the tens digit to the next column on the left. For example, 8 + 3 = 11, so write 1 and carry 1.

Why do I need to align the numbers properly?

+

Place value alignment ensures you're adding units to units, tens to tens, and hundreds to hundreds. If numbers aren't aligned, you'll add the wrong digits together and get an incorrect answer.

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

+

When one number is shorter (like 53 vs 978), treat the missing digits as zeros. So in the hundreds place, you're adding 9 + 0 + any carryover.

How do I check if my vertical addition is correct?

+

Use horizontal addition to verify: $978 + 53 = 1031$ . You can also try adding in reverse order: $53 + 978 = 1031$ . Both should give the same result!

What happens when I have multiple carryovers?

+

Handle each carryover one column at a time. In this problem: units gives carryover 1, tens (7+5+1) gives carryover 1, hundreds (9+1) gives carryover 1 to thousands place.

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Solve Vertical Addition: 978 + 53 Step-by-Step

Vertical Addition with Carrying Operations

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