Solve Vertical Addition: 21 + 59 Step-by-Step

Vertical Addition with Carrying Over

21+59776 \begin{aligned} &21 \\ +& \\ &59 \\ &\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 We'll place the ones, and remember 1 above
00:12 We'll add tens with tens, remember to add 1 to the calculation
00:19 We'll place in the tens
00:21 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

21+59776 \begin{aligned} &21 \\ +& \\ &59 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we will perform the following steps:

  • Step 1: Align the given numbers vertically according to their place values.
  • Step 2: Add the digits in the ones and tens places, carrying over if necessary.

Let's break down the calculation process:

Step 1: Write the numbers in a vertical format.
021+059776 \begin{aligned} &\phantom{0}21 \\ +&\phantom{0}59 \\ &\underline{\phantom{776}} \end{aligned}

Step 2: Start by adding the ones digits: 1+9=101 + 9 = 10. Since 10 is a two-digit number, we write 0 in the ones place and carry 1 over to the tens place.

Step 3: Now, add the tens digits, including the carried 1: 2+5+1=82 + 5 + 1 = 8.

Since there is no further place value beyond tens in this problem, the result of the addition is:

021+059880 \begin{aligned} &\phantom{0}21 \\ +&\phantom{0}59 \\ &\underline{\phantom{8}80} \end{aligned}

Therefore, the solution to the problem is 80.

3

Final Answer

80

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value with ones under ones
  • Technique: Add ones first: 1+9=10 1 + 9 = 10 , write 0 and carry 1
  • Check: Verify by adding horizontally: 21+59=80 21 + 59 = 80

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry over when sum exceeds 9
    Don't just write 10 in the ones place when adding 1 + 9 = wrong answer of 720! This ignores place value rules. Always write the units digit (0) 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 in addition?

+

When you add digits and get a number 10 or greater, you write the ones digit in that column and carry the tens digit to the next column on the left. It's like exchanging 10 ones for 1 ten!

Why do I have to align the numbers by place value?

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Aligning by place value ensures you're adding ones to ones and tens to tens. If numbers aren't lined up correctly, you'll get the wrong answer!

What if I forget to carry and just write the full number?

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Writing the full sum (like 10) in one column creates numbers with too many digits. For example, writing 10 in the ones place would give you 720 instead of the correct answer 80.

Can I add from left to right instead?

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It's better to add from right to left (ones, then tens) because carrying affects the column to the left. Adding left to right makes carrying more confusing!

How do I check my vertical addition answer?

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You can check by adding the numbers horizontally: 21+59=80 21 + 59 = 80 . You can also try adding in a different order: 59+21=80 59 + 21 = 80 .

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