Solve Vertical Addition: 75 + 15 Step-by-Step

Vertical Addition with Regrouping

75+15776 \begin{aligned} &75 \\ +& \\ &15 \\ &\underline{\phantom{776}} & \\ \end{aligned}

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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, and remember 1 above
00:12 Add tens with tens, remember to add 1 to the calculation
00:19 Place in the tens position
00:22 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

75+15776 \begin{aligned} &75 \\ +& \\ &15 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Align the numbers by place value:
    75+15 \begin{aligned} &75 \\ + &15 \\ \end{aligned}

  • Step 2: Add the units digits: 5+5=105 + 5 = 10. Write down 00 in the units place and regroup by carrying over 11 to the tens place.

  • Step 3: Add the tens digits, including the carry: 7+1+1=97 + 1 + 1 = 9.

By following these steps, the sum of 7575 and 1515 is 9090.

Therefore, the solution to the problem is 9090.

3

Final Answer

90

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Stack numbers by place value before adding
  • Technique: Add units first: 5+5=105 + 5 = 10, write 0 and carry 1
  • Check: Verify by adding horizontally: 75+15=9075 + 15 = 90

Common Mistakes

Avoid these frequent errors
  • Forgetting to carry when sum exceeds 9
    Don't just write 10 in the units place = wrong answer like 7510! When digits add to 10 or more, you must write the units digit and carry the tens digit to the next column. Always regroup by carrying the extra value to the left.

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' or 'regroup' mean?

+

When adding digits gives you 10 or more, you write down the units digit and carry the tens digit to the next column. For example: 5+5=105 + 5 = 10 means write 0 and carry 1.

Why do I need to align the numbers vertically?

+

Alignment ensures you're adding like place values together - units with units, tens with tens. Misalignment leads to wrong answers because you'd be mixing different place values.

What if there's nothing to carry?

+

That's perfectly normal! If the sum of digits is 9 or less, just write that digit down and move to the next column. Carrying only happens when sums reach 10 or higher.

Can I add from left to right instead?

+

It's much harder! Adding from right to left (units first) is the standard method because any carrying affects the column to the left, making the process cleaner and more reliable.

How do I check if my answer is correct?

+

Try these methods:

  • Add the numbers horizontally: 75+1575 + 15
  • Use subtraction: 9075=1590 - 75 = 15
  • Estimate: 75+1575 + 15 should be close to 80+20=10080 + 20 = 100

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Arithmetic Operations questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations