Solve Vertical Subtraction: 118 minus 9

Vertical Subtraction with Borrowing

118    9776 \begin{aligned} &118 \\ -& \\ &~~~~9 \\ &\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 consider subtraction of 2 digits, and then we'll place
00:06 8 is less than 9
00:09 Therefore we'll subtract 1 from the tens and add this amount to the ones
00:14 Meaning now instead of 8 we'll have 18
00:21 Subtract the ones from the ones plus the ten
00:24 Place in the ones
00:26 Place 0 in the missing digits
00:29 Subtract tens from tens, and place in tens
00:33 Subtract hundreds from hundreds, and place in hundreds
00:37 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

118    9776 \begin{aligned} &118 \\ -& \\ &~~~~9 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Set up the subtraction problem vertically, aligning the digits by place value.
  • Step 2: Begin with the units place.
  • Step 3: Consider any necessary borrowing from the higher place value.
  • Step 4: Complete the subtraction in all place values.

Now, let's work through each step:

Step 1: Align the numbers vertically as follows:

1189 \begin{array}{c} 1 & 1 & 8 \\ - & & 9 \\ \hline \end{array}

Step 2: Start from the units column. Here we have 88 (minuend) and 99 (subtrahend). Since 88 is less than 99, we cannot directly subtract.

Step 3: Borrow 1 from the tens place of 118118 which makes the tens place 00, and the 88 in the units place becomes 1818.

Step 4: Compute 189=918 - 9 = 9. Place the result under the units column.

Step 5: In the tens column, now we have 00=00 - 0 = 0 since after borrowing, the tens of 118118 are reduced.

Step 6: In the hundreds column, copy the 11 as there is no subtraction required here.

The final subtraction will look like this:

10189109 \begin{array}{c} 1 & 0 & 18 \\ - & & 9 \\ \hline 1 & 0 & 9 \\ \end{array}

The answer to 1189118 - 9 is 109\textbf{109}.

Therefore, the solution to the subtraction problem is 109109.

3

Final Answer

109

Key Points to Remember

Essential concepts to master this topic
  • Borrowing: When subtracting digit is larger, borrow from next place value
  • Technique: Convert 8 to 18 by borrowing 1 from tens place
  • Check: Add your answer to subtrahend: 109 + 9 = 118 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting smaller from larger digit regardless of position
    Don't compute 9 - 8 = 1 when you see 8 - 9! This ignores place value rules and gives 111 instead of 109. Always subtract the bottom digit from the top digit, borrowing when needed.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &105 \\ -& \\ &~~~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

Why can't I just subtract 8 - 9 and get a negative number?

+

In place value subtraction, each column must give a positive result. When the top digit is smaller, you borrow from the next column to make subtraction possible.

What happens to the tens place when I borrow?

+

The tens place decreases by 1! In this problem, the 1 in the tens place becomes 0 after we borrow for the units place. Remember: borrowing affects both columns.

How do I know when to borrow?

+

Borrow whenever the top digit is smaller than the bottom digit in any column. Look at each column from right to left before you start subtracting.

Can I check my work without adding?

+

Yes! You can also estimate: 1189118 - 9 should be close to 12010=110120 - 10 = 110. Since 109 is close to 110, it makes sense!

What if I need to borrow from zero?

+

When borrowing from 0, you need to borrow from the next column first. This creates a chain reaction - borrow from hundreds to make tens become 10, then borrow from tens for units.

🌟 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