Decimal Subtraction: Solve 113.1 - 102.32 Using Vertical Format

Decimal Subtraction with Borrowing Across Columns

Circle the correct answer to the following exercise:

113.1-102.32

❤️ 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 Place 0 in the appropriate position, place the decimal point in the appropriate position
00:07 Subtract accordingly, and place
00:11 When we need to subtract a number larger than what we have
00:14 Borrow from the next number
00:17 The digit decreases by 1, and the previous digit increases by 10
00:20 Now subtract from the larger number
00:24 Borrow from the next number
00:27 The digit decreases by 1, and the previous digit increases by 10
00:31 Now subtract from the larger number
00:34 Place and continue to subtract and place accordingly
00:42 Reduce the 4
00:45 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

Circle the correct answer to the following exercise:

113.1-102.32

2

Step-by-step solution

To avoid confusion in solving the exercise, we will first add the digit 0 to the number 113.1 in the following way:

113.10102.32 113.10\\-102.32\\

Now let's solve the exercise in order:

Let's subtract the hundreds after the decimal point:

02= 0-2=

Since we cannot subtract, we'll borrow ten from the tenths digit after the decimal point and get:

102=8 10-2=8

Let's subtract the tenths after the decimal point, remembering that we borrowed ten, so we get:

113=03 1-1-3=0-3

Since we cannot subtract, we'll borrow ten from the hundreds digit of the whole number and get:

103=7 10-3=7

Finally, let's subtract the whole numbers before the decimal point accordingly.

Remember that we borrowed ten from the hundreds digit, so:

312=0 3-1-2=0

10=1 1-0=1

11=0 1-1=0

And we get:

113.10102.32010.78 113.10\\-102.32\\010.78

3

Final Answer

10.78

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Line up decimal points vertically for accurate column subtraction
  • Zero Padding: Add zeros to make equal decimal places: 113.10 - 102.32
  • Verification: Add your answer to the subtrahend: 10.78 + 102.32 = 113.10 ✓

Common Mistakes

Avoid these frequent errors
  • Not aligning decimal points correctly
    Don't line up the last digits instead of decimal points = completely wrong answer! This misaligns place values and gives results like 13.28 instead of 10.78. Always align decimal points first, then add zeros to match decimal places.

Practice Quiz

Test your knowledge with interactive questions

\( \text{0.6+0}.5= \)

+=

FAQ

Everything you need to know about this question

Why do I need to add a zero to 113.1?

+

Adding zero makes 113.10 so both numbers have the same decimal places. This prevents confusion when borrowing and ensures you're subtracting in the correct columns.

What does 'borrowing' mean in decimal subtraction?

+

Borrowing means taking 10 from the next column when you can't subtract. For example, when 0-2 is impossible, borrow 10 from the tenths place to get 10-2=8.

How do I know which column to borrow from?

+

Always borrow from the column immediately to the left. Start from the rightmost column and work left, borrowing only when the top digit is smaller than the bottom digit.

What if I get a different answer than the choices?

+

Check your decimal point alignment first! Then verify each borrowing step. Most errors come from misaligned decimals or forgetting to reduce borrowed digits by 1.

Can I check my answer without adding?

+

Yes! Use estimation: 113102=11 113 - 102 = 11 , so your answer should be close to 11. Since 10.78 is near 11, it's reasonable!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Decimal Fractions - Basic 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