Subtract Decimals: Find 39.2 - 13.421 with Proper Alignment

Decimal Subtraction with Borrowing Across Zeros

Circle the correct answer for the following exercise:

39.2-13.421

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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 point in the appropriate position
00:06 Subtract accordingly, and place
00:09 When we need to subtract a number larger than what we have
00:12 Borrow from the next number
00:15 The digit will decrease by 1, and the previous digit will increase by 10
00:19 We'll do this twice
00:22 Now subtract from the larger number
00:25 Place and continue to subtract and place accordingly
00:29 Borrow from the next number
00:32 The digit will decrease by 1, and the previous digit will increase by 10
00:35 Now subtract from the larger number
00:40 Place and continue to subtract and place accordingly
00:48 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 for the following exercise:

39.2-13.421

2

Step-by-step solution

In order to avoid confusion whilst solving the exercise, add two zeros to the number 39.2 as follows:

39.20013.421 39.200\\-13.421\\

Now let's proceed solve the exercise in the correct order:

Subtract the thousands after the decimal point:

01= 0-1=

Given that we cannot subtract, we will instead borrow ten from the tenths digit after the decimal point (note that the hundreds digit is 0 therefore we cannot borrow from there)

After borrowing ten from the tenths digit, the hundreds digit will become 10 and from it we'll borrow ten to solve our exercise.

The hundreds digit will become 9 and we'll get the exercise:

101=9 10-1=9

Let's subtract the hundreds after the decimal point:

92=7 9-2=7

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

214=14 2-1-4=1-4

Due to the fact that we cannot subtract, we will instead borrow ten from the tens digit of the whole number as shown below:

114=7 11-4=7

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

Remember that we borrowed ten from the tens digit, therefore:

913=5 9-1-3=5

31=2 3-1=2

We should obtain the following result:

39.20013.42125.779 39.200\\-13.421\\25.779

3

Final Answer

25.779

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Add zeros to match decimal places before subtracting
  • Borrowing: When subtracting 0-1, borrow through multiple place values
  • Check: Add your answer to the smaller number: 25.779 + 13.421 = 39.2 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to add zeros for proper alignment
    Don't subtract 39.2 - 13.421 without adding zeros = wrong place value alignment! This causes errors in every digit position. Always add zeros to make 39.200 - 13.421 first.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I need to add zeros to 39.2?

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Adding zeros helps you align place values correctly. Without zeros, you might subtract in wrong positions. Change 39.2 to 39.200 so each decimal place lines up properly.

What happens when I need to borrow from zero?

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When borrowing from zero, you need to keep going left until you find a non-zero digit. Borrow from there, then work your way back to where you started borrowing.

How do I borrow from the hundreds place when it's zero?

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You can't borrow directly from zero! Instead, borrow from the tenths place first (making it 1), then borrow from that to make the hundreds place 10.

Why does borrowing make the calculation so complicated?

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Borrowing through zeros takes extra steps, but following the systematic approach prevents errors. Work from right to left, one place value at a time.

How can I check if my subtraction is correct?

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Use addition to check: Add your answer to the number you subtracted. If you get the original number, you're correct! 25.779+13.421=39.200 25.779 + 13.421 = 39.200

What if I get confused about which direction to borrow?

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Always borrow from left to right (from larger to smaller place values). Think: you're taking 10 from a bigger place and giving it to the smaller place that needs help.

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