Solve Decimal Subtraction: 20.2 - 10.4 Step-by-Step

Q: How do I know when I need to borrow?

You need to borrow whenever the top digit is smaller than the bottom digit in any column. In $ 20.2 - 10.4 $, since 2

Q: What happens to the decimal point during borrowing?

The decimal point stays in the same position throughout the entire process. Borrowing only affects the digits, not the decimal point placement.

Q: How can I check if my decimal subtraction is correct?

Use addition to check: Add your answer to the number you subtracted. If you get the original number, you're correct! $ 9.8 + 10.4 = 20.2 $ ✓

Q: Is there an easier way to do this without borrowing?

You could think of it as $ 20.2 - 10.4 = (20 - 10) + (0.2 - 0.4) = 10 + (-0.2) = 9.8 $, but borrowing is the standard method that works for all cases.

Decimal Subtraction with Borrowing Across Places

$20.2-10.4=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We'll use long subtraction for calculation

00:08 We'll place the decimal point in the appropriate position

00:11 The digit is smaller than the digit we need to subtract from

00:14 So we'll borrow from the next possible digit

00:18 The larger digit will decrease by 1, and our digit will increase by 10

00:24 Now we'll use the same method and borrow from the first digit

00:40 Now we'll subtract from the larger number and place it

00:50 We'll continue to subtract and place accordingly

01:06 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$20.2-10.4=$

Step-by-step solution

To solve this problem, we'll perform the following steps:

Step 1: Align the decimal points of $20.2$ and $10.4$ .
Step 2: Subtract starting from the rightmost digits (tenths place).

Now, let's work through each step:

Step 1: We align the two numbers with their decimal points:
$20.2$
$-10.4$
_____

Step 2: Subtract the digits from right to left:

Tenths place: $2 - 4$ can't be done directly, so we need to look at the whole number.
Units place: We need to borrow from the $20$ , making the $0$ a $10$ and reducing the hundreds digit: this gives us $12.0 - 10.4$ .
Now, tenths place calculation $2 - 4 = -2$ , but with borrowing from next digit $(10) + (2 - 4) = 8$ .
Units place results into $20 - 10 = 10$ . Including borrows, results into $9$ .

The final subtraction shows that $20.2 - 10.4 = 9.8$ .

Therefore, the solution to the problem is $\mathbf{9.8}$

Final Answer

9.8

Key Points to Remember

Essential concepts to master this topic

Alignment: Always line up decimal points vertically before subtracting
Borrowing: When $2 - 4$ is impossible, borrow from units place
Check: Add your answer to the smaller number: $9.8 + 10.4 = 20.2$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to borrow when subtracting larger digits
Don't try to subtract $2 - 4$ and get -2 = wrong negative answer! This ignores place value rules and creates incorrect results. Always borrow from the next higher place value when the top digit is smaller than the bottom digit.

Practice Quiz

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FAQ

Everything you need to know about this question

Why can't I just subtract 2 - 4 and get -2?

In decimal subtraction, we work within each place value column. When the top digit is smaller, we borrow from the next column to make subtraction possible, just like with whole numbers!

How do I know when I need to borrow?

You need to borrow whenever the top digit is smaller than the bottom digit in any column. In $20.2 - 10.4$ , since 2 < 4 in the tenths place, borrowing is required.

What happens to the decimal point during borrowing?

The decimal point stays in the same position throughout the entire process. Borrowing only affects the digits, not the decimal point placement.

How can I check if my decimal subtraction is correct?

Use addition to check: Add your answer to the number you subtracted. If you get the original number, you're correct! $9.8 + 10.4 = 20.2$ ✓

Is there an easier way to do this without borrowing?

You could think of it as $20.2 - 10.4 = (20 - 10) + (0.2 - 0.4) = 10 + (-0.2) = 9.8$ , but borrowing is the standard method that works for all cases.

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