Solve the Decimal Subtraction: 12.3 - 5.4

Q: Why do I need to line up the decimal points?

Lining up decimal points ensures you're subtracting like place values - tenths from tenths, ones from ones. Without proper alignment, you'll get completely wrong answers!

Q: Can I just ignore the decimal point and add it back later?

No! The decimal point's position is crucial for getting the right answer. Always keep track of place values throughout your calculation.

Q: How do I know if I borrowed correctly?

After borrowing, check that your top number got smaller in one place and larger by 10 in the next place. For example: 12.3 becomes 11.13 when you borrow.

Q: What if my answer has fewer decimal places?

That's normal! $ 12.3 - 5.4 = 6.9 $ has one decimal place because the subtraction resulted in zero hundredths, which we don't need to write.

Decimal Subtraction with Borrowing

$12.3-5.4=$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this problem together.

00:07 We'll use long subtraction to find the answer.

00:12 Don't forget, place the decimal point correctly.

00:16 Notice if a digit is smaller than the one you're subtracting from.

00:21 If it is, we need to borrow from the next digit.

00:26 The larger digit decreases by one, and our digit increases by ten.

00:32 Subtract from the larger number and place it in the answer. Like this!

00:40 If the digit is still smaller, we borrow again.

00:44 Use the same method: borrow and subtract.

00:52 Keep subtracting. Remember to place each result correctly.

01:03 Continue this process until you finish all the digits.

01:11 And there you have it! That's the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

$12.3-5.4=$

Step-by-step solution

To solve this problem, we will perform the subtraction of two decimal numbers: $12.3$ and $5.4$ .

Here are the steps to follow:

Align the decimals: Write the numbers $12.3$ and $5.4$ vertically with their decimal points aligned.
Subtract the numbers digit by digit: Start from the rightmost digit (tenths place).
$\phantom{x} \, \, 12.3$
$- \, \, \, 5.4$
$\rule{1cm}{0.4pt}$
From the tenths place, $3 - 4$ requires borrowing. Borrow $1$ from the units place of the top number, turning $12.3$ into $12.2$ and making the tenths digit $3+10=13$ . Subtract: $13 - 4 = 9$ .
In the units place, $2 - 5$ needs borrowing as well. Borrow from the tens place: change $12$ into $11$ and $2$ becomes $12$ . Then subtract: $12 - 5 = 7$ .
Since no borrowing is needed in the tens place, retain $1$ as is.
Therefore, the final result is $6.9$ .

Thus, the result of $12.3 - 5.4$ is $6.9$ .

Final Answer

6.9

Key Points to Remember

Essential concepts to master this topic

Alignment: Always line up decimal points vertically before subtracting
Borrowing: When subtracting 3 - 4, borrow 1 to make 13 - 4 = 9
Check: Add your answer to the smaller number: 6.9 + 5.4 = 12.3 ✓

Common Mistakes

Avoid these frequent errors

Not borrowing correctly across decimal places
Don't forget to borrow when the top digit is smaller than the bottom digit = wrong answers like 7.9 or 7.1! This happens when you subtract 3 - 4 = 1 instead of borrowing. Always borrow 1 from the next place value to make subtraction possible.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I need to line up the decimal points?

Lining up decimal points ensures you're subtracting like place values - tenths from tenths, ones from ones. Without proper alignment, you'll get completely wrong answers!

What happens when I need to borrow from a decimal?

Borrowing works the same way! When you borrow 1 from the ones place in $12.3$ , the 2 becomes 1, and the 3 in tenths becomes 13 tenths.

Can I just ignore the decimal point and add it back later?

No! The decimal point's position is crucial for getting the right answer. Always keep track of place values throughout your calculation.

How do I know if I borrowed correctly?

After borrowing, check that your top number got smaller in one place and larger by 10 in the next place. For example: 12.3 becomes 11.13 when you borrow.

What if my answer has fewer decimal places?

That's normal! $12.3 - 5.4 = 6.9$ has one decimal place because the subtraction resulted in zero hundredths, which we don't need to write.

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