Solve: Subtracting 6.54 from 17 in Vertical Format

Decimal Subtraction with Borrowing Across Places

176.54-

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's go ahead and solve this problem.
00:07 First, put a zero in any missing digit spots.
00:11 Make sure to mark the decimal point clearly.
00:14 Now, let's start subtracting, beginning from the right side and moving left.
00:19 If a digit is too small to subtract, we'll need to borrow.
00:24 Borrow from the next digit, reducing it by one, and increase our smaller digit by ten.
00:36 Do this again if needed. Now, subtract using the larger number.
00:41 Calculate carefully, and place each result where it belongs.
00:47 Keep subtracting and placing correctly until you're done.
01:13 And there you have it, the solution to our problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

176.54-

2

Step-by-step solution

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

  • Step 1: Align the numbers 17 17 and 6.54 6.54 for vertical subtraction.
  • Step 2: Perform the subtraction starting with the rightmost digit.
  • Step 3: Borrow from the whole part if needed to subtract the decimal part correctly.

Now, let's work through each step:
Step 1: Write the numbers vertically with the decimal point aligned:
017.00 6.54 \begin{array}{c} \phantom{0}17.00 \\ -\ 6.54 \\ \hline \end{array} Step 2: Start subtracting from the rightmost column, which are the hundredths:
Subtract 4 4 from 0 0 . Since we can't subtract a larger number from a smaller one, we'll need to borrow.
Step 3: Borrow 1 from the tenths place, making 0 0 in the tenths as 9, and the hundredths as 10. This borrowing changes 17.00 17.00 to 16.9(10) 16.9(10) .
Subtract 4 4 from 10 10 which gives 6 6 in the hundredths:
 9.46 \begin{array}{c} \phantom{\ }9.46 \\ \hline \end{array} Finally, verify the operations: Subtract 5 5 from 9 9 to give 4 4 in the tenths:
Subtract 6 6 from the left part itself given 16 16 now, leaving 10 10 in the units:
Step 5: Combine these to get our final result 10.46 10.46 .

Therefore, the correct solution to the problem is 10.46 10.46 , which matches choice 3 3 in the provided options.

3

Final Answer

10.46

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Write decimal points directly above each other vertically
  • Borrowing: Convert 17 to 16.10 when subtracting from hundredths place
  • Verification: Add your answer 10.46 + 6.54 = 17.00 ✓

Common Mistakes

Avoid these frequent errors
  • Not aligning decimal points properly
    Don't line up the rightmost digits like whole numbers = misplaced decimal in answer! This creates errors in place value positioning. Always align decimal points vertically and add zeros as placeholders (17.00 - 6.54).

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I need to write 17 as 17.00?

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Writing 17 as 17.00 helps you see the decimal places clearly! This makes it easier to align with 6.54 and shows you have tenths and hundredths places to work with.

When do I need to borrow in decimal subtraction?

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You need to borrow when the digit you're subtracting is larger than the digit above it. For example, you can't subtract 4 from 0 in the hundredths place without borrowing first.

How does borrowing work with decimals?

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Borrowing in decimals works just like whole numbers! When you borrow 1 from the tenths place, it becomes 10 hundredths. So 17.00 becomes 16.9(10) when you borrow.

What if I get confused during borrowing?

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Take it one step at a time! Start from the rightmost column and work left. If you can't subtract, borrow from the next column to the left, then continue.

How can I check if my decimal subtraction is correct?

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Use addition to check! Add your answer to the number you subtracted: 10.46+6.54=17.00 10.46 + 6.54 = 17.00 . If you get the original number, you're correct!

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