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
00:00 Solve
00:03 Place 0 in the missing digits, mark the decimal point
00:06 Start subtracting from right to left
00:09 The digit is too small for subtraction, so we'll borrow from the next possible one
00:14 The next digit will decrease by 1, and our digit will increase by 10
00:20 Again, the next digit will decrease by 1, and our digit will increase by 10
00:32 Now let's subtract from the larger number
00:35 Calculate and place accordingly
00:43 Continue subtracting, calculating, and placing accordingly
01:09 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

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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