Solve: 310 - 110.352 Using Vertical Subtraction Method

Decimal Subtraction with Borrowing Across Zeros

Circle the correct answer to the following exercise:

310-110.352

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's solve the problem together.
00:11 We'll begin by placing a zero in the right spots.
00:15 When we need to subtract a bigger number than what we have available.
00:22 We borrow from the next digit.
00:25 This makes the current digit smaller by one, and raises the previous digit by ten.
00:34 Continue this method until you reach the last digit.
00:56 Now, subtract from the larger number.
01:01 We'll keep borrowing, subtracting, and repositioning as needed.
01:15 Once again, borrow from the next digit.
01:19 The current digit becomes one less and the previous gets ten more.
01:24 Subtract again from the larger number.
01:28 Keep subtracting and placing numbers correctly.
01:31 And that's how we solve this problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Circle the correct answer to the following exercise:

310-110.352

2

Step-by-step solution

In order to avoid confusion whilst solving the exercise, add three zeros to the number 310 as follows:

310.000110.352 310.000\\-110.352\\

Proceed to solve the exercise in the correct order:

Let's subtract the thousands after the decimal point:

02= 0-2=

Given that we cannot subtract, we will instead borrow ten from the tens digit of the whole number before the decimal point, due to the fact that the other numbers are also zeros.

The tens digit of the whole number before the decimal point will become 0, and the hundreds digit of the whole number before the decimal point will become 10

We'll borrow ten from the hundreds digit before the decimal point and it will change from 10 to 9, and now the tenths digit after the decimal point will become 10

We'll borrow ten from the tenths digit after the decimal point and it will change from 10 to 9, and now the hundredths digit after the decimal point will become 10

We'll borrow ten from the hundredths digit after the decimal point and it will change from 10 to 9, and now the thousandths digit after the decimal point will become 10

Now that we know how to solve the exercise, let's subtract the thousands after the decimal point:

102=8 10-2=8

Let's subtract the hundreds after the decimal point:

95=4 9-5=4

Let's subtract the tenths after the decimal point:

93=6 9-3=6

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

90=9 9-0=9

01= 0-1=

Given that we cannot subtract, we will instead borrow ten from the ones digit of the whole number and we should obtain the following:

101=9 10-1=9

Remember that we borrowed ten from the ones digit, as shown below:

311=1 3-1-1=1

And we obtain:

310.000110.352199.648 310.000\\-110.352\\199.648

3

Final Answer

199.648

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Add zeros to align decimal places before subtracting
  • Borrowing: When subtracting 0-2, borrow from leftmost non-zero digit
  • Check: Add your answer to subtrahend: 199.648 + 110.352 = 310.000 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to align decimal places properly
    Don't start subtracting 310 - 110.352 without adding zeros = wrong alignment! This causes errors in place value positioning. Always write 310 as 310.000 first to match decimal places.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I need to add zeros to 310?

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Adding zeros helps you align the decimal places correctly! Write 310 as 310.000 so each digit lines up with the corresponding place value in 110.352.

How do I borrow when there are multiple zeros?

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Start from the leftmost non-zero digit and work your way right. In this problem, borrow from the hundreds place (3), then cascade the borrowing through each zero until you reach the digit you need.

What happens to each digit when I borrow?

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The digit you borrow from decreases by 1, and the digit you borrow to increases by 10. Keep track of each change as you work from left to right.

How can I check if my subtraction is correct?

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Use addition to verify: Add your answer (199.648) to the number you subtracted (110.352). If you get the original number (310.000), your answer is correct!

Why is borrowing across zeros so confusing?

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It's like a chain reaction! Each zero becomes 10 when you borrow from it, but then becomes 9 after lending to the next digit. Practice with simpler examples like 10023 100 - 23 first.

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