Decimal Subtraction: Solving 435.001 - 321.55 Step by Step

Decimal Subtraction with Borrowing Across Zeros

Circle the correct answer for the following exercise:

435.001-321.55

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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 appropriate place, place the decimal point in the appropriate place
00:06 Subtract accordingly, and place
00:10 When we need to subtract a number larger than what we have
00:13 Borrow from the next possible number
00:17 The next digit decreases by 1, and the previous digit increases by 10
00:20 We'll do this twice
00:24 Now subtract from the larger number
00:27 Place and continue to subtract and place accordingly
00:40 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

Circle the correct answer for the following exercise:

435.001-321.55

2

Step-by-step solution

In order to avoid confusion when solving the exercise, add the digit 0 to the number 321.550 as follows:

435.001321.550 435.001\\-321.550\\

Let's proceed to solve the exercise in order:

Subtract the thousands after the decimal point:

10=1 1-0=1

Subtract the hundreds after the decimal point:

05= 0-5=

Given that we cannot subtract, we will instead borrow a ten from the hundreds digit of the whole number (note that the tenths digit after the decimal point is also 0)

Now the tenths digit after the decimal point is 10, we will borrow from it a ten as shown below:

105=5 10-5=5

Let's subtract the tenths after the decimal point, remembering that we borrowed a ten, therefore:

1015=4 10-1-5=4

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

Let's remember that we borrowed a ten from the hundreds digit, therefore:

511=3 5-1-1=3

32=1 3-2=1

43=1 4-3=1

And we obtain the following result:

435.001321.550113.451 435.001\\-321.550\\113.451

3

Final Answer

113.451

Key Points to Remember

Essential concepts to master this topic
  • Alignment Rule: Line up decimal points before subtracting to maintain place value
  • Borrowing Technique: Add zeros when needed: 321.55 becomes 321.550 to match digits
  • Check Method: Add your answer to the subtracted number: 113.451 + 321.55 = 435.001 ✓

Common Mistakes

Avoid these frequent errors
  • Not borrowing correctly across zeros in decimal places
    Don't subtract 0-5 directly when you can't = negative digits and wrong answers! When you encounter 0-5, you must borrow from the next higher place value, even if it's across the decimal point. Always work systematically: borrow 1 from tenths (making it 10), then subtract normally.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I need to add a zero to make 321.55 into 321.550?

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Adding zeros helps you line up the decimal places properly! Since 435.001 has three decimal places and 321.55 has only two, adding a zero makes them match for easier subtraction.

What happens when I need to borrow across the decimal point?

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You treat it just like borrowing with whole numbers! The decimal point doesn't block borrowing - you can borrow from the ones place to help the tenths place, just like borrowing between any other place values.

How do I know when I need to borrow?

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You need to borrow whenever the top digit is smaller than the bottom digit you're trying to subtract from it. For example, you can't do 0-5, so you must borrow to make it 10-5.

Why does borrowing work with decimals?

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Borrowing works because place values stay the same with decimals! Just like 1 ten = 10 ones, we also have 1 tenth = 10 hundredths and 1 hundredth = 10 thousandths.

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: 113.451+321.55 113.451 + 321.55 . If you get the original number (435.001), your answer is right!

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