Subtract Decimals: 76 - 10.3213 Step-by-Step Solution

Decimal Subtraction with Borrowing

Circle the correct answer for the following exercise:

76-10.3213

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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 positions
00:09 When we need to subtract a number larger than what we have
00:12 Borrow from the next possible number
00:20 The digit will decrease by 1, and the previous digit will increase by 10
00:23 Use the same method and continue until we reach the last digit
00:57 Now subtract from the larger number
01:04 Place and continue to subtract and place accordingly
01:22 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:

76-10.3213

2

Step-by-step solution

In order to avoid confusion whilst solving the exercise, add four zeros to the number 76 as follows:

76.000010.3213 76.0000\\-10.3213\\

Now let's proceed to solve the exercise in the correct order:

Let's subtract the tens of thousands after the decimal point:

03= 0-3=

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

The tens digit of the whole number before the decimal point will become 5, and 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

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

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

103=7 10-3=7

Let's subtract the thousandths after the decimal point:

91=8 9-1=8

Let's subtract the hundredths after the decimal point:

92=7 9-2=7

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:

50=5 5-0=5

71=6 7-1=6

And we obtain the following answer:

76.000010.321365.6787 76.0000\\-10.3213\\65.6787

3

Final Answer

65.6787

Key Points to Remember

Essential concepts to master this topic
  • Alignment: Add zeros to align decimal places properly
  • Borrowing: When 0 - 3 is impossible, borrow from left digits
  • Verification: Check that 65.6787 + 10.3213 = 76.0000 ✓

Common Mistakes

Avoid these frequent errors
  • Not aligning decimal places before subtracting
    Don't subtract 76 - 10.3213 without adding zeros = misaligned digits and wrong answer! This puts whole numbers against decimal places incorrectly. Always write 76 as 76.0000 first to align 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 76?

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Adding zeros like 76.0000 helps you align the decimal places correctly. Without this, you might subtract the wrong digits and get an incorrect answer!

What does borrowing mean in decimal subtraction?

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Borrowing means taking 10 from the digit to the left when you can't subtract. For example, when 0 - 3 is impossible, borrow 10 from the next digit to make it 10 - 3 = 7.

Why do I borrow from so far left in this problem?

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Since we have 76.0000 and need to subtract from the rightmost zero, we must borrow through all the zeros until we reach the 7 in the tens place. Each borrowing changes a 0 to 9 and passes 10 to the right.

How can I check if my answer is correct?

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Add your answer to the number you subtracted: 65.6787+10.3213 65.6787 + 10.3213 . If you get the original number (76), your subtraction is correct!

What if I get confused with all the borrowing?

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Take it step by step! Start from the rightmost digit and work left. Remember: when you borrow, the digit giving becomes smaller by 1, and the digit receiving becomes bigger by 10.

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