Solve: 768 minus 74 - Three-Digit Subtraction Problem

Three-Digit Subtraction with Borrowing

768  74776 \begin{aligned} &768 \\ -& \\ &~~74 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Solve
00:03 Each time consider borrowing 2 digits, and then we'll place
00:06 Subtract ones from ones, and place in ones
00:09 6 is less than 7
00:13 Therefore we subtract 1 from hundreds, and add this amount to tens
00:17 Meaning now instead of 6 we will have 16
00:20 Subtract tens from tens plus the ten
00:24 Place in tens
00:27 Place 0 in the missing digits
00:30 Subtract hundreds from hundreds, and place in hundreds
00:33 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

768  74776 \begin{aligned} &768 \\ -& \\ &~~74 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this subtraction problem of 76874768 - 74, we'll use vertical subtraction with borrowing:

Let's lay out the subtraction:

7 6 80 7 4 \begin{array}{c} &7\ 6\ 8 \\ - & \phantom0\ 7\ 4 \\ \hline \end{array}

Follow these steps:

  • Step 1: Start with the ones column. Subtract 4 from 8. Since 8 is larger, we simply do 84=48 - 4 = 4.

  • Step 2: Move to the tens column. Subtract 7 from 6. Here, 6 is smaller than 7, so we need to borrow from the hundreds column.
    - Cross out the "7" in hundreds place and reduce it by 1 to make it "6".
    - Change 6 in the tens place to 16.
    - Now, perform the subtraction: 167=916 - 7 = 9.

  • Step 3: Move to the hundreds column. Subtract 0 from 7 (after reduction): 70=67 - 0 = 6.

Thus, the result of the subtraction is:

6 9 4 \begin{array}{c} 6\ 9\ 4 \\ \end{array}

Therefore, the answer to the subtraction problem is 694694.

3

Final Answer

694

Key Points to Remember

Essential concepts to master this topic
  • Rule: Borrow from the next higher place value when needed
  • Technique: Change 6 to 16, reduce 7 to 6: 167=9 16 - 7 = 9
  • Check: Add your answer to the subtrahend: 694+74=768 694 + 74 = 768

Common Mistakes

Avoid these frequent errors
  • Subtracting smaller from larger regardless of position
    Don't do 8 - 6 = 2 in the tens place when you have 6 - 7 = wrong answer! This ignores place value and gives 724 instead of 694. Always borrow when the top digit is smaller than the bottom digit.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &105 \\ -& \\ &~~~~3 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

Why can't I just subtract 6 - 7 = -1?

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In basic subtraction, we don't use negative numbers! When the top digit is smaller, you must borrow from the next column to make it larger. This keeps all digits positive.

How do I remember which direction to borrow?

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Always borrow from left to right (higher place values to lower). Take 1 from hundreds, give 10 to tens. Think: "Big brother helps little brother!"

What if I need to borrow from zero?

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You'll need to borrow from the next non-zero digit first! For example, in 300 - 74, borrow from hundreds to make tens = 10, then borrow from tens to make ones = 10.

How can I check if my borrowing is correct?

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Add your answer back to what you subtracted: 694+74 694 + 74 . If you get the original number (768), your borrowing was perfect!

Is there a pattern to borrowing?

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  • When you borrow 1 from a place value, it becomes 10 in the next lower place
  • Always reduce the lending digit by 1
  • Always add 10 to the borrowing digit

What's the easiest way to avoid borrowing mistakes?

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Work column by column from right to left. Don't rush! Cross out and rewrite the new numbers clearly after each borrow so you don't get confused.

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