Solve Vertical Subtraction: 76 minus 57 Step-by-Step

Multi-Digit Subtraction with Borrowing

7657776 \begin{aligned} &76 \\ -& \\ &57 \\ &\underline{\phantom{776}} & \\ \end{aligned}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:03 Let's solve a subtraction problem.
00:06 First, we'll subtract two digits each time.
00:10 Since 6 is less than 7.
00:13 We need to borrow 1 from the tens place.
00:17 So, 6 becomes 16.
00:20 Now, subtract 7 from 16.
00:23 Write the result in the one's place.
00:27 Next, subtract the tens digits.
00:31 And there you have it, the final answer!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

7657776 \begin{aligned} &76 \\ -& \\ &57 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this vertical subtraction problem 765776 - 57, let's go through the steps:

  • Step 1: Align the numbers by place value.
    The problem is set up vertically as follows: 7657 \begin{aligned} & 76 \\ - & 57 \\ \end{aligned}
  • Step 2: Start with the units digit.
    From the 6 in the units place of 76, subtract the 7 in the units place of 57:
    Since 6 is less than 7, we need to borrow 1 ten from the tens place of 76.
    The tens digit of 76 changes from 7 to 6 (since we borrowed one ten), and the units digit becomes 16.
  • Step 3: Subtract the units digit.
    Subtract 7 from 16, resulting in 9.
    This is written in the units place of the answer.
  • Step 4: Subtract the tens digit.
    In the tens column, subtract 5 (from 57) from 6 (the new tens of 76 after borrowing), resulting in 1.

The final calculation looks like this:

765719 \begin{aligned} & 76 \\ - & 57 \\ \hline & 19 \\ \end{aligned}

Therefore, the result of the subtraction is 1919.

3

Final Answer

19

Key Points to Remember

Essential concepts to master this topic
  • Borrowing Rule: When top digit is smaller, borrow 1 from left neighbor
  • Technique: Change 76 to 616 by borrowing: 16 - 7 = 9
  • Check: Add your answer to subtrahend: 19 + 57 = 76 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting smaller number from larger in each column
    Don't subtract 6 - 7 = 1 by switching the order = wrong answer 11 or 29! This ignores place value and borrowing rules. Always borrow from the left column 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 and get 1?

+

Because place value matters! The 6 represents 6 ones, and you can't take away 7 ones from just 6 ones. You need to borrow from the tens place first.

What happens to the tens digit when I borrow?

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The tens digit decreases by 1 because you're lending one ten (which equals 10 ones) to the units place. So 7 tens becomes 6 tens after borrowing.

How do I remember when to borrow?

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Simple rule: If the top digit is smaller than the bottom digit in any column, you must borrow! Look at each column from right to left.

Can I check my subtraction answer?

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Yes! Add your answer to the number you subtracted. If you get the original number, you're correct: 19+57=76 19 + 57 = 76

What if I need to borrow from zero?

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When borrowing from 0, you need to keep going left until you find a digit you can borrow from. The 0 becomes 10, then you borrow 1 from it.

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