Solve the Subtraction Equation: 7800 minus 690

Subtraction Algorithm with Borrowing Across Zeros

Solve the equation:

7800690= 7800-690=

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the equation:

7800690= 7800-690=

2

Step-by-step solution

To solve the problem 78006907800 - 690, we will follow these steps:

  • Identify the numbers: The minuend is 7800, and the subtrahend is 690.
  • Perform the subtraction: We will subtract 690 from 7800.
  • Calculate step-by-step:

Let's perform the subtraction 78006907800 - 690:

Arrange the numbers so that they align by place value:

7800 690 \begin{array}{c} 7800 \\ -\ 690 \\ ------ \end{array}

Subtract each column starting from the rightmost digit (units place):

  • The units place: 00=00 - 0 = 0.
  • The tens place: Since 898 - 9 would require borrowing, borrow 1 (100) from 700, making it 7 becomes 6 (600, or 60 in the borrowed context) and 10 becomes 18 in the tens column. Now 189=918 - 9 = 9.
  • The hundreds place: After borrowing, 66=06 - 6 = 0.
  • The thousands place: 70=77 - 0 = 7.

Writing down the results of each place value, we find that:

7800 6907110 \begin{array}{c} 7800 \\ -\ 690 \\ ------ \\ 7110 \end{array}

Thus, the solution to 78006907800 - 690 is 71107110.

The correct answer, according to the multiple-choice options provided, is choice 2: 7110\mathbf{7110}.

3

Final Answer

7110 7110

Key Points to Remember

Essential concepts to master this topic
  • Rule: Align numbers by place value before subtracting vertically
  • Technique: Borrow from thousands: 7800 becomes 7710 when borrowing for tens
  • Check: Add result to subtrahend: 7110 + 690 = 7800 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to borrow when subtracting larger digits
    Don't try 0 - 9 = -9 in tens place without borrowing = negative impossible result! This creates wrong digits and completely incorrect answers. Always borrow from the next column when the top digit is smaller.

Practice Quiz

Test your knowledge with interactive questions

Choose the correct answer:

\( 693+705=\text{ ?} \)

FAQ

Everything you need to know about this question

Why can't I just subtract 0 - 9 in the tens place?

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You can't have negative digits in standard subtraction! When the top digit is smaller, you must borrow from the next column to make the subtraction possible.

How do I borrow when there's a zero in the hundreds place?

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First borrow from the thousands place to make the hundreds place 10, then immediately borrow 1 from that to make the tens place 10. This creates a chain reaction of borrowing.

What does borrowing actually mean?

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Borrowing means taking 1 from a higher place value (like taking 100 from hundreds) and adding 10 to the lower place value (making tens worth 10 more). It's like trading bills for coins!

How can I check if my subtraction is correct?

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Add your answer to the number you subtracted. If you get the original larger number, you're right! For example: 7110+690=7800 7110 + 690 = 7800

Is there an easier way to do this subtraction?

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You could break it down: 7800700+10=7100+10=7110 7800 - 700 + 10 = 7100 + 10 = 7110 . But learning the standard algorithm helps with all subtraction problems!

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