Solve 507 minus 69: Vertical Subtraction Problem

Subtraction with Borrowing Across Zeros

507  69776 \begin{aligned} &507 \\ -& \\ &~~69 \\ &\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 subtract 2 digits, and then place
00:06 7 is less than 9
00:09 The tens digit is also equal to 0 so we can't borrow from it
00:13 We'll borrow a hundred from the hundreds for the tens
00:17 So now instead of 0 we'll have 10, in the tens!
00:20 And now we'll borrow ten from the tens for the ones
00:23 Which will turn the tens from 10 to 9
00:26 So now instead of 7 we'll have 17, in the ones!
00:31 Now subtract ones from ones, and place in ones
00:35 Subtract tens from tens, and place in tens
00:40 Place 0 in the missing digits
00:44 Subtract hundreds from hundreds, and place in hundreds
00:47 And that's the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

507  69776 \begin{aligned} &507 \\ -& \\ &~~69 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Align the two numbers for vertical subtraction
  • Step 2: Subtract digit by digit, starting from the right
  • Step 3: Borrow when necessary, particularly across zeros

Now, let's work through each step:
Step 1: Write the numbers vertically, aligning by place values:
50769 \begin{array}{c} 507 \\ - 69 \\ \hline \end{array}

Step 2: Start subtracting from the units (right-most) digit:
Units column: 7 (from 507) minus 9 (from 69). Since 7 is smaller than 9, borrow 1 from the tens column.

Step 3: Borrowing across zeros:
Borrowing from the tens column requires rolling up to the hundreds column because there is a 0 in the tens place. Change 5 in the hundreds place to 4, making the tens place 10. Now the tens column has 9 after lending 1 to the units column, making it 17.
Subtract 9 from 17 in the units place to get 8.

Step 4: Subtract the tens column:
9 (from borrowing adjustment) minus 6 (from 69) is 3.

Step 5: Subtract the hundreds column:
4 (from borrowing adjustment) minus 0 (from 69) is 4.

Therefore, the subtraction result is:
438 \begin{array}{c} 438 \\ \end{array}

Thus, the solution to the problem is 438 438 .

3

Final Answer

438

Key Points to Remember

Essential concepts to master this topic
  • Borrowing Rule: When subtracting larger from smaller digit, borrow from left
  • Zero Strategy: Borrow from hundreds (5→4), make tens 10, then 9 after lending
  • Verify: Check answer by adding: 438 + 69 = 507 ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to adjust all affected digits when borrowing across zeros
    Don't just change the units place when borrowing across a zero = wrong calculation! The zero can't lend anything, so you must borrow from the hundreds place first. Always change 507 to 4-10-7, then subtract to get the tens place as 9 before lending to units.

Practice Quiz

Test your knowledge with interactive questions

\( \begin{aligned} &15 \\ -& \\ &~~4 \\ &\underline{\phantom{776}} & \\ \end{aligned} \)

FAQ

Everything you need to know about this question

Why can't I just subtract 9 from 7 in the units place?

+

You cannot subtract a larger number from a smaller one in subtraction! Since 7 < 9, you need to borrow 10 from the tens place, making it 17 - 9 = 8.

What do I do when there's a zero in the tens place?

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Zeros can't lend anything! You need to borrow from the next column to the left. Change the hundreds digit from 5 to 4, and the zero becomes 10. Now you can lend from the tens to the units place.

How do I keep track of all the changes when borrowing?

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Write it step by step: 507 → 4-10-7 → 4-9-17. First borrow from hundreds to tens, then from tens to units. Each step shows what happens to all three digits.

Is there an easier way to check my answer?

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Yes! Add your answer to the number you subtracted. If 438 + 69 = 507, then your subtraction is correct. Addition is the opposite of subtraction!

What if I get confused about which direction to borrow?

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Always borrow from left to right - from a larger place value to a smaller one. Think: hundreds → tens → units. You're moving value from bigger places to smaller places.

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