Subtract 659 from 3008: Column Method Practice Problem

Column Subtraction with Multi-Step Borrowing

3008  659776 \begin{aligned} &3008 \\ -& \\ &~~659 \\ &\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 it's considered a borrowing of 2 digits, and then we'll place
00:06 8 is less than 9
00:09 The tens digit is also equal to 0 so we cannot borrow from it
00:12 The hundreds digit is also equal to 0 so we cannot borrow from it
00:15 We'll borrow a thousand from the thousands for the hundreds
00:19 So now instead of 0 we'll have 10, in hundreds!
00:22 And now we'll borrow ten from the hundreds for the tens
00:25 Which will change the hundreds from 10 to 9
00:29 So now instead of 0 we'll have 10, in tens!
00:32 And now we'll borrow ten from the tens for the ones
00:35 Which will change the tens from 10 to 9
00:39 So now instead of 8 we'll have 18, in ones!
00:42 Now we'll subtract ones from ones, and place in ones
00:47 Subtract tens from tens, and place in tens
00:53 Subtract hundreds from hundreds, and place in hundreds
00:57 Place 0 in the borrowed digits
01:01 Subtract thousands from thousands, and place in thousands
01:04 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

3008  659776 \begin{aligned} &3008 \\ -& \\ &~~659 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

To solve this problem, we will subtract 659 from 3008 using borrowing in the subtraction process:

  1. Line up the numbers with the larger number on top: 23008659 \begin{array}{c} \phantom{2}3008 \\ -659 \\ \end{array}

  2. Begin subtraction from the rightmost column (units place), where we have 898 - 9. Since 88 is smaller than 99, we need to borrow.

  3. Move to the tens place, which is also 00. Since we cannot borrow from a 00, move left to the hundreds place.

  4. The hundreds place is also 00, so continue to the thousands column, where we have 33:

  5. Decrease the 33 to 22 and make the hundreds column 1010. Now borrow from the hundreds column, turning it into 99 and the tens column into 1010.

  6. Finally, borrow 11 from the tens column to assist the units column: 2939   659 \begin{array}{c} {2939} \\ -~~~659 \\ \end{array} We can now do 189=918 - 9 = 9.

  7. Proceed to the tens column. 95=49 - 5 = 4.

  8. The hundreds column: 96=39 - 6 = 3.

  9. The thousands column: 20=22 - 0 = 2.

Writing down the final subtraction gives us:

29393008       65929392349 \begin{array}{c} \phantom{2939}3008 \\ -~~~~~~~659 \\ \overline{\phantom{2939}2349} \\ \end{array}

Therefore, the solution to the problem is 2349.

3

Final Answer

2349

Key Points to Remember

Essential concepts to master this topic
  • Borrowing Rule: Start from rightmost column and work left systematically
  • Zero Borrowing: Skip zeros by continuing left: 3000 becomes 2990 after borrowing
  • Verification: Add your answer to subtrahend: 2349 + 659 = 3008 ✓

Common Mistakes

Avoid these frequent errors
  • Borrowing incorrectly from zeros
    Don't try to borrow directly from a zero in the next column = impossible borrowing! You can't take 1 from 0. Always continue left until you find a non-zero digit, then work backwards making each zero become 9 and reducing the non-zero by 1.

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

What do I do when I need to borrow from a zero?

+

Keep moving left until you find a non-zero digit! In 3008 - 659, you go from the 0 in tens place to the 0 in hundreds place, then finally to the 3 in thousands place.

Why does borrowing from 3000 make it look like 2990?

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When you borrow from the 3, it becomes 2. Each zero you passed through becomes 10, then loses 1 to help the next column, leaving 9. So: thousands=2, hundreds=9, tens=9, units=10.

How can I check if my borrowing was correct?

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After borrowing, make sure you can actually do the subtraction in each column! You should have: 18-9=9, 9-5=4, 9-6=3, 2-0=2 giving you 2349.

Is there an easier way than borrowing through multiple zeros?

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Column subtraction with borrowing is the standard method you need to master. With practice, the borrowing pattern through zeros becomes automatic!

What if I get a negative number in a column?

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This means you forgot to borrow! You should never subtract a larger digit from a smaller one. Always borrow first to make the top digit larger.

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