Solve Vertical Subtraction: 482 minus 65 Step-by-Step

Vertical Subtraction with Regrouping

482  65776 \begin{aligned} &482 \\ -& \\ &~~65 \\ &\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 a subtraction of 2 digits, and then we'll place
00:06 2 is less than 5
00:09 Therefore we'll subtract 1 from the tens, and add this amount to the ones
00:14 Meaning now instead of 2 we'll have 12
00:20 Subtract the ones from the ones plus ten
00:23 Place in the ones
00:26 Subtract tens from tens, and place in tens
00:30 Place 0 in the missing digits
00:34 Subtract hundreds from hundreds, and place in hundreds
00:38 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

482  65776 \begin{aligned} &482 \\ -& \\ &~~65 \\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Set up the numbers for vertical subtraction.

  • Step 2: Perform subtraction starting from the rightmost digit (units place).

  • Step 3: Apply regrouping whenever the top digit is smaller than the digit below.

Now, let's work through each step:
Step 1: Write the numbers in vertical format aligning by place value:

48265 \begin{array}{c} 482 \\ - 65 \\ \hline \end{array}

Step 2: Subtract the digits in the units place:25 \quad 2 - 5 . Since 2 is smaller than 5, we need to regroup.

Regrouping: Borrow 10 from the tens place, making 2 become 12. The 8 in the tens place decreases by 1 to 7.

48712  65 \begin{array}{c} 4 &\cancel{8}7 \, &12 \\ -\ \ &6&5 \\ \hline \end{array}

Subtract in the units place: 125=7 12 - 5 = 7 .

Step 3: Move to the tens place: Now subtract 76=1 7 - 6 = 1 .

Finally, subtract in the hundreds place: As there’s no digit to subtract from 4, it remains 4 4 .

Therefore, after performing the subtraction, the result is:

417 \begin{array}{c} 417 \\ \end{array}

Thus, the solution to the problem is 417 417 , which corresponds to choice 2.

Therefore, the solution to the problem is 417 417 .

3

Final Answer

417

Key Points to Remember

Essential concepts to master this topic
  • Setup: Align numbers by place value in vertical format
  • Technique: Borrow 10 when top digit is smaller: 212 2 \rightarrow 12 , 87 8 \rightarrow 7
  • Check: Add your answer to the subtracted number: 417+65=482 417 + 65 = 482

Common Mistakes

Avoid these frequent errors
  • Subtracting the larger digit from the smaller digit
    Don't compute 2 - 5 as "take 2 from 5" = wrong answer 423! This ignores place value and creates incorrect results. Always borrow from the next column when the top digit is smaller.

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 2 - 5 and write 3?

+

Because you'd be ignoring place value! When the top digit is smaller, you must borrow from the next column. The 2 becomes 12, and you subtract 12 - 5 = 7.

What happens to the tens place when I borrow?

+

The tens digit decreases by 1 because you borrowed 10 from it. In this problem, the 8 becomes 7, so you calculate 7 - 6 = 1 in the tens place.

How do I know when I need to regroup?

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Look at each column from right to left. Whenever the top digit is smaller than the bottom digit, you need to borrow from the column to the left.

Can I check my answer without adding?

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Yes! You can also estimate: 482 is close to 480, and 65 is close to 70. So 480 - 70 = 410, which is very close to our answer of 417.

What if there's a zero in the number I'm borrowing from?

+

You'll need to borrow from further left! Keep moving left until you find a non-zero digit, then work your way back, turning zeros into 9s as you borrow.

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