Solve Vertical Subtraction: 53 minus 36

Subtraction with Borrowing Across Places

5336776 \begin{aligned} &53 \\ -& \\ &36\\ &\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 we consider a shortage of 2 digits, and then we put
00:06 3 is less than 6
00:09 Therefore we subtract 1 from the tens and add this amount to the ones
00:15 Meaning now instead of 3 we'll have 13
00:20 We subtract the ones from the ones plus the ten
00:23 We put in the ones
00:27 We subtract tens from tens, and put in the tens
00:30 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

5336776 \begin{aligned} &53 \\ -& \\ &36\\ &\underline{\phantom{776}} & \\ \end{aligned}

2

Step-by-step solution

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

  • Step 1: Align the numbers by their place values, so the digits in the same position are directly on top of each other.

  • Step 2: Subtract the digits in the ones place and perform borrowing if necessary.

  • Step 3: Subtract the digits in the tens place after performing any borrowing from the previous step.

Now, let's work through each step:

Step 1: Align the numbers vertically:

5336 \begin{aligned} & 53 \\ - & 36 \\ \end{aligned}

Step 2: Starting with the ones place, we see that 3 (in the minuend) is less than 6 (in the subtrahend). So we need to borrow.

  • Borrow 1 from the tens place of 53, giving the tens place a value of 4. The borrowed number converts the ones place's 3 into 13.

Now subtract: 136=713 - 6 = 7.

The new arrangement looks like this:

54  13   3    612312345 \begin{aligned} \cancel{5}&4 ~~13 \\ -~~~&3~~~~6 \\ \overline{\phantom{123}}& \overline{\phantom{12345}} \\ \end{aligned}

Step 3: Move to the tens place. After borrowing, the new value is 4.

Subtract: 43=14 - 3 = 1.

Thus, the final result is:

533617 \begin{aligned} & 53 \\ - & 36 \\ & \underline{17} \\ \end{aligned}

Therefore, the result of the subtraction 533653 - 36 is 17\boxed{17}.

3

Final Answer

17

Key Points to Remember

Essential concepts to master this topic
  • Borrowing Rule: When top digit is smaller, borrow from next place
  • Technique: Convert 3 to 13 by borrowing 1 from tens (5 becomes 4)
  • Check: Add your answer to subtrahend: 17 + 36 = 53 ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting smaller from larger regardless of position
    Don't subtract 3 - 6 = 3 by flipping to 6 - 3! This ignores place value and gives wrong answers like 23 instead of 17. Always borrow 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 - 3 when I see 3 - 6?

+

Because position matters in subtraction! When you flip numbers, you're changing the problem completely. Always subtract the bottom number from the top number in each column.

What does borrowing actually mean?

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Borrowing means trading one ten for ten ones! When you borrow 1 from the tens place (5), it becomes 4 tens, and the ones place (3) becomes 13 ones.

How do I know when I need to borrow?

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You need to borrow whenever the top digit is smaller than the bottom digit in any column. Look at each column from right to left!

What if the tens digit is 0 and I need to borrow?

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You'll need to borrow from the hundreds place first! Turn 0 into 10, then borrow 1 from there. It's like borrowing through multiple places.

Can I check my answer another way besides adding?

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Yes! You can also count up from 36 to 53: 36 + ? = 53. Count: 36 + 4 = 40, then 40 + 13 = 53, so 4 + 13 = 17 ✓

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