Two-Digit Subtraction: Solving 53 - 38 Using Block Decomposition

Block Regrouping with Borrowing Strategy

If we have 53 blocks in total and we remove 38 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

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Step-by-step written solution

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1

Understand the problem

If we have 53 blocks in total and we remove 38 of those blocks, how many blocks remain? Remember you can break down a row of 10 blocks into single units.

2

Step-by-step solution

Let's solve the subtraction problem to find out how many blocks remain:

Given:

  • Total number of blocks = 53 53
  • Number of blocks removed = 38 38

We need to perform the subtraction of 38 38 from 53 53 :

Set up the subtraction column:

  • 5835 \begin{array}{c} \phantom{-} 5\phantom{8} \\ - \, 3\phantom{5} \\ \hline \end{array} Tens digit (5) minus 3 is 2.
  • 2338 \begin{array}{c} \phantom{2}3 \\ - \phantom{3}8 \\ \hline \end{array} Units column requires borrowing: change 5 5 tens to 4 4 tens and add 10 to units.
  • 1131815 \begin{array}{c} \phantom{1}13 \\ - \phantom{1}8 \\ \hline \phantom{1}5 \end{array}

Final calculation gives 15 15 .

Therefore, the number of blocks remaining is 15 15 .

3

Final Answer

15 15

Key Points to Remember

Essential concepts to master this topic
  • Regrouping Rule: Trade one ten-block for ten single units when needed
  • Borrowing Technique: Change 53 53 to 4 4 tens and 13 13 units: 138=5 13 - 8 = 5
  • Visual Check: Count remaining blocks in diagram: 1 1 ten plus 5 5 units equals 15 15

Common Mistakes

Avoid these frequent errors
  • Subtracting smaller digit from larger digit without borrowing
    Don't subtract 83=5 8 - 3 = 5 in the units column = wrong answer of 25 25 ! This ignores place value rules and gives an impossible result larger than what you started with. Always borrow from the tens place when the units digit being subtracted is larger.

Practice Quiz

Test your knowledge with interactive questions

If we have 85 blocks in total, how many blocks will remain if we remove 4 tens and 1 one?

FAQ

Everything you need to know about this question

Why can't I just subtract 3 from 8 in the units place?

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Because we're subtracting 38 from 53, not the other way around! The 3 3 in 53 53 is smaller than the 8 8 in 38 38 , so we need to borrow from the tens place first.

How do I know when I need to borrow?

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You need to borrow when the top digit is smaller than the bottom digit in any column. In this case, 3<8 3 < 8 in the units column, so borrowing is required.

What does borrowing actually mean with blocks?

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Borrowing means trading one ten-block for 10 single unit blocks. So 5 5 tens and 3 3 units becomes 4 4 tens and 13 13 units - same total value!

How can I check if my answer is correct?

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Add your answer back to what you subtracted: 15+38=53 15 + 38 = 53 ✓. If you get your original number, the subtraction is correct!

Why does the diagram show the blocks this way?

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The diagram shows visual groupings to help you see tens and units clearly. The large rectangles represent ten-blocks, and the small squares represent single unit blocks.

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