Subtract 19 from 48 Using Base-10 Blocks: Visual Mathematics

Subtraction with Regrouping Base-10 Blocks

If we have 48 blocks in total and we remove 19 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 48 blocks in total and we remove 19 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

To solve the problem of finding how many blocks remain after removing 19 from 48, we will perform the subtraction operation and handle regrouping if necessary:

Step 1: Start with the original number of blocks: 48 48 .

Step 2: We need to subtract 19 from this total. Let's write this subtraction vertically:

4819 \begin{array}{c} 48 \\ - 19 \\ \hline \end{array}

Step 3: In the units column (rightmost column), we have 8 (from 48) and we need to subtract 9. Since 8 is smaller than 9, we regroup from the tens column. This leaves us with:

  • Convert one 10 from the tens place in 48, leaving 3 tens, and add that 10 to the units column, making it 18.
  • Now subtract 9 from 18 in the units column. This results in 9.

Step 4: Proceed to the tens column. We regrouped once, so we're left with 3 tens (from original 4 tens). Subtract 1 ten (from the 19) from 3 tens, leaving us with 2 tens.

Thus, the remaining amount after performing the subtraction is:

381929 \begin{array}{c} 3 & 8 \\ - 1 & 9 \\ \hline 2 & 9 \\ \end{array}

Therefore, the number of blocks remaining is 29 \boxed{29} .

3

Final Answer

29 29

Key Points to Remember

Essential concepts to master this topic
  • Regrouping Rule: Exchange one ten for ten ones when needed
  • Technique: Convert 4 tens 8 ones to 3 tens 18 ones
  • Check: Count remaining blocks or add answer to subtracted amount ✓

Common Mistakes

Avoid these frequent errors
  • Subtracting smaller from larger regardless of position
    Don't subtract 8 - 9 = 1 in the ones place! This ignores place value and gives 19 instead of 29. Always regroup from the tens place when the ones digit is too small for subtraction.

Practice Quiz

Test your knowledge with interactive questions

If we have 67 blocks in total, how many blocks will remain if we remove 5 tens and 4 ones?

FAQ

Everything you need to know about this question

Why can't I just subtract 8 - 9 = 1 in the ones place?

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Because you can't take away 9 ones when you only have 8 ones! You need to borrow from the tens place first. Think of it like breaking a 10billintoten10 bill into ten 1 bills.

How do I know when I need to regroup?

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You need to regroup when the digit you're subtracting from is smaller than the digit you're subtracting. In this case, 8 < 9, so we must regroup.

What happens to the tens place when I regroup?

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When you take one ten and break it into ones, the tens place decreases by 1. So 4 tens becomes 3 tens, but you gain 10 ones in the ones place.

Can I use base-10 blocks to check my answer?

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Yes! Start with 48 blocks (4 tens + 8 ones), remove 19 blocks (1 ten + 9 ones), and count what's left. You should have 2 tens and 9 ones = 29 blocks total.

Is there another way to think about this problem?

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You can think of it as counting up from 19 to 48. From 19 to 20 is 1, from 20 to 48 is 28, so 1 + 28 = 29 total.

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