Break up 31 into 3 tens and 1 one

Question

Break up 11 into 1 ten and 1 one
So we're going to make an array using base ten blocks, that has ? columns and 11 ?.

Answer 1

Let's break down your request step by step.

1. Breaking up 31 into base ten blocks:

   • 31 can be represented as 3 tens (which equals 30) and 1 one.
   • So, \( 31 = 3 \times 10 + 1 \times 1 \).

2. Breaking up 11 into base ten blocks:

   • 11 can be represented as 1 ten and 1 one.
   • So, \( 11 = 1 \times 10 + 1 \times 1 \).

3. Creating an array using base ten blocks:

   • You mentioned that we're going to make an array that has "? columns" and "11 ?".
   • From the breakdowns:
     • We already established that 31 can be arranged in columns of tens and ones. To find out how to represent 11 in a similar format, we could see how they relate.

Arranging in columns:

• If we're considering the number 11, we can interpret it as having:
  • 1 column of tens (representing 1 ten).
  • 1 column of ones (representing 1 one).

Putting it together, if we're making an array using base ten blocks for 31 and 11, it seems like you would be interested in:

• Array representation for 31: 3 columns (for the 3 tens) and 1 column (for the 1 one).
• Array representation for 11: 1 column (for the 1 ten) and 1 column (for the 1 one).

So, the final interpretation would be:

• You can create an array with 1 column of tens and 1 column of ones to represent 11. If you're directly constructing, you could be looking for an array with 3 columns for tens and 1 column for ones to give a visual representation of 31.

If you're asking how many columns the total array would have:

• If you're looking at the maximum representation of either, you can use 3 columns for tens (from 31) and if you align the 1 column of tens from 11, the total makes 4 columns (3 for the tens and possibly 1 for the ones for 31).

In summary:

• The array has 3 columns for tens and 1 column for ones, for a total of 4 columns visually if you track the sum resemblance.

Answer 2

how many columns

Answer 3

To clarify how many columns there are based on your earlier descriptions of breaking up 31 and 11:

1. For 31:

   • You have 3 columns for tens (from breaking down 31 into 3 tens) and 1 column for ones.

2. For 11:

   • You have 1 column for tens (from breaking down 11 into 1 ten) and 1 column for ones.

Now, if we consider how many columns are created for both numbers in an array:

• For 31, you could say it creates 4 columns total:
  • 3 columns (tens) + 1 column (ones) = 4 columns.

Thus, if we are structuring it based on the largest number (which can potentially represent both depending on context), you would typically represent the columns based on the composition of the larger number:

• If we only consider 31 for the entirety of the array, we have 4 columns (3 tens + 1 one).

So to directly answer your question: The array has 4 columns when considering how we can break down 31.