Suppose you have 4 mats, 44 strips, and 11 units for a total count of 851 . Briefly describe the exchanges you would make to keep the same total count but have the
smallest possible number of manipulative pieces.
What exchanges would give the smallest possible number of manipulatives?
A. Replace mat(s) with strip(s) and replace strip(s) with unit(s).
B. Replace unit(s) with strip(s).
C. Replace strip(s) with mat(s).
D. Replace mat(s) with strip(s).
E. Replace unit(s) with strip(s) and replace strip(s) with mat(s).
F. Replace strip(s) with unit(s).

Ask by Sandoval Cook. in the United States

Mar 31,2025

Question

Suppose you have 4 mats, 44 strips, and 11 units for a total count of 851 . Briefly describe the exchanges you would make to keep the same total count but have the
smallest possible number of manipulative pieces.
What exchanges would give the smallest possible number of manipulatives?
A. Replace mat(s) with strip(s) and replace strip(s) with unit(s).
B. Replace unit(s) with strip(s).
C. Replace strip(s) with mat(s).
D. Replace mat(s) with strip(s).
E. Replace unit(s) with strip(s) and replace strip(s) with mat(s).
F. Replace strip(s) with unit(s).

Ask by Sandoval Cook. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

To minimize the number of manipulative pieces, we need to make exchanges that result in the smallest possible number of pieces while maintaining the same total count.

Let's analyze the options:

A. Replace $$ \square $$ mat(s) with $$ \square $$ strip(s) and replace $$ \square $$ strip(s) with $$ \square $$ unit(s).
This option involves replacing mats with strips and strips with units. However, we need to consider the total count and the number of pieces after each exchange.

B. Replace $$ \square $$ unit(s) with $$ \square $$ strip(s).
This option involves replacing units with strips. We need to check if this exchange maintains the same total count.

C. Replace $$ \square $$ strip(s) with $$ \square $$ mat(s).
This option involves replacing strips with mats. We need to check if this exchange maintains the same total count.

D. Replace $$ \square $$ mat(s) with $$ \square $$ strip(s).
This option involves replacing mats with strips. We need to check if this exchange maintains the same total count.

E. Replace $$ \square $$ unit(s) with $$ \square $$ strip(s) and replace $$ \square $$ strip(s) with $$ \square $$ mat(s).
This option involves replacing units with strips and strips with mats. We need to check if this exchange maintains the same total count.

F. Replace $$ \square $$ strip(s) with $$ \square $$ unit(s).
This option involves replacing strips with units. We need to check if this exchange maintains the same total count.

Let's calculate the total count after each exchange and determine which option results in the smallest possible number of manipulative pieces.
Calculate the value by following steps:
- step0: Calculate:
  $$4	imes 44+11$$
- step1: Multiply the numbers:
  $$176+11$$
- step2: Add the numbers:
  $$187$$
The total count is 187.

Now, let's analyze each option:

A. Replace $$ \square $$ mat(s) with $$ \square $$ strip(s) and replace $$ \square $$ strip(s) with $$ \square $$ unit(s):
- 4 mats = 44 strips
- 44 strips = 11 units
- Total count = 4 mats + 11 units = 15 units

B. Replace $$ \square $$ unit(s) with $$ \square $$ strip(s):
- 11 units = 44 strips
- Total count = 44 strips

C. Replace $$ \square $$ strip(s) with $$ \square $$ mat(s):
- 44 strips = 4 mats
- Total count = 4 mats

D. Replace $$ \square $$ mat(s) with $$ \square $$ strip(s):
- 4 mats = 44 strips
- Total count = 44 strips

E. Replace $$ \square $$ unit(s) with $$ \square $$ strip(s) and replace $$ \square $$ strip(s) with $$ \square $$ mat(s):
- 11 units = 44 strips
- 44 strips = 4 mats
- Total count = 4 mats

F. Replace $$ \square $$ strip(s) with $$ \square $$ unit(s):
- 44 strips = 11 units
- Total count = 11 units

The smallest possible number of manipulative pieces is achieved by option B, where 11 units are replaced with 44 strips, resulting in a total count of 44 strips.
Replace 11 units with 44 strips to minimize the number of manipulative pieces to 44 strips.

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