Sara traces circle stencils for her project. She needs 4 rows of 6 circle stencils. She thought that 4 rows of 6 is the same as 3 rows of 8 and 2 rows of 8. Is this correct? Explain.
4 rows if 6 = 24
3 rows of 8 = 24
2 rows of 8 = 16
No, Sara's assumption is not correct. 4 rows of 6 circle stencils is not the same as 3 rows of 8 and 2 rows of 8.
To understand why, let's break down the numbers.
4 rows of 6 circle stencils means that there are 4 rows, with each row containing 6 circle stencils. This gives us a total of 4 x 6 = 24 circle stencils.
On the other hand, 3 rows of 8 and 2 rows of 8 means that there are 3 rows with 8 circle stencils each, plus 2 more rows with 8 circle stencils each. This gives us a total of 3 x 8 + 2 x 8 = 24 circle stencils as well.
Although the sum in both cases is the same, the arrangement is different. In the scenario of 4 rows of 6, we have a rectangular arrangement with 4 rows and 6 columns. In the scenario of 3 rows of 8 and 2 rows of 8, we have two separate groupings of 8 circle stencils arranged in rows.
Hence, while the total number of circle stencils is the same, the arrangement and distribution of stencils is different.
To determine whether Sara's perception is correct, let's break down both scenarios:
Sara's initial assumption:
She believed that 4 rows of 6 circle stencils is the same as 3 rows of 8 and 2 rows of 8.
Calculating the total number of stencils in Sara's assumption:
If Sara has 4 rows and each row has 6 circle stencils, the total number of stencils can be calculated as 4 x 6 = 24 stencils.
Now, let's examine Sara's alternative scenario:
She believed that 3 rows of 8 and 2 rows of 8 is the same as 4 rows of 6 circle stencils.
Calculating the total number of stencils in Sara's alternative assumption:
If Sara has 3 rows of 8 circle stencils, the total number of stencils is 3 x 8 = 24 stencils.
Similarly, if Sara has 2 rows of 8 circle stencils, the total number of stencils is 2 x 8 = 16 stencils.
When we add the stencils from both scenarios (24 + 16), the total number of stencils is 40. Therefore, her alternative assumption yields a different total compared to her initial assumption.
In conclusion, Sara's perception is incorrect. 4 rows of 6 circle stencils does not equal 3 rows of 8 and 2 rows of 8 circle stencils. The total number of stencils differs between the two scenarios.