Let's break down Diya's modeling process to see whether her conclusion is correct.
Diya starts with 2.82, which she needs to divide by 3.
1. She regroups 2 as 20 tenths. This is accurate since 2 whole can be thought of as 20 tenths (20 x 0.1 = 2).
2. Next, she regroups 0.82 as 7 tenths plus 10 hundredths. This seems incorrect because 0.82 is equal to 8 tenths (0.8) plus 2 hundredths (0.02), not 7 tenths plus 10 hundredths.
If we correct Diya's regrouping, we would regroup 2.82 as follows:
- 20 tenths (from the 2 whole)
- 8 tenths (from the 0.8 part)
- 2 hundredths (from the 0.02 part)
Now, to divide these by 3:
- 20 tenths divided by 3 is 6 tenths (since 20/3 = 6 with a remainder of 2, but we're considering only whole tenths)
- The 2 remaining tenths when combined with the 8 tenths become 10 tenths which, when divided by 3, gives us a quotient of 3 tenths (since 10/3 = 3 with a remainder of 1, but again, we're considering only whole tenths).
- The 1 remaining tenth becomes 10 hundredths when combined with the 2 hundredths we already have from the 0.02, which gives us 12 hundredths (10 + 2).
- 12 hundredths divided by 3 gives us 4 hundredths (since 12/3 = 4).
Now adding the pieces together:
- 6 tenths from the 20 tenths = 0.6
- 3 tenths from the 10 tenths = 0.3
- 4 hundredths = 0.04
The correct sum is 0.6 + 0.3 + 0.04 = 0.94.
Therefore, the correct conclusion about Diya's quotient of 0.94 is:
The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04.
Please note that initially, we identified an error in the regrouping, which should technically lead to Diya's process being incorrect. However, coincidentally the error in regrouping (claiming 0.8 as 7 tenths instead of 8 tenths) did not affect the final answer since 2 tenths were not accounted for in her division but were leftover to combine with the 0.02, inadvertently leading to the same correct quotient.
Diya used modeling to find 2.82 divided by 3, She regrouped 2 as 20 tenths and regrouped 0.8 as 7 tenths plus 10 hundredths, she divided all of the tenths and hundredths into three equal groups, each group had 9 tenths and 4 hundredths. She decided that 2.82 divided by 3 = 0.94, which of the following is the correct conclusion about Diya’s quotient of 0.94
The quotient is incorrect because each of the three groups should have 4 tenths and 7 hundredths. The quotient is 0.47
The quotient is incorrect because each of the three groups should have 7 tenths and 6 hundredths. The correct quotient is 0.76
The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04
The quotient is correct because 28 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04
1 answer
1 answer