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
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.