Diya used modeling to find 2.82 divide by 3

Question

She regrouped 2 as 20 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 divide 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 correct quotient is 0.47.

The quotients 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 09 and 12 hundredths divided by 3 is 0.04.

The quotients is correct because 28 tenths divided by 3 is 0.9 and 12 hundredths divide by 3 is 0.04

GPT-4o mini · Answer

Let's analyze Diya's calculations to determine if her quotient of 0.94 is correct.

Understanding Diya's regrouping: Diya initially thinks of 2.82 as:
- 2 as 20 tenths (which is actually correct since 2 = 20/10)
- 8 as 8 tenths (which is actually 8/10)
- 0.2 as 2 hundredths (which is actually 2/100)
So, 2.82 can be represented as:
- 28 tenths + 2 hundredths = 28 tenths and 2 hundredths in total.
Dividing into three equal groups: Now, let's divide:
- Tenths: 28 tenths divided by 3 equals 9 tenths (since 3 goes into 28 nine times with some remainder).
- To see the exact division: 28 tenths / 3 = 9 tenths with a remainder of 1 tenth (which is 10 hundredths).
- This leaves us with 1 tenth = 10 hundredths, bringing the total to 12 hundredths.
Calculating the division:
- Each group would contain:
  - 9 tenths (or 0.9) and 12 hundredths (or 0.12).
- So, when adding these together:
  - 0.9 + 0.12 = 0.9 + 0.04 = 0.94.

From this breakdown, we can see that Diya's calculation is actually correct:

Conclusion: The correct answer is the fourth option:

"The quotient is correct because 28 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04."

So Diya's final result of 0.94 is indeed accurate.