Question

Diya used modeling to find 2.82÷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÷3=0.94. Which of the following is the correct conclusion about Diya's quotient of 0.94? 1) The quotient is incorrect because each of the three groups should have 4 tenths and 7 hundredths. The correct quotient is 0.47. 2) The quotient is incorrect because each of the three groups should have 4 tenths and 7 hundredths. The correct quotient is 0.47. 3) The quotient is incorrect because each of the three groups should have 7 tenths and 6 hundredths. The correct quotient is 0.76. 4) The quotient is incorrect because each of the three groups should have 7 tenths and 6 hundredths. The correct quotient is 0.76. 5) The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04. 6) The quotient is correct because 27 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04. 7) The quotient is correct because 28 tenths divided by 3 is 0.9 and 12 hundredths divided by 3 is 0.04.

Answer 1

the correct quotient of
`\( 2.82 / 3 \)` is
`\( 0.69 \)`, and not
`\( 0.94 \)` as Diya concluded.

Let's analyze Diya's approach to dividing 2.82 by 3 and see if her conclusion that the quotient is 0.94 is correct.

Diya's method:

1. She regrouped 2 as 20 tenths.

2. She regrouped 0.82 as 7 tenths and 10 hundredths.

3. She then divided the tenths and hundredths by 3.

Now, let's follow her method:

-
`\( 2 \)` tenths divided by 3 is
`\( (20)/(3) \)` tenths, which equals to
`\( 6 \)` tenths with
`\( 2 \)` tenths remaining.

-
`\( 2 \)` remaining tenths is
`\( 20 \)` hundredths, added to the
`\( 7 \)` tenths previously regrouped from 0.82 and the
`\( 10 \)` hundredths gives us
`\( 27 \)` hundredths in total.

-
`\( 27 \)` hundredths divided by 3 is
`\( (27)/(3) \)` hundredths, which equals to
`\( 9 \)` hundredths.

Adding these together:

-
`\( 6 \) tenths is \( 0.6 \)`.

-
`\( 9 \) hundredths is \( 0.09 \)`.

So,
`\( 0.6 + 0.09 = 0.69 \)`.

Therefore, the correct quotient of
`\( 2.82 / 3 \)` is
`\( 0.69 \)`, and not
`\( 0.94 \)` as Diya concluded.

Looking at the given options, none of them correctly states that the quotient is
`\( 0.69 \)`. There may be an error in the options provided, as none of them match the correct calculation. However, the correct conclusion is closest to options 3 and 4, except for the quotient value which should be 0.69 instead of 0.76. Diya's quotient of 0.94 is incorrect because the division of tenths and hundredths she performed does not give 9 tenths and 4 hundredths per group.