Question
Sunita and Jamie want to find the product of 4.3 × 5.8. They find the fraction form of the factors,
43
10
×
58
10
. Then they try to apply the Distributive Property to find the product of the numerators. Who gets the correct answer?
Sunita
43 × 58 = (40 + 3) × (50 + 8)
= (40 × 50) + (40 × 8) + (3 × 50) + (3 × 8)
= 2494
Jamie
43 × 58 = (40 + 50) × (3 + 8)
= (40 × 3) + (40 × 8) + (50 × 3) + (50 × 8)
= 990
43
10
×
58
10
. Then they try to apply the Distributive Property to find the product of the numerators. Who gets the correct answer?
Sunita
43 × 58 = (40 + 3) × (50 + 8)
= (40 × 50) + (40 × 8) + (3 × 50) + (3 × 8)
= 2494
Jamie
43 × 58 = (40 + 50) × (3 + 8)
= (40 × 3) + (40 × 8) + (50 × 3) + (50 × 8)
= 990
Answers
Answered by
GPT-4o mini
To determine who got the correct answer, we need to carefully evaluate both Sunita's and Jamie's calculations using the Distributive Property.
**Sunita's Calculation:**
She correctly breaks it down as:
\( 43 \times 58 = (40 + 3) \times (50 + 8) \)
Using the Distributive Property:
\[
(40 + 3) \times (50 + 8) = (40 \times 50) + (40 \times 8) + (3 \times 50) + (3 \times 8)
\]
Calculating each part:
- \( 40 \times 50 = 2000 \)
- \( 40 \times 8 = 320 \)
- \( 3 \times 50 = 150 \)
- \( 3 \times 8 = 24 \)
Now, adding these results:
\[
2000 + 320 + 150 + 24 = 2494
\]
Sunita's answer of 2494 is correct.
**Jamie's Calculation:**
He incorrectly breaks it down as:
\( 43 \times 58 = (40 + 50) \times (3 + 8) \)
However, this is not a valid application of the distributive property since he is grouping terms incorrectly. The correct grouping is based on the place values (tens and units) as done by Sunita.
To verify what Jamie computed:
The terms he used were:
\[
(40 + 50) \times (3 + 8) = (40 \times 3) + (40 \times 8) + (50 \times 3) + (50 \times 8)
\]
However, his groupings were wrong:
- \( 40 \times 3 = 120 \)
- \( 40 \times 8 = 320 \)
- \( 50 \times 3 = 150 \)
- \( 50 \times 8 = 400 \)
But since he added wrong pairs, it doesn't follow the original setup. The correct setup to use is by separating the tens and units correctly as per Sunita's version.
Therefore, Jamie's answer cannot be correctly evaluated since his setup is invalid, ending with the wrong calculations.
**Conclusion:**
Sunita gets the correct answer, which is 2494, and Jamie does not because he applied the Distributive Property incorrectly.
**Sunita's Calculation:**
She correctly breaks it down as:
\( 43 \times 58 = (40 + 3) \times (50 + 8) \)
Using the Distributive Property:
\[
(40 + 3) \times (50 + 8) = (40 \times 50) + (40 \times 8) + (3 \times 50) + (3 \times 8)
\]
Calculating each part:
- \( 40 \times 50 = 2000 \)
- \( 40 \times 8 = 320 \)
- \( 3 \times 50 = 150 \)
- \( 3 \times 8 = 24 \)
Now, adding these results:
\[
2000 + 320 + 150 + 24 = 2494
\]
Sunita's answer of 2494 is correct.
**Jamie's Calculation:**
He incorrectly breaks it down as:
\( 43 \times 58 = (40 + 50) \times (3 + 8) \)
However, this is not a valid application of the distributive property since he is grouping terms incorrectly. The correct grouping is based on the place values (tens and units) as done by Sunita.
To verify what Jamie computed:
The terms he used were:
\[
(40 + 50) \times (3 + 8) = (40 \times 3) + (40 \times 8) + (50 \times 3) + (50 \times 8)
\]
However, his groupings were wrong:
- \( 40 \times 3 = 120 \)
- \( 40 \times 8 = 320 \)
- \( 50 \times 3 = 150 \)
- \( 50 \times 8 = 400 \)
But since he added wrong pairs, it doesn't follow the original setup. The correct setup to use is by separating the tens and units correctly as per Sunita's version.
Therefore, Jamie's answer cannot be correctly evaluated since his setup is invalid, ending with the wrong calculations.
**Conclusion:**
Sunita gets the correct answer, which is 2494, and Jamie does not because he applied the Distributive Property incorrectly.