Natasha and Jorge were asked to find the quotient to the decimal division problem 18.8÷1.6. Natasha says her answer is 11.75. Jorge says his answer is 1.175. a. Who is correct? Natasha or Jorge? b. Explain how you know who is correct. Include in your explanation at least one possible error the student who was incorrect made.
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To determine who is correct, we need to divide 18.8 by 1.6 and compare the answer to Natasha's and Jorge's responses.
a. To find the quotient, we divide 18.8 by 1.6:
18.8 ÷ 1.6 = 11.75
Natasha's answer is indeed correct. Therefore, Natasha is correct, not Jorge.
b. Natasha's calculation is accurate, as 18.8 divided by 1.6 equals 11.75. On the other hand, Jorge made an error by misplacing the decimal point in his answer. He placed the decimal two places to the right instead of one, resulting in 1.175. This indicates that Jorge made a mistake while determining where to place the decimal.
Based on the information provided, Natasha is correct, and Jorge is incorrect.
To determine who is correct, we can calculate the quotient ourselves.
Dividing 18.8 by 1.6:
18.8 ÷ 1.6 = 11.75
Therefore, Natasha's answer of 11.75 is correct.
One possible error Jorge could have made is incorrect placement of the decimal point. He may have mistakenly moved the decimal point one place to the right, resulting in an incorrect answer of 1.175.
a. Natasha is correct.
b. To determine who is correct, we need to perform the division calculation 18.8 ÷ 1.6 and compare the results.
To start, let's divide 18.8 by 1.6 using long division:
11.75
____________
1.6 | 18.8
First, divide 1 by 1.6, which results in approximately 0.625. Write this above the line.
Next, multiply 0.625 by 1.6, which gives us 1 (tenths place).
Subtract 1 from 18.8, which equals 17.8. Bring down the next digit (8) and place it next to 17.
Divide 17.8 by 1.6, which results in approximately 11.125 (hundredths place).
Multiply 0.125 by 1.6, which gives us 0.2 (thousandths place).
Subtract 0.2 from 17.8, which equals 17.6.
The process continues until we achieve the desired level of precision. However, since the problem does not specify how many decimal places are required, we will stop here.
Therefore, the correct quotient for 18.8 ÷ 1.6 is 11.75.
Now, let's discuss the errors made by each student:
- Natasha's Error (Incorrect): Natasha mistakenly places the decimal point one digit too early. Instead of 11.75, the correct answer is 1.175. Her error is in incorrectly calculating the decimal places when dividing.
- Jorge's Error (Incorrect): Jorge also places the decimal point one digit to the right. Instead of 1.175, the correct answer is 11.75. His error is in incorrectly calculating the decimal places when dividing.
In conclusion, Natasha is correct with her answer of 11.75 for the quotient 18.8 ÷ 1.6.