Natasha and Jorge were asked to find the quotient to the decimal division problem 18.8÷1.6

Question

. 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.(2 points)

Answer 1

To solve the decimal division problem \( 18.8 \div 1.6 \), we can perform the calculation as follows:

1. First, let's eliminate the decimals by multiplying both numbers by 10. This gives us: \[ 18.8 \times 10 = 188 \] \[ 1.6 \times 10 = 16 \] So we now need to calculate: \[ 188 \div 16 \]

2. Next, we perform the division:

   • 16 goes into 18 once (1), which gives us: \[ 1 \times 16 = 16 \] Subtracting gives \( 18 - 16 = 2 \), and bringing down the next digit (8) gives us 28.
   • 16 goes into 28 once (1), which gives us: \[ 1 \times 16 = 16 \] Subtracting gives \( 28 - 16 = 12 \), and bringing down the next digit (0) gives us 120.
   • 16 goes into 120 seven times (7), which gives us: \[ 7 \times 16 = 112 \] Subtracting gives \( 120 - 112 = 8 \).

3. Therefore, \( 188 \div 16 = 11.75 \).

Thus, based on the above calculations:

• a. Natasha is correct with her answer of 11.75.
• b. I know Natasha is correct because the calculation shows \( 18.8 \div 1.6 = 11.75 \). Jorge likely made an error by incorrectly positioning the decimal point in his answer of 1.175. He may have miscalculated the number of decimal places to move when converting from division, which often happens if a student doesn't properly scale the numbers by the same factor before performing the division.