To determine who is correct between Natasha and Jorge regarding the quotient of the decimal division problem \( 18.8 \div 1.6 \), we can perform the division.
First, we can eliminate the decimals by multiplying both numbers by 10:
\[ 18.8 \div 1.6 = \frac{188}{16} \]
Now, we need to divide \( 188 \) by \( 16 \).
Performing the division:
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\( 16 \) goes into \( 18 \) once. \[ 16 \times 1 = 16 \] Subtract \( 16 \) from \( 18 \): \[ 18 - 16 = 2 \] Bring down the next digit (8), making it \( 28 \).
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\( 16 \) goes into \( 28 \) once. \[ 16 \times 1 = 16 \] Subtract \( 16 \) from \( 28 \): \[ 28 - 16 = 12 \] Bring down a \( 0 \), making it \( 120 \).
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\( 16 \) goes into \( 120 \) seven times. \[ 16 \times 7 = 112 \] Subtract \( 112 \) from \( 120 \): \[ 120 - 112 = 8 \] Bring down a \( 0 \), making it \( 80 \).
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\( 16 \) goes into \( 80 \) five times. \[ 16 \times 5 = 80 \] Subtract \( 80 \) from \( 80 \): \[ 80 - 80 = 0 \]
Combining the results from the divisions, we find:
\[ 18.8 \div 1.6 = 11.75 \]
Thus, \( 11.75 \) is the correct answer.
Conclusion:
a. Natasha is correct.
b. We know Natasha is correct because the actual calculation of \( 18.8 \div 1.6 \) results in \( 11.75 \). Jorge's answer of \( 1.175 \) is incorrect and likely stems from a common mistake: he may have erroneously moved the decimal point too far to the left, perhaps forgetting to account for the fact that both numbers were scaled up by a factor of 10 during the calculation. This error would have resulted in an incorrect quotient.
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