Answer :
To help your friend correct the error, let's carefully go through the expression \(3 + \frac{x^2}{y}\) step by step, ensuring we follow the correct order of operations:
1. Square -2:
[tex]\[ (-2)^2 = 4 \][/tex]
2. Divide the squared result by 4:
[tex]\[ \frac{4}{4} = 1.0 \][/tex]
3. Add this result to 3:
[tex]\[ 3 + 1.0 = 4.0 \][/tex]
Now, revisit the steps your friend took:
1. Your friend writes:
[tex]\[ 3 + (-2)^2 \div 4 \][/tex]
2. Here, your friend correctly squares -2:
[tex]\[ 3 + 4 \div 4 \][/tex]
3. But then incorrectly subtracts 4 instead of dividing:
[tex]\[ 3 - 4 \div 4 = 3 - 1 = 2 \][/tex]
To avoid this mistake, the division should be done before any addition/subtraction after the squaring step. The correct order should be to square \(-2\) first, then divide the result by 4, and finally add 3.
Thus, the correct approach is:
B. Square -2, then divide.
This matches our correct calculations and steps. The correct result is 4.0, and the correct option is B.
1. Square -2:
[tex]\[ (-2)^2 = 4 \][/tex]
2. Divide the squared result by 4:
[tex]\[ \frac{4}{4} = 1.0 \][/tex]
3. Add this result to 3:
[tex]\[ 3 + 1.0 = 4.0 \][/tex]
Now, revisit the steps your friend took:
1. Your friend writes:
[tex]\[ 3 + (-2)^2 \div 4 \][/tex]
2. Here, your friend correctly squares -2:
[tex]\[ 3 + 4 \div 4 \][/tex]
3. But then incorrectly subtracts 4 instead of dividing:
[tex]\[ 3 - 4 \div 4 = 3 - 1 = 2 \][/tex]
To avoid this mistake, the division should be done before any addition/subtraction after the squaring step. The correct order should be to square \(-2\) first, then divide the result by 4, and finally add 3.
Thus, the correct approach is:
B. Square -2, then divide.
This matches our correct calculations and steps. The correct result is 4.0, and the correct option is B.
