Jillian simplified the expression 7+3⋅(10−6)2 in the following way:
7+3⋅(10−6)2
7+3⋅(4)2
7+3⋅16
10⋅16
160
Part A: Explain, using complete sentences, what Jillian's error was.
Part B: Show how the expression should have been simplified using a similar format.
Assuming you meant:
7+3*(10−6)^2
Here are the proper steps, you decide where the error was in the original
= 7+3*(4)^2
= 7+3*16
= 7+48
= 55
Part A: Jillian's error was incorrectly simplifying the expression when she squared the result inside the parentheses. Instead of squaring the 4, she combined the numerical values of the expression without properly following the order of operations.
Part B: To simplify the expression correctly, we need to follow the correct order of operations (parentheses, exponents, multiplication/division, and addition/subtraction):
7 + 3 * (10 - 6)^2
= 7 + 3 * 4^2
= 7 + 3 * 16
= 7 + 48
= 55
So, the expression should have been simplified as 55.
Part A: Jillian's error was that she did not follow the correct order of operations when simplifying the expression. According to the order of operations, parentheses should be evaluated before any other operation. However, she simplified the expression without first evaluating the expression inside the parentheses.
Part B: To simplify the expression correctly, we need to follow the order of operations. First, we evaluate the expression inside the parentheses.
Inside the parentheses: (10 - 6) = 4.
Now we substitute the value back into the original expression: 7 + 3 * 4^2.
Next, we simplify the exponent: 4^2 = 4 * 4 = 16.
Now the expression becomes: 7 + 3 * 16.
Finally, we perform the multiplication: 3 * 16 = 48.
Lastly, we add the remaining terms: 7 + 48 = 55.
Therefore, the correct simplification of the expression should be 55.