Question

"Archie simplified the problem incorrectly.

Archie
310 – 20 = 2 * 5+ 13
310-20 = 10 + 13
310 - 2 + 13
310-15
295
What two mistakes did Archie make when he simplified the
expression
Your answer
) How do the parentheses change the expression? Simplify to help
you justify your answer 310 - 20 + 2 x (5 + 13)"

Answer 1

Archie made two errors: not applying the distributive property and incorrect subtraction. The correct simplification of the expression '310 - 20 + 2 * (5 + 13)' is 326. Parentheses indicate that the enclosed operations are to be completed first and affect the outcome significantly.

Step-by-step explanation:

The student, Archie, made two mistakes when simplifying the expression '310 - 20 = 2 * (5 + 13)'. The first mistake was not applying the distributive property correctly; instead of multiplying 2 by both 5 and 13, he simply added 5 and 13 together. The second mistake was incorrect subtraction, resulting from the first error. Let's now simplify the expression correctly following the order of operations and the distributive property:

1. Calculate the expression inside the parentheses: (5 + 13) = 18.
2. Apply the distributive property by multiplying 2 with the result from step 1: 2 * 18 = 36.
3. Subtract 20 from 310: 310 - 20 = 290.
4. Add the result from step 2 to the result from step 3: 290 + 36 = 326.

Therefore, the correct simplified expression is 326.

Parentheses change the expression by dictating which operations should be performed first. By enclosing 5 and 13 in parentheses and placing a multiplication sign before them, we define that the sum of 5 and 13 should be multiplied by 2 first, prior to being added or subtracted from any other number in the expression.