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QuestionIdentify Shelly's mistake in the order of operations for 22(3−8)÷5−12^{2}(3-8) \div 5-1. Where did she go wrong?

Studdy Solution

STEP 1

Assumptions1. The original expression is (3−8)÷5−1^{}(3-8) \div5-1 . Shelly's steps are as follows - Step1 =(−5)÷5−1=^{}(-5) \div5-1 - Step =4(−5)÷5−1=4(-5) \div5-1 - Step3 =−20÷5−1=-20 \div5-1 - Step4 =−20÷4=-20 \div4 - Step5 =−5=-5
3. We need to find the step where Shelly made a mistake.

STEP 2

Let's evaluate the original expression step by step and compare it with Shelly's steps.
First, we need to perform the operation in the parentheses.
22(−8)÷5−1=22(−5)÷5−12^{2}(-8) \div5-1 =2^{2}(-5) \div5-1

STEP 3

Shelly's Step1 matches our calculation, so she did not make a mistake in this step.
Now, let's simplify the expression further by calculating the exponent.
22(−5)÷5−1=(−5)÷5−12^{2}(-5) \div5-1 =(-5) \div5-1

STEP 4

Shelly's Step2 matches our calculation, so she did not make a mistake in this step.
Now, let's simplify the expression further by performing the multiplication.
4(−)÷−1=−20÷−14(-) \div-1 = -20 \div-1

STEP 5

Shelly's Step3 matches our calculation, so she did not make a mistake in this step.
Now, let's simplify the expression further by performing the division.
−20÷5−1=−4−1-20 \div5-1 = -4-1

STEP 6

Shelly's Step4 does not match our calculation. She incorrectly calculated −20÷5−1-20 \div5-1 as −20÷4-20 \div4 instead of −4−1-4-1. Therefore, Shelly made a mistake in Step4.
The correct solution isShelly made a mistake in Step4.

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