Question

jordan tried to evaluate an expression. here is his work:
(60 ÷ 3·2 + 2) − (2 + 3) + 2³
= (20·2 + 2) − 5 + 2³ step 1
= (40 + 2) − 5 + 2³ step 2
= 42 − 5 + 2³ step 3
= 42 − 5 + 8 step 4
= 42 − 13 step 5
= 29 step 6
is jordans work correct?
no, jordan made a mistake going from the given expression to step 1. jord should have multiplied 3 and 2 before dividing. the order of operations says to multiply before you divide.
no, jordan made a mistake going from step 4 to step 5. jordan should have subtracted 5 from 42 before adding. the order of operations says to add and subtract from left to right.

Explanation:

Step1: Analyze the order of operations

In mathematics, for expressions with multiple operations, we follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division (from left - to - right), Addition and Subtraction (from left - to - right)).
For the given expression \((60\div3\cdot2 + 2)-(2 + 3)+2^{3}\), in the part \(60\div3\cdot2\), division and multiplication are at the same level and should be performed from left - to - right. So \(60\div3\cdot2=(60\div3)\cdot2 = 20\cdot2=40\). Jordan's Step 1 is correct for this part.
For the exponent \(2^{3}=2\times2\times2 = 8\), which is also correct in Jordan's work.

Step2: Check the addition and subtraction order

In Step 4, we have \(42-5 + 8\). According to the order of operations (left - to - right for addition and subtraction), we should first calculate \(42-5=37\), and then \(37 + 8=45\). But Jordan calculated \(5 + 8=13\) first and then \(42-13\).

Answer:

No, Jordan made a mistake going from Step 4 to Step 5. Jordan should have subtracted 5 from 42 before adding. The order of operations says to add and subtract from left to right.