Question

select the correct answer.
a mistake was made in the steps shown to simplify the expression. which step includes the mistake?
\\(\frac{1 + 3^2}{5} + |-10| \div 2\\)
step 1: \\(= \frac{1 + 3^2}{5} + 10 \div 2\\)
step 2: \\(= \frac{1 + 9}{5} + 10 \div 2\\)
step 3: \\(= \frac{10}{5} + 10 \div 2\\)
step 4: \\(= 2 + 10 \div 2\\)
step 5: \\(= 12 \div 2\\)
step 6: \\(= 6\\)
\\(\bigcirc\\) a. step 5
\\(\bigcirc\\) b. step 1
\\(\bigcirc\\) c. step 3
\\(\bigcirc\\) d. step 4

Explanation:

Step1: Recall Order of Operations

Order of operations (PEMDAS/BODMAS) is Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Step2: Analyze Each Step

• Step 1: Simplify absolute value \(|-10| = 10\), correct.
• Step 2: Simplify exponent \(3^2 = 9\), correct.
• Step 3: Add \(1 + 9 = 10\) in numerator, correct.
• Step 4: Divide \(\frac{10}{5}=2\), correct.
• Step 5: Here, instead of performing division \(10\div2\) first (as per order of operations: division before addition), addition \(2 + 10\) was done. This is the mistake.
• Step 6: Follows from incorrect Step 5.

Answer:

A. Step 5