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\\)
a. step 1
b. step 3
c. step 4
d. step 5

Explanation:

Step 1: Analyze Step 1

The original expression is \(\frac{1 + 3^2}{5} + \vert -10 \vert \div 2\). First, calculate the exponent and absolute value. \(3^2 = 9\), \(\vert -10 \vert = 10\). So Step 1: \(\frac{1 + 9}{5} + 10 \div 2\) (Wait, the given Step 1 is \(\frac{1 + 3^2}{5} + 10 \div 2\)? Wait no, the user's Step 1 is written as \(\frac{1 + 3^2}{5} + 10 \div 2\)? Wait the image shows Step 1: \(\frac{1 + 3^2}{5} + 10 \div 2\)? Wait no, let's re - examine. The original expression is \(\frac{1 + 3^2}{5}+\vert - 10\vert\div2\). Let's compute each step:

First, \(3^2=9\), so \(1 + 3^2=1 + 9 = 10\), \(\vert - 10\vert=10\).

Step 1: The expression in Step 1 is \(\frac{1 + 3^2}{5}+10\div2\)? Wait no, the user's Step 1 is written as \(\frac{1 + 3^2}{5}+10\div2\)? Wait the image shows Step 1: \(\frac{1 + 3^2}{5}+10\div2\)? Wait no, let's check the steps again.

Wait the steps are:

Step 1: \(\frac{1 + 3^2}{5}+10\div2\) (Wait, no, the original expression has \(\vert - 10\vert\div2\), and \(\vert - 10\vert = 10\), so \(\vert - 10\vert\div2=10\div2\). Then \(3^2 = 9\), so \(1+3^2=1 + 9 = 10\), so \(\frac{1 + 3^2}{5}=\frac{10}{5}=2\).

Wait Step 1: The given Step 1 is \(\frac{1 + 3^2}{5}+10\div2\)? Wait no, the user's Step 1 is written as \(\frac{1 + 3^2}{5}+10\div2\)? Wait the image shows Step 1: \(\frac{1 + 3^2}{5}+10\div2\)? Wait maybe I misread. Wait the original problem's Step 1: Let's look at the image again. The first step is \(\frac{1 + 3^2}{5}+10\div2\)? Wait no, the original expression is \(\frac{1 + 3^2}{5}+\vert - 10\vert\div2\). So \(\vert - 10\vert = 10\), so \(\vert - 10\vert\div2 = 10\div2\). And \(3^2=9\), so \(1 + 3^2=1+9 = 10\). So Step 1 should be \(\frac{1 + 9}{5}+10\div2\) (since \(3^2 = 9\)), but the given Step 1 is \(\frac{1 + 3^2}{5}+10\div2\)? Wait no, the user's Step 1 is written as \(\frac{1 + 3^2}{5}+10\div2\)? Wait maybe the mistake is in Step 1? Wait no, let's check each step:

Wait let's compute the expression correctly:

Original expression: \(\frac{1+3^{2}}{5}+\vert - 10\vert\div2\)

First, calculate the exponent: \(3^{2}=9\)

Then, calculate the numerator of the fraction: \(1 + 9=10\)

So \(\frac{1 + 9}{5}=\frac{10}{5}=2\)

Calculate the absolute value: \(\vert - 10\vert = 10\), then \(10\div2 = 5\)

Then add the two results: \(2 + 5=7\)

Now let's check the given steps:

Step 1: \(\frac{1 + 3^{2}}{5}+10\div2\) (This is correct so far, because \(\vert - 10\vert=10\))

Step 2: \(\frac{1 + 9}{5}+10\div2\) (Since \(3^{2}=9\), this is correct)

Step 3: \(\frac{10}{5}+10\div2\) (Since \(1 + 9 = 10\), this is correct)

Step 4: \(2+10\div2\) (Since \(\frac{10}{5}=2\), this is correct)

Step 5: \(12\div2\) (Wait, \(2 + 10\div2=2 + 5 = 7\), but \(2+10 = 12\), then \(12\div2\) is wrong. Because according to the order of operations (PEMDAS/BODMAS), we should do division before addition. So \(10\div2 = 5\), then \(2+5 = 7\), not \(2 + 10\) first. So Step 5 is wrong? Wait no, Step 4 is \(2+10\div2\), then Step 5: \(12\div2\). Wait, \(2+10\div2\): we need to do division first, \(10\div2 = 5\), then \(2 + 5=7\). But in Step 5, they did \(2 + 10=12\) first, then \(12\div2\), which is a mistake in the order of operations. Wait but let's check the options. The options are A. Step 1, B. Step 3, C. Step 4, D. Step 5.

Wait let's re - evaluate each step:

Step 1: \(\frac{1 + 3^{2}}{5}+10\div2\) (Correct, because \(\vert - 10\vert = 10\), \(3^{2}=9\))

Step 2: \(\frac{1 + 9}{5}+10\div2\) (Correct, \(3^{2}=9\))

Step 3: \(\frac{10}{5}+10\div2\) (Correct, \(1 + 9 = 10\))

Step 4: \(2+10\div2\) (Correct, \(\frac{10}{5}=2\))

Step 5: \(12\div2\) (Wrong, because we should do \(10\div2 = 5\) first, then \(2+5 = 7\), not \(2 + 10=12\) then divide by 2)

But wait, maybe I misread the original expression. Wait the original expression is \(\frac{1 + 3^{2}}{5}+\vert - 10\vert\div2\). Let's check the steps again.

Wait Step 4: \(2 + 10\div2\), Step 5: \(12\div2\). The error is in Step 5. Because according to the order of operations, we must perform division before addition. So \(10\div2 = 5\), then \(2+5 = 7\), not \(2 + 10=12\) and then \(12\div2\). So the mistake is in Step 5.

Answer:

D. Step 5