To solve the given mathematical expression [tex]\(\left(\frac{5^2+3}{|-0.5|}\right) - 16.4 \div 4\)[/tex], we need to break it down step by step.
Part A: Explain what the missing expression should be for Step 3.
Firstly, let’s follow the steps outlined in the expression:
Step 1:
The original expression given is:
[tex]\[
\left(\frac{5^2+3}{|-0.5|}\right) - 16.4 \div 4
\][/tex]
Step 2:
Evaluate the absolute value and rewrite the expression:
[tex]\[
\left(\frac{5^2+3}{0.5}\right) - 16.4 \div 4
\][/tex]
Now, let’s simplify the term inside the parentheses in steps.
Step 3:
Calculate [tex]\(5^2 + 3\)[/tex]:
[tex]\[
5^2 = 25
\][/tex]
[tex]\[
25 + 3 = 28
\][/tex]
So, the expression becomes:
[tex]\[
\left(\frac{28}{0.5}\right) - 16.4 \div 4
\][/tex]
Thus, for Step 3, the missing expression is:
[tex]\[
\left(\frac{28}{0.5}\right) - 16.4 \div 4
\][/tex]
Part B: Explain what the missing expression should be for Step 6.
Next, let’s simplify it further:
Step 4:
Calculate the quotient [tex]\(\frac{28}{0.5}\)[/tex]:
[tex]\[
\frac{28}{0.5} = 56
\][/tex]
So, the expression becomes:
[tex]\[
56 - 16.4 \div 4
\][/tex]
Step 5:
Calculate the division [tex]\(16.4 \div 4\)[/tex]:
[tex]\[
16.4 \div 4 = 4.1
\][/tex]
Step 6:
Substitute back into the expression:
[tex]\[
56 - 4.1
\][/tex]
Therefore, the missing expression for Step 6 is:
[tex]\[
56 - 4.1
\][/tex]
Final Result:
Evaluate the final subtraction:
[tex]\[
56 - 4.1 = 51.9
\][/tex]
So, the step-by-step solution ensures that the intermediate and final results are consistent. The missing expression for Step 3 is [tex]\(\left(\frac{28}{0.5}\right) - 16.4 \div 4\)[/tex], and the missing expression for Step 6 is [tex]\(56 - 4.1\)[/tex].
