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Basic Algebra and Graphing for Electric Circuits
16 questions By Tony R. Kuphaldt
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Question 7 of 16
Follow proper order of operations to evaluate these expressions:
$$\frac{13 + 2}{3} + 8 = $$
$$25 + (3+2)^2 x 2 = $$
Reveal answer$$\frac{13 + 2}{3} + 8 = 13$$
$$25 + (3+2)^2 x 2 = 75$$
Notes:Nothing special here - just simple arithmetic problems that cannot be solved correctly unless proper order of operations is followed.
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Question 8 of 16
Follow proper order of operations to evaluate these expressions:
$$\frac{15 - 3}{3} + 7 = $$
$$20 + (1+3)^2 x 3 = $$
Reveal answer$$\frac{15 - 3}{3} + 7 = 11$$
$$20 + (1+3)^2 x 3 = 68$$
Notes:Nothing special here - just simple arithmetic problems that cannot be solved correctly unless proper order of operations is followed.
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Question 9 of 16
When evaluating an expression such as this, it is very important to follow proper order of operations. Otherwise, the correct result will be impossible to arrive at:
3 log25 + 14 To show what the proper order of operations is for this expression, I show it being evaluated step by step here
3 log25 + 14 3 log32 + 14 3 ×1.5051 + 14 4.5154 14 18.5154 Do the same for each of the following expressions:
- 10 − 25 × 2 + 5
- − 8 + 103 × 51
- 124 × (3 + 11)
- 21(7 − 4) ×40
- \(log \sqrt{6 + 35^2}\)
- \(\sqrt{(\frac{220}{16}-2.75)} x 2\)
Footnotes:
By the way, this is a highly recommended practice for those struggling with mathematical principles: document each and every step by re-writing the expression. Although it takes more paper and more effort, it will save you from needless error and frustration
!Reveal answerI’ll let you determine and document the proper order of operations, but here are the results of each expression:
- 10 − 25 ×2 5 = −35
- −8 103 ×51 = 50992
- 124 ×(3 11) = 290304
- 21(7 − 4) ×40 = 370440
- \(log \sqrt{6 + 35^2} = 1.5451\)
- \(\sqrt{(\frac{220}{16}-2.75)} x 2 = 4.6904\)
Notes:Order of operations is extremely important, as it becomes critical to recognize proper order of evaluation when ßtripping” an expression down to isolate a particular variable. In essence, the normal order of operations is reversed when ündoing” an expression, so students must recognize what the proper order of operations is.
Related Tools:
- Performance-Based Assessments for DC Circuit Competencies
- Conventional Transistor Overview and Special Transistors
Question 3, answer - the ‘+’ symbol is missing from ‘= a^(m+n)’.
Question 7, question and answer - second equation should have a multiplication symbol, not the ‘variable x’.
Question 8, question and answer - second equation should have a multiplication symbol, not the ‘variable x’.
Question 9, question - the ‘+’ symbol is missing between ‘4.5154 ‘+’ 14’.
Question 9, answer:
- the ‘+’ symbol is missing: 10 − 25 ×2 ‘+’ 5 = −35
- the ‘+’ symbol is missing: −8 ‘+’ 10^3 ×51 = 50992
- the ‘+’ symbol is missing: 12^4 ×(3 ‘+’ 11) = 290304
Question 9, question and answer: The square root should enclose the whole equation, and the equation should have a multiplication symbol, not the ‘variable x’.
Question 13, question and answer: The table columns need spacing and the ‘+’ symbol is missing from the headings ‘2x + 1’.
These are all correct in the PDF version.