Welcome to MATH 114
A short orientation to how the course works and what to expect.
Watch videoHow to work through this module
- 1. Learn — read the concepts below and watch the short video.
- 2. Practice — work the examples, then test yourself with the check questions.
- 3. Submit — when you feel ready, complete the Module 1 homework and quiz in Canvas.
Learn the Concepts
1 · Reasoning and logical fallacies
Logic is the study of careful reasoning. An argument uses premises (facts or assumptions) to support a conclusion. A fallacy looks like an argument, but the premises don't actually support the conclusion — it only feels convincing.
Common fallacies to recognize
- Appeal to popularity — it must be true because many people believe it.
- False cause — assuming one event caused another just because it came first.
- Appeal to ignorance — it's false because no one has proven it true (or vice versa).
- Hasty generalization — a broad conclusion from too few examples.
- False dilemma — presenting only two options when more exist.
- Appeal to emotion — persuading with feelings instead of evidence.
- Personal attack (ad hominem) — attacking the person rather than the argument.
- Circular reasoning — using the conclusion as its own support.
- Red herring — changing the subject to a distraction.
- Straw man — misrepresenting an argument to make it easy to knock down.
Learn the Concepts
2 · Evaluating information
Quantitative reasoning starts with trustworthy information. Before you rely on a claim, statistic, or article, run through five quick checks:
- Source — who produced it, and are they credible?
- Date — is the information current enough to matter?
- Accuracy — can you confirm it with another independent source?
- Hidden agenda — is someone trying to sell or persuade you?
- Big picture — does it fit with what is already well established?
Learn the Concepts
3 · Core number skills
Simplifying fractions
Divide the numerator and denominator by their greatest common divisor (GCD), or cancel shared prime factors until nothing is left in common.
Rounding decimals
Find the digit in the place you are rounding to. If the next digit is 5 or more, round up; otherwise leave it and drop the rest.
Evaluating expressions
Substitute the given values for each variable, then simplify one step at a time, following the order of operations.
Translating words into algebra
Watch for the keywords that signal each operation:
| Operation | Signal words |
|---|---|
| Addition | sum, plus, more than, increased by |
| Subtraction | difference, minus, less than, decreased by |
| Multiplication | product, times, of, multiplied by |
| Division | quotient, divided by, per, shared among |
Worked Examples
See it done, step by step
Try each one yourself first, then open the solution to check your work.
Example 1 — Simplify the fraction 36/27
Find the largest number that divides both 36 and 27.
The GCD of 36 and 27 is 9. Divide both parts by 9:
36 ÷ 9 = 4 and 27 ÷ 9 = 3, so 36/27 = 4/3.
Example 2 — Round 3.14159 to the hundredths place
The hundredths digit is the second after the decimal point (the first 1 → it's the "4").
The hundredths digit is 4; the next digit is 1, which is less than 5, so we keep the 4 and drop the rest.
Result: 3.14.
Example 3 — Evaluate b − 5a when a = 4 and b = 35
Substitute the values, then simplify.
b − 5a = 35 − 5(4) = 35 − 20 = 15.
Example 4 — Translate: "three times the difference of a number and ten"
"Difference of a number and ten" is (x − 10); "three times" multiplies it by 3.
Expression: 3(x − 10). The parentheses matter — 3x − 10 would be a different quantity.
Watch & Review
Resources for this module
Homework 1 help
Walkthrough support for the first homework set, including HW 1 #8.
Watch videoLecture slides
The Module 1 slides covering reasoning and number skills.
Open slidesPrintable one-page summary
A condensed reference sheet you can print for review.
Open summaryCheck Yourself
Quick self-check
No grade here — just a confidence check before you submit. Answer, then reveal.
1. "Everyone is buying this phone, so it must be the best." Which fallacy is this?
Appeal to popularity — popularity is not the same as quality.
2. Simplify 18/24.
GCD is 6: 18 ÷ 6 = 3, 24 ÷ 6 = 4, so 3/4.
3. Translate: "five less than twice a number."
2x − 5. "Less than" reverses the order, so it is not 5 − 2x.
Ready to turn it in?
When you have learned the concepts and feel good about the practice, complete the Module 1 homework and quiz in Canvas. Canvas has the due dates and is where your work is graded.
Submit in Canvas