General Education: Mathematics 📐

Mathematics in the LET (General Education) focuses on fundamental concepts that every teacher should master. This module is designed to be your ultimate cheat sheet.

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1. Order of Operations (PEMDAS)

When solving expressions with multiple operations, always follow the PEMDAS rule:

Letter	Meaning	Operation	Priority
P	Parentheses	( ), [ ], { }	1
E	Exponents	$x^2$, $\sqrt{x}$	2
M	Multiplication	$\times$ (Left to Right)	3
D	Division	$\div$ (Left to Right)	3
A	Addition	$+$ (Left to Right)	4
S	Subtraction	$-$ (Left to Right)	4

Example: $5 + 2 \times (10 - 3)^2$

• Parentheses: $5 + 2 \times (7)^2$
• Exponents: $5 + 2 \times 49$
• Multiplication: $5 + 98$
• Addition: 103

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2. Number Properties & Theory

Prime vs. Composite

• Prime Numbers: Numbers with exactly two factors: 1 and itself. (2, 3, 5, 7, 11, 13, 17, 19...)
• Composite Numbers: Numbers with more than two factors. (4, 6, 8, 9, 10...)
• Note: 1 is neither prime nor composite. 2 is the only even prime number.

GCF and LCM

• GCF (Greatest Common Factor): The largest number that divides into all numbers in a set.
• LCM (Least Common Multiple): The smallest number that is a multiple of all numbers in a set.

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3. Fractions, Decimals, & Percentages

This is a high-frequency topic in the LET.

Converting to Percent

To convert a fraction or decimal to a percentage, multiply by 100 and add the % sign.

• $0.75 \rightarrow 75$
• $3/5 \rightarrow 0.6 \rightarrow 60$

The Percentage Formula

The "PB-R" Triangle is your best friend:

• Percentage (P): $P = R \times imes B$
• Rate (R): $R = P / B$
• Base (B): $B = P / R$

LET Sample Question: What is 15% of 120?

• $R = 0.15$, $B = 120$
• $P = 0.15 \times imes 120 = **18**$

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4. Ratio and Proportion

• Ratio: A comparison of two quantities (e.g., $2:3$).
• Proportion: Two ratios that are equal (e.g., $2:3 = 4:6$).
• Rule: The product of the means equals the product of the extremes.
  • If $a/b = c/d$, then $ad = bc$.

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5. Geometry Cheat Sheet

Essential Formulas

Shape	Area ($A$)	Perimeter/Circumference ($C$)
Rectangle	$L \times imes W$	$2L + 2W$
Square	$s^2$	$4s$
Triangle	rac{1}{2}bh	$a + b + c$
Circle	$\pi r^2$	$2\pi r$

Visual Breakdown: The Circle 🔵

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6. Basic Algebra

Solving for $x$ usually involves isolating the variable.

• Rule of Equality: Whatever you do to one side, you must do to the other.

Example: Solve for $x$ in $3x + 5 = 20$

1. Subtract 5: $3x = 15$
2. Divide by 3: $x = 5$

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💡 LET Exam Tips (Math)

1. Work backwards: If you're stuck, plug the multiple-choice answers into the equation.
2. Estimate: If the answer choices are far apart, round numbers to quickly eliminate wrong options.
3. Units matter: Ensure all measurements are in the same unit before calculating.

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🔗 Related Topics

• Science (GenEd) - Apply math formulas to physics and chemistry.
• Social Studies (GenEd) - Interpreting statistics and graphs.

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Practice Quiz

Ready to test your skills? Try the GenEd Mathematics Quiz.