310105aA (2) Math Skills
Page 1: Identifying Functions and Limits
Function Notation: f(x)
Composite Function: juj(x) = &ansen!
Algebraic Expressions:
Example: (AF = F(x))
Example: (x = \pm 4.7) involves square root operations
Reference to limits: (C = \lim f(x))
Page 2: Objectives
Mathematical Skills:
Perform Fraction Calculations
Convert fractions to decimals
Convert decimals (non-repeating) to fractions
Ratios & Proportions
Understand Percentages
Execute arithmetic operations in the correct sequence
Transpose equations
Page 3: Introduction to Fractions
Limits and Fractions:
Example showing limits (AF=F(x))
Need for clear understanding of fractions in calculations:
Common issues with fractions highlighted,
Example: (Aj St; (x) d x + C)
Page 4: Fraction Terminology
Key Terms:
Numerator: The top part of a fraction
Denominator: The bottom part of a fraction
Examples of fraction limits: (AF = F(x)) and (d = \lim)
Page 5: Types of Fractions
Proper Fractions: Numerator is less than the denominator.
Improper Fractions: Numerator is greater than the denominator.
Mixed Fractions: A whole number and a proper fraction combined.
Page 6: Reducing Fractions
Steps to Reduce Fractions:
List Factors: Factors of 25 are {1, 5, 25}, factors of 50 are {1, 2, 5, 10, 25, 50}.
Divide numerator and denominator by the largest common factor.
Example: 25/50 reduced by dividing both by 25 gives ( \frac{1}{2} ).
Page 7: Multiplying and Dividing Fractions
Multiplication Steps:
Multiply numerators: 3 × 4 = 12
Multiply denominators: 8 × 5 = 40
Reduce if necessary: Result is ( \frac{3}{10} )
Division Steps:
Reciprocate second fraction:
Example: ( \frac{3}{4} ÷ \frac{8}{5} = \frac{3}{4} × \frac{5}{8} = \frac{15}{32} )
Page 8: Adding and Subtracting Fractions
Finding Common Denominator:
Example of adding fractions with common denominator:
( \frac{3}{8} + \frac{4}{5} ): Common denominator is 40.
Calculation yields ( \frac{47}{40} ).
Subtracting Example:
Calculation yields ( \frac{1}{15} ).
Page 9: Converting Between Fractions and Decimals
To Convert Fraction to Decimal: Divide the numerator by the denominator.
Examples: 1/4 = 0.25, 7/8 = 0.875.
To Convert Decimal to Fraction:
Write decimal over 1, multiply by powers of 10 until decimal is a whole number, then reduce.
Page 10: Ratios and Proportions
Definition of Ratio: Relationship between two numbers; express as '15 to 20' or '15:20'.
Order Matters: Make sure the order is correct based on what is being compared (e.g., ducks to geese).
Cross Multiplication: (\frac{6}{8}) verification for equivalence when comparing ratios.
Page 11: Understanding Proportions
Proportions: A specific quantity comparison to the whole.
Example Calculation: Cross multiply to solve proportions:
(\frac{15}{20}) cross multiply to check equivalences.
Page 12: Proportion Example
Application of Proportions:
Mixing Cement: If the ratio is 25:2 parts, calculate for 3 parts, resulting in 37.5.
Page 13: Percentages
Definition: A way to express numbers as a fraction of 100.
Percentage Calculation Example:
35% of 300 = 105.
Calculating Percentage of a Percentage: Convert both to fractions or decimals and multiply.
Page 14: Practical Percentage Calculation
Example: Scoring 50 out of 75:
Calculate percentage to evaluate understanding and study habits.
Page 15: Self-Test Completion
Complete exercises 8-12 from ILM310105aA.
Page 16: Mathematical Operations Sequence
BEDMAS Rule: Brackets, Exponents, Divide, Multiply, Addition, Subtraction.
Operations must be performed in this order from left to right.
Page 17: Apply BEDMAS to Example
Example provided showing complex calculation:
Stepwise application of BEDMAS yielding final results.
Page 18: Transposing Equations
Important Rule: What is done to one side must be done to the other to maintain equality.
Example equation solved by transposing.
Page 19: Note on Clarity
Emphasizes precision in mathematical notation and equivalencies.
Page 20: Conclusion
Reference to complete Self Test for ILM310105aA.