Key Concepts in Mathematics Part 1

Fundamental operations include addition, subtraction, multiplication, and division.
Order of operations follows the rules PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).
Properties of numbers consist of commutative (order does not matter), associative (grouping does not matter), and distributive (multiplying a number by a sum).

A fraction represents the relationship between two integers, written as a/b where 'a' is the numerator and 'b' is the denominator.
Operations on fractions include addition, subtraction, multiplication, and division.
Simplifying fractions involves reducing to the lowest terms, while finding common denominators is essential for addition and subtraction.

A decimal is a fractional representation in base 10.
Conversion between fractions and decimals can involve long division or multiplication to achieve equivalent values.
Performing operations with decimals requires careful alignment of decimal points for accurate results.

A percentage quantifies a part per hundred, often denoted by the symbol %.
Conversions between fractions, decimals, and percentages simplify calculations and comparisons.
Calculating the percentage of a quantity involves multiplying the quantity by the percentage expressed as a decimal.

A ratio compares two quantities, often written as a:b.
A proportion establishes that two ratios are equivalent, typically expressed as a fraction equation.
Solving problems with ratios and proportions may require cross-multiplication or scaling methods.

Variables represent unknown values, while constants are fixed numbers.
Simple equations consist of expressions that can be solved for the variable.
Solving linear equations with one variable entails isolating the variable on one side of the equation.

Basic shapes include triangles, squares, and circles, each with unique properties.
Perimeter measures the length around a shape, while area calculates the space contained within it.
Volume measures the three-dimensional space occupied by solid figures like cubes and cylinders.

Measures of central tendency include mean (average), median (middle value), and mode (most frequent value).
The range quantifies the difference between the highest and lowest values in a data set.
Basic probability concepts involve the likelihood of an event occurring, often expressed as a ratio of favorable outcomes to total outcomes.

A function is a relationship that pairs each input (x) with exactly one output (y).
The domain refers to all possible inputs, while the range includes all possible outputs.
Evaluating functions requires substituting specific input values to find the corresponding output.

Categories include natural numbers (1, 2, 3...), whole numbers (0 and natural numbers), integers (positive and negative whole numbers), rational numbers (fractions), and irrational numbers (non-fractional decimals).
Real numbers encompass all the aforementioned types, excluding imaginary numbers.
Exponents represent repeated multiplication, while square roots represent the inverse operation of squaring a number.

Regular practice with exercises solidifies understanding and retention of concepts.
Breaking down complex problems into simpler parts makes them more manageable.
Visual aids like graphs and diagrams enhance comprehension of abstract ideas.
Reviewing mistakes fosters learning and helps avoid repeating errors.