Notes, summaries, assignments, exams, and problems for Mathematics

Fundamental Number Concepts

Fraction Definition

A fraction is an expression a / b, where a (the numerator) and b (the denominator) are integers, and b must not be zero.

Equivalent Fractions

Two fractions, a / b and c / d, are considered equivalent, written as a / b = c / d, if the cross-product holds true: a · d = b · c.

Understanding Decimal Numbers

Decimal numbers express quantities that include incomplete units. A decimal number has two parts separated by a comma (or decimal point): the integer part (located to the left) and the fractional part (located to the right).

Types of Decimal Numbers

• Terminating Decimal: A decimal number is terminating (or accurate) when it has a finite number of decimal places.
• Periodic Decimal (Repeating): A decimal

Unit 7: Statistical Study Fundamentals

Statistical studies are crucial because governments base their environmental management plans on their findings. A proper study requires several key steps:

• Knowing the objective data
• Ordering the data
• Analyzing the data
• Drawing conclusions

Labor 1: Planning

Planning involves addressing two main questions:

What do we know?

This is answered by using a questionnaire. Questionnaire types include:

• Open Questionnaires: Respondents provide answers they deem appropriate.
• Limited Questionnaires: Responses are restricted to a fixed set of options.
• Closed Questionnaires (Note: This often overlaps with limited questionnaires in practice).

The final set of responses collected is called statistical variables. These fall into two... Continue reading "Statistical Study Process: Planning to Interpretation" »

The definition of a weighted average:

What is a Weighted Average?

A weighted average is the result of multiplying each number in a set by a value assigned to it (its weight), and then calculating the arithmetic mean of the resulting products. It's used when the components contributing to the average are not equally important.

For example, if a teacher states that an examination is worth 40% of the final mark, another is worth 35%, and a third is worth 25%, the weighted average would be calculated as follows:

mediaPond = (ex1 * 40 + ex2 * 35 + ex3 * 25) / 100

Basically, it's an average of a dataset that allows you to define the degree of importance for each data point's contribution to the average.

If the data are 2, 3, 5, 7, 9, 6, 8, the average... Continue reading "Understanding Weighted Averages: Definition and Applications" »