Mathematics: Fundamental Operations

Study Notes

Understanding Fundamental Operations

Understanding fractions, decimals, and percentages is essential for various mathematical applications.
Key operations include addition, subtraction, multiplication, and division across all three concepts.

Operations on Fractions

Addition of fractions requires a common denominator for accurate computation.
Subtraction follows the same principle as addition in finding a common denominator.
Multiplication of fractions involves multiplying numerators and denominators directly.
Division of fractions is performed by multiplying the first fraction by the reciprocal of the second.

Operations on Decimals

Addition and subtraction of decimals require aligning decimal points for accurate calculations.
Multiplication of decimals involves multiplying as whole numbers, then placing the decimal point based on the total digits in both factors.
Division of decimals may require moving the decimal point in the divisor to make it a whole number, and similarly adjust the dividend.

Working with Percentages

Percentages represent a fraction out of 100 and can be converted from both fractions and decimals.
To find a percentage, divide the part by the whole and multiply by 100.
Percent increases and decreases are calculated by determining the difference and dividing it by the original amount, then multiplying by 100.

Application in Business Context

Understanding these operations allows for solving real-world problems involving profit margins, discounts, and financial calculations.
Accurate manipulation of fractions, decimals, and percentages is vital in fields such as accounting and finance.

Kinds of Quantitative Research

Quantitative research can be categorized into several designs: descriptive, correlational, ex post facto, quasi-experimental, and experimental.

Descriptive Design

Focuses solely on describing a phenomenon as it occurs, without experimental manipulation or predefined hypotheses.
Aims to provide an understanding of the subject's characteristics.
Example: Assessing the frequency of different physical activities among high school students during the quarantine period.

Correlational Design

Examines the relationship between two or more variables without indicating causation.
Data collection is done through observation.
Example: Analyzing the connection between the frequency of physical activity and academic achievement among students.

Ex Post Facto Design

Investigates relationships between past events and current conditions, examining potential causes of existing phenomena.
"Ex post facto" translates to "after the fact," focusing on hindsight analysis without experimental manipulation.
Example: Exploring how parents' academic achievements influence their children's obesity rates.

Quasi-Experimental Design

Used to identify cause-and-effect relationships between variables but lacks a full experimental approach due to absence of random assignment.
Independent variables are identified but not manipulated; pre-existing groups are used for comparison.
Example: Studying the impact of unemployment on attitudes towards safety protocols during Enhanced Community Quarantine (ECQ) in certain areas.

Experimental Design

Aims to establish cause-and-effect relationships through rigorous methods, including random assignment of subjects and experimental manipulation of variables.
Provides stronger validity and conclusive results compared to quasi-experimental designs.
Example: Comparing the effects of different blended learning methods on elementary students' reading comprehension.

Description

This quiz covers essential operations with fractions, decimals, and percentages necessary for effective mathematical applications. It includes addition, subtraction, multiplication, and division techniques specific to each concept. Test your understanding and skills on these fundamental mathematical operations.