Mathematics: Fundamental Operations

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.