Percentages. Percentages are one of the most practical topics in mathematics - used daily in discounts, grades, interest rates, statistics, and even health data. But beyond their everyday use, percentages teach us how to compare quantities fairly and meaningfully. What is a Percentage? The word “percent” comes from the Latin per centum , meaning “by the hundred.” A percentage is simply a fraction with a denominator of 100 . So, 25 % = 25 100 = 0.25 This means 25 out of every 100 parts . Percentages are useful because they let us compare things on the same scale , even if their original values are very different. Converting Between Fractions, Decimals, and Percentages To work easily with percentages, you should know how to convert between fractions, decimals, and percentages. From Fraction to Percentage: Multiply the fraction by 100%. For example: 3 4 × 100 % = 75 % So, 3 4 \frac{3}{4} ...
Posts
- Get link
- X
- Other Apps
Ratio and Proportion Introduction Ratios and proportions are some of the most practical concepts in mathematics. They help us describe relationships between quantities and maintain balance or fairness in everyday situations. 1. What Is a Ratio? A ratio is a way of comparing two or more quantities of the same kind. If quantity a a a is compared to quantity b b b , their ratio is written as: a : b or a b a : b \quad \text{or} \quad \frac{a}{b} For example: The ratio of 10 apples to 5 oranges is 10 : 5 = 2 : 1 10 : 5 = 2 : 1 The ratio of 12 boys to 18 girls is 12 : 18 = 2 : 3 12 : 18 = 2 : 3 Important: Ratios compare quantities in the same unit . You cannot compare 3 meters to 4 kilograms. Simplifying Ratios To simplify a ratio, divide both terms by their highest common factor (HCF) . Example 1: Simplify 20 : 15 20 : 15 HCF of 20 and 15...
- Get link
- X
- Other Apps
Change of Subject of a Relation Introduction In algebra, you often meet formulas where one quantity depends on others — like A = πr^2 A = π r 2 or v = u + a t But sometimes, you’re asked to make another letter the subject . For example, instead of A = π r 2 A = πr^2 A = π r 2 , you might need to make r the subject. This process is called “Change of Subject of a Relation.” It simply means rearranging a formula so that one specific variable stands alone on one side of the equation- usually the left-hand side. What It Means If we have an equation: y = 3 x + 2 and we want to make x the subject , it means we must rewrite it as: x = something in terms of y It’s like solving for x x — isolating it by performing the same operatio...