Standard Form
? Video Tutorial Standard Form (scientific notation): Expresses large or small numbers in the format $a times 10^n$, where $a$ is between 1 and 10. This simplifies calculations with extreme values. Converting to Standard Form: Move the decimal point to make a number between 1 and 10. For example, 26,000 becomes $2.6 times 10^4$ by […]
Fractions and Ratios
? Video Tutorial Understanding Ratios: Ratios compare two or more quantities, showing their relative sizes. The order of numbers in a ratio matters, e.g., 2:3 is different from 3:2. Dividing Amounts by Ratio: To split an amount like £200 in a 7:3 ratio, divide the total by the sum of parts, then multiply by each […]
Percentage Calculation
? Video Tutorial Percentage Calculation Components: The base value (original amount), percentage rate (relative percentage), and percentage value (calculated absolute amount). Applying Percentage Discount: To find a discount, multiply the base value by the percentage rate. For a £10 item with a 20% discount, the discount is £2, making the final price £8. Increasing BaseValue […]
Interest and Interest Rate Calculation
? Video Tutorial Understanding Principal and Interest: The principal is the initial amount of money invested, while interest is the extra amount earned based on a set interest rate, typically yearly. Calculating Simple Interest: Interest is calculated by multiplying the principal by the interest rate. For example, £100 at 5% interest results in £5 interest […]
Simple Interest and Compound Interest
? Video Tutorial Simple Interest Calculation: For multi-year periods, multiply the first year’s interest by the number of years. For example, £100 at 5% over 3 years earns 3 × £5 in total. Compound Interest Growth: Compound interest increases each year because interest is added to the principal. The formula is: principal times (1 + […]
Direct and Inverse Proportion
? Video Tutorial Identifying Direct Proportionality: In directly proportional situations, doubling one quantity doubles the other. The formula is typically $y = kx$, where $k$ is the constant unit rate. Identifying Inverse Proportionality: Inversely proportional relationships keep the product of the two quantities constant. The formula is usually $xy = k$, where $k$ is a […]
Adding and Subtracting Fractions
? Video Tutorial Adding and Subtracting Like Fractions: For fractions with the same denominator, add or subtract the numerators, then simplify the result if possible. Adding and Subtracting Unlike Fractions: Find the lowest common denominator, convert both fractions, then add or subtract the numerators. Proper, Improper, and Mixed Fractions: Proper fractions have a smaller numerator […]
Multiplying Fractions
? Video Tutorial Basic Fraction Multiplication: To multiply two fractions, multiply their numerators and denominators. Simplify the result if possible. Cross-Cancelling for Simplification: Before multiplying, look for common factors between any numerator and denominator to reduce fractions early, making calculations easier. Multiplying Fractions by Whole Numbers: Rewrite the whole number as a fraction over 1, […]
Dividing Fractions
? Video Tutorial Dividing Fractions: Change the division sign to multiplication and flip the second fraction (use its reciprocal). Then, multiply and simplify. Dividing by a Whole Number: Treat the whole number as a fraction over 1. For example, dividing by 6 is the same as multiplying by $large frac{1}{6} $. Dividing Mixed Fractions: Convert […]
Fractions and Percentages
? Video Tutorial Understanding Percentages: A percentage represents a fraction with a denominator of 100. For example, 70% means 70 out of 100, which is equivalent to 7/10. Converting Fractions to Percentages: Adjust the denominator to 100 by scaling both the numerator and denominator, then express it with a % symbol (e.g., 6/25 = 24/100 […]