Year 8 Mathematics: Integers, Fractions, Decimals & Percentages

This cheat sheet covers fundamental Year 8 mathematics concepts including integers, fractions, decimals, and percentages, focusing on their properties, operations, and conversions.

Core Principles

• Integers: Whole numbers, positive or negative, including zero.
• Fractions: Represent parts of a whole; can be proper, improper, or mixed.
• Decimals: Numbers expressed in base-10, with a decimal point separating whole and fractional parts.
• Percentages: Represent parts of a whole as a fraction of 100.
• Number Properties: Understanding multiples, factors, prime and composite numbers.
• Order of Operations: Following a specific sequence (BOMDAS/PEMDAS) for calculations.
• Conversions: Seamlessly transforming between fractions, decimals, and percentages.

Action Steps

• Master integer operations: addition, subtraction, multiplication, and division.
• Simplify fractions using the highest common factor (HCF).
• Convert between mixed numbers and improper fractions.
• Apply divisibility tests for quick checks.
• Use prime factorization for HCF and LCM calculations.
• Understand decimal place value for rounding and calculations.
• Convert fractions to decimals by division and decimals to fractions by place value.
• Convert between fractions, decimals, and percentages using multiplication/division by 100.
• Apply the unitary method to solve percentage problems.
• Calculate percentage increase and decrease accurately.
• Differentiate between profit and loss calculations.
• Practice the order of operations (BOMDAS) diligently.

Key Terms

• Integer: A whole number (not a fractional number) that can be positive, negative, or zero.
• Factor: A number that divides exactly into another number, leaving no remainder.
• Multiple: The result of multiplying a number by an integer.
• Prime Number: A whole number greater than 1 that has only two factors: 1 and itself.
• Composite Number: A whole number greater than 1 that has more than two factors.
• HCF (Highest Common Factor): The largest factor that two or more numbers have in common.
• LCM (Lowest Common Multiple): The smallest multiple that two or more numbers have in common.
• Terminating Decimal: A decimal number that has a finite number of digits after the decimal point.
• Recurring Decimal: A decimal number that has an infinite number of digits after the decimal point, with a repeating pattern.
• Unitary Method: A method to find the value of a unit (e.g., 1%) and then use it to find the value of any other quantity.