Key GCSE Maths Skills: Proportion, Ratio & Number
Key GCSE Maths Skills: Proportion, Ratio & Number
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Key GCSE Maths Skills: Proportion, Ratio & Number
What do you already know about proportions and prime factors?
Learning Objective
At the end of the lesson you will be able to solve GCSE Higher Tier problems involving proportion, ratio, reverse percentage, factors, primes, and surds.
What are Proportion and Ratio?
Proportion and ratio are ways of comparing values. They help us understand relationships between numbers.
Direct and Inverse Proportion
Direct proportion means that as one value increases, another increases at the same rate. Inverse proportion means that as one increases, the other decreases.
Working with Ratios
Ratios compare amounts or quantities. You often simplify ratios or use them to divide amounts proportionally.
Percentage Change
Percentage change tells us how much a value increases or decreases in relation to its original value. Use the formula: change/original × 100.
Reverse Percentages
Reverse percentage problems work backwards to find an original amount before a percentage change.
Factors and Multiples
A factor divides exactly into a number. A multiple is a number you get when you multiply a number by an integer.
Prime Numbers
Prime numbers have only two factors: 1 and themselves. Recognising primes is useful in many mathematical problems.
Prime Factor Decomposition
Every number can be broken down into a product of primes (its prime factors), which helps with calculations involving roots and fractions.
Understanding Powers and Roots
Powers (exponents) show how many times a number is multiplied by itself. Roots are the opposite operation.
What are Surds?
A surd is a square root (or higher root) that cannot be simplified to a rational number, like \( \sqrt{2} \) or \( \sqrt{5} \).
Basic Operations with Surds
You can add, subtract, and multiply surds of the same form. You can also simplify them by factoring inside the root.
Quick Recall: Key Terms
Proportion: Relationship between two quantities; Ratio: Comparison of values; Percentage: Part per hundred.
Proportion, Ratio, Percentage
Factors, Primes, Surds
Factors: Numbers that divide another exactly; Primes: Numbers with two factors; Surds: Irrational roots.
Summary
You can now solve problems involving ratio, proportion, reverse percentages, factors, multiples, primes, powers and surds. Practise further to master these skills.
Well done! Ready for Practice Questions?
Write down 3 things you learned in this lesson.
Write down 2 things you want to know more about.
Ask 1 question about something you haven't quite understood yet.
