GCSE Maths · Fractions · Higher · Summary
GCSE Maths Fractions (Higher): summary and key words
Part of the GCSE Maths fractions chapter (Higher). Chapter overview · Foundation version of this lesson · whole chapter on one page
Chapter summary
| Skill | Method |
|---|---|
| Brackets and mixed numbers | BIDMAS; mixed → improper first; simplify at the end |
| Fractional change | Increase by a/b: × (1 + a/b). Decrease: × (1 − a/b). Multiply successive multipliers |
| Reverse problems | final ÷ multiplier = original |
| Terminating test | Simplest form; denominator only has prime factors 2 and 5 |
| Recurring → fraction | x = decimal; multiply by 10, 100… to line up; subtract; solve |
| Simplify algebraic fractions | Factorise top and bottom, cancel common factors (never terms) |
| Multiply / divide algebraic | Factorise, flip the second for division, cancel |
| Add / subtract algebraic | Common denominator, combine numerators, expand and simplify |
| Equations with fractions | Multiply every term by the common denominator |
| Proof | Use algebra; each step shown; end exactly at the stated result |
Can you…?
- I can handle brackets, mixed numbers and negative fractions.
- I can solve multi-step and reverse fraction problems.
- I can decide if a fraction terminates, and convert recurring decimals to fractions.
- I can simplify, multiply and divide algebraic fractions.
- I can add and subtract algebraic fractions.
- I can solve equations containing fractions.
- I can write short algebraic proofs involving fractions.
Key terms
- Algebraic fraction
- A fraction with algebra in the numerator or denominator.
- Common factor
- A factor shared by two or more terms or numbers.
- Counter-example
- A single example that shows a statement is false.
- Multiplier
- The number you multiply by to apply a percentage or fractional change.
- Recurring decimal
- A decimal with a digit or block of digits that repeats forever.
- Telescoping sum
- A sum in which most terms cancel in pairs.
- Terminating decimal
- A decimal that ends.