Fractions, Decimals and Surds
Types of fractions and fast ways to compare them, converting between fraction, decimal and percentage form, turning a recurring decimal into a fraction, and the basics of surds and rationalising a denominator.
What you will be able to do
- Classify fractions and compare a set of them quickly.
- Convert between fraction, decimal and percentage form both ways.
- Convert a pure or mixed recurring decimal into a fraction.
- Simplify a surd expression and rationalise a denominator.
What is inside this lesson
- 1Types of fractions, and comparing them fast
- 2Fraction, decimal, percentage
- 3Recurring decimal to fraction
- 4Surds and rationalising
- 5Worked example: comparing a set
- 6Worked example: recurring decimal to fraction
- 7Worked example: rationalising a denominator
- 8Common mistakes
- 9Quick revision
- 10Practice
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Types of fractions, and comparing them fast
Types. Proper: numerator smaller than denominator, value below 1 (3/5). Improper: numerator at least as large, value 1 or more (7/4). Mixed: a whole number with a proper fraction (1 and 3/4 = 7/4). Like fractions share a denominator; equivalent fractions reduce to the same lowest-terms fraction. Always reduce with the HCF before using a fraction.
Comparing quickly:
- Cross-multiplication for two fractions: to compare a/b and c/d, compare a times d with b times c; the larger product belongs to the larger fraction.
- Same numerator: the fraction with the smaller denominator is larger (3/7 is larger than 3/8).
- Same denominator: the larger numerator is larger.
- Reference point: compare each with 1/2 or 1. 5/9 is just over 1/2; 7/15 just under; so 5/9 is larger.
- Decimal glance: for a messy set, convert two or three to decimals to one or two places and rank.
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