Introduction
Fractions, decimals and simplification form the numerical backbone of almost every quantitative section in BCS, Bank and IT-officer examinations. Whether you are computing a percentage of a budget, converting a recurring decimal, comparing two ratios, or racing through a long arithmetic expression under time pressure, you are really doing fraction and decimal arithmetic combined with clean simplification. Examiners love this topic because a single well-designed question can test ordering of operations, conversion skill, mental arithmetic, and speed all at once. Master it and you convert some of the easiest marks on the paper into guaranteed points — and you build the fluency that every later topic (percentage, ratio, profit-loss, algebra) silently depends on.
This lesson builds the ideas from first principles: what a fraction actually means, how decimals are just fractions with denominators that are powers of ten, why simplification rules are the way they are, and how to move between all these forms fast and without error.
Learning objectives
- Understand what a fraction represents and identify proper, improper, mixed, like, unlike and equivalent fractions.
- Add, subtract, multiply and divide fractions confidently, and reduce any fraction to its lowest terms.
- Convert freely between fractions, decimals and percentages, including terminating and recurring decimals.
- Apply the correct order of operations (BODMAS/BIDMAS) to simplify long numerical expressions.
- Compare and order fractions and decimals quickly using cross-multiplication and benchmarking.
- Avoid the classic exam traps and use speed techniques suited to timed multiple-choice tests.