Simplification and approximation: the cheapest marks in the paper

Simplification and approximation are usually five or six questions in a bank prelims quantitative section, and they are the closest thing the paper offers to free marks. They test one thing only: whether you can carry out a chain of arithmetic quickly and in the right order. There is no concept to learn and no trap of interpretation, which is exactly why losing them hurts so much.

Candidates drop these marks for two reasons, and both are habits rather than gaps in knowledge. They round when they should be exact, and they compute exactly when they were invited to round.

Read the question type from the word and the options

The single most useful half-second is deciding which of the two you are looking at.

Simplification asks for the exact value. The options are usually close together, so an estimate will not separate them, and you must actually finish the arithmetic.

Approximation almost always contains the word “approximately”, and its options are spread far apart. That spread is a permission slip: it tells you how much you are allowed to round without changing which option is closest.

Getting this wrong in either direction is the classic self-inflicted loss. Rounding a simplification question lands you between two adjacent options; computing an approximation question exactly wastes fifteen seconds you did not have.

BODMAS is an ordering discipline, not a rule to recite

Everyone knows brackets, orders, division and multiplication, then addition and subtraction. The marks are lost not in knowing the order but in keeping the working ordered under time pressure.

• Resolve everything inside brackets first, and do not carry a bracket forward unresolved hoping it will cancel.
• Convert “of” to multiplication immediately, since “1/2 of 80” is simply 40.
• Handle division and multiplication left to right, then addition and subtraction. The errors cluster where a subtraction is done before a multiplication that preceded it.
• Write intermediate results down. Trying to hold a four-step chain in your head is where a correct method produces a wrong number.

The speed comes from recall, not cleverness

A simplification question is only fast if the components are instant. The candidates who finish these in thirty seconds are not calculating faster; they are recalling instead of calculating.

• Tables to twenty-five, squares to thirty and cubes to fifteen should be recall, not working. The fraction, square and cube values worth memorising are the foundation this entire topic stands on.
• Common fraction-to-percentage conversions save the most time: knowing 1/8 is 12.5% or 5/6 is about 83.3% turns a division into a lookup.
• Percentages are easier as fractions. Twelve and a half per cent of a number is that number divided by eight; multiples of 25% are quarters. Reach for the fraction before the decimal.

Approximation: round with intent, then check the gap

The method is not “round everything” but “round each number to the nearest value that makes the arithmetic clean, then verify the options can survive it”.

1. Replace each awkward number with a near round value. 6798 becomes 6800, 48.7% becomes 50%, √288 becomes about 17 because 17² is 289.
2. Do the easy arithmetic on the round values.
3. Look at your answer against the options. If one option is clearly nearest and the others are far, you are done. If two options straddle your estimate, redo the one term that most affects the result with less rounding.

Square and cube roots are the most common approximation ingredient, and they are fast if you anchor to the nearest perfect square or cube. √150 is a little under 12.5 because 12² is 144 and 13² is 169; you rarely need more precision than that.

Where the marks leak

Rounding an exact question. Already said, and worth repeating, because it is the single biggest source of lost marks in this topic. Check the options before you decide how much precision to keep.

Compounding rounding errors. In a long approximation, rounding every term the same direction pushes the result off. If you rounded three numbers up, round the next one down to keep the estimate centred.

Losing a sign or a decimal place. The arithmetic is easy, which breeds carelessness. A misplaced decimal in a division is the most common wrong answer, so glance at the order of magnitude of your result before you commit.

Doing the hard part first. If an expression has one ugly term and three clean ones, resolve the clean ones and hold the ugly one to the end, where you can often see it barely affects the answer.

Practice that transfers

The way to improve is volume under a tight clock with immediate correction, because what you are building is fluency rather than understanding. Do blocks of ten to fifteen questions against a four-minute clock, and afterwards separate the two failure types: questions you got wrong because the arithmetic slipped, and questions you got wrong because you rounded when you should not have. The second kind is fixed by a habit, not by more practice.

Work through the simplification and approximation practice set, which mixes BODMAS chains, fraction work and approximation questions, and keep drilling the underlying calculation speed so that the components are recall rather than work.