CSEC MATHEMATICS · MODULE 1 · LESSON A2

Computation: Fractions, Decimals, Percentages and Powers

Order of operations, working with fractions and decimals, converting among fractions, decimals and percentages, finding percentages of quantities, and powers and roots.

Fundamentals of Secondary Level MathematicsM1 1.2M1 1.3M1 1.4M1 1.11M1 1.13≈ 40 min🎮 3 games
Before you start

By the end of this lesson you can…

Step 1 · Watch

Explainer video

5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.

LESSON A2 · EXPLAINER

Computation: Fractions, Decimals, Percentages and Powers

Marks in Paper 02 are won or lost in the first question — and it is nearly always computation. Master these skills and you bank points before the hard questions start.

Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.

Step 2 · Read

Key notes

Copy these into your notebook in your own words — that is how they stick.

BODMAS

Brackets, Orders, Division/Multiplication, Addition/Subtraction. Work left to right at the same level.

Fractions

Add/subtract with a common denominator; multiply across; divide by flipping the second fraction. Simplify answers; mixed numbers → improper first.

Conversions

Fraction → decimal: divide. Decimal → %: ×100. % → fraction: ÷100 and simplify.

% of a quantity

Convert to a decimal and multiply: 15% of 240 = 0.15 × 240.

One quantity as a %

part ÷ whole × 100.

% change

Increase: × (1 + r/100). Decrease: × (1 − r/100). % change = change ÷ original × 100.

Powers & roots

x^(m/n) = (ⁿ√x)^m. x⁻ⁿ = 1/xⁿ. x⁰ = 1.

Calculator skill

Use brackets and the fraction key; check the answer is sensible before moving on.

EXAM TIPS & COMMON MISTAKES

  • “Show that” and “giving your answer in exact form” questions: leave answers as fractions or surds, not rounded decimals.
  • Percentage change is ALWAYS found against the original value, not the new value.
  • Do not subtract percentages: 20% off then 20% on does not return to the start (×0.8 × 1.2 = 0.96).
  • For mixed numbers like 2⅓ × 1½, convert to 7/3 × 3/2 first — adding the whole numbers separately is a classic error.
Play & practise

Games

3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Mathematics Arcade.

Step 3 · Practise

Paper 1 practice — multiple choice

8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.

Adapted from CSEC P1 May/June 2024, Item 1

1. (−3)² + (−2)² is equal to

Answer: B. (−3)² = 9 and (−2)² = 4, so the sum is 13.
CSEC Paper 01 style · SO 1.3

2. Evaluate 7 − 3 × 2 + 8 ÷ 4.

Answer: A. Multiply and divide first: 7 − 6 + 2 = 3.
CSEC Paper 01 style · SO 1.3

3. 2/3 + 3/4 is equal to

Answer: C. 8/12 + 9/12 = 17/12 = 1 5/12.
CSEC Paper 01 style · SO 1.4

4. The fraction 3/8 expressed as a percentage is

Answer: C. 3 ÷ 8 = 0.375 = 37.5%.
CSEC Paper 01 style · SO 1.11

5. What is 15% of $240?

Answer: D. 0.15 × 240 = 36.
CSEC Paper 01 style · SO 1.13

6. In a class of 180 students, 45 are absent. What percentage of the class is absent?

Answer: B. 45/180 × 100 = 25%.
CSEC Paper 01 style · SO 1.2

7. The value of 27^(2/3) is

Answer: B. 27^(2/3) = (∛27)² = 3² = 9.
CSEC Paper 01 style · SO 1.11

8. The price of a shirt is increased by 25% from $80. The new price is

Answer: A. 80 × 1.25 = 100.
Step 4 · Apply

Paper 2 practice — structured questions

Write full answers, then reveal the mark scheme and tick the points you earned (17 marks in total). Show all your working — method marks count. Your answers are saved on this device.

CSEC Paper 02 style · Module 1 (Computation)

Question 1 [9 marks]

A calculator may be used.

(a) Evaluate, giving the answer as a mixed number in its simplest form: 2 1/3 + 1 3/4. [3]

MARK SCHEME — (a) (max 3)

(b) Write 0.45 as a fraction in its simplest form and as a percentage. [2]

MARK SCHEME — (b) (max 2)

(c) In a school of 1 250 students, 36% are in Forms 1–3. (i) How many students are in Forms 1–3? (ii) The number in Forms 4 and 5 is 20% of the number in Forms 1–3. How many are in Forms 4 and 5? [4]

MARK SCHEME — (c) (max 4)

CSEC Paper 02 style · Module 1 (Percentage change and indices)

Question 2 [8 marks]

Use these to answer the parts below.

(a) The price of a phone increases from $1 200 to $1 380. Calculate the percentage increase. [3]

MARK SCHEME — (a) (max 3)

(b) Evaluate, showing working: (i) 16^(1/2) × 27^(1/3) (ii) 2⁻³ [3]

MARK SCHEME — (b) (max 3)

(c) Evaluate 5 + 18 ÷ 3² − (−4)(2). [2]

MARK SCHEME — (c) (max 2)

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Sources

Where this topic appears in CSEC papers

Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.