Fractions, Decimals, Percentages and Ratio
Fractions, Decimals, Percentages and Ratio
This domain tests equivalence between fractions, decimals and percentages, arithmetic with fractions, percentage change, and sharing in a given ratio. Exam questions often ask you to compare values written in different forms or to reverse a percentage change.
Core rules
- A fraction is simplified by dividing numerator and denominator by their GCD. To add or subtract fractions, use a common denominator; to multiply, multiply numerators and denominators; to divide by a fraction, multiply by its reciprocal.
- Percent means 'per hundred': 37% = 37/100 = 0.37. A percentage increase of 15% uses the multiplier 1.15; a decrease of 10% uses 0.90.
- Ratio a:b has total parts a+b. One part = total ÷ (a+b). Keep the order of the ratio when assigning shares.
- To convert a fraction to a decimal, divide numerator by denominator; to convert a decimal to a percentage, multiply by 100.
Worked example
Increase 240 by 15%, then decrease the result by 10%. First increase: 240 × 1.15 = 276. Then decrease: 276 × 0.90 = 248.4. The final value is 248.4. Note that the net change is not 5%; it is a 3.5% increase overall because the multipliers compound: 1.15 × 0.90 = 1.035.
Traps
Adding percentage changes instead of multiplying multipliers; forgetting to convert a percentage to a decimal before multiplying; using the wrong base after a change; reversing ratio order; cancelling across an addition sign, which is invalid.