Percentages, Ratios & Basic Algebra

Percentages, Proportions & Basic Algebra

Percentage calculations and linear proportions appear frequently on the ParaPro test, both as pure mathematical calculations and within classroom distribution scenarios.

1. Benchmark Percentage Shortcuts

To solve percentage questions quickly without a calculator, build your answers from core mental benchmarks:

10% Benchmark: Move decimal point 1 place left (e.g. 10% of 240 = 24).
1% Benchmark: Move decimal point 2 places left (e.g. 1% of 240 = 2.4).
50% Benchmark: Divide by 2 (e.g. 50% of 240 = 120).
25% Benchmark: Divide by 4 (e.g. 25% of 240 = 60).

2. Setting Up Proportions

When two ratios are equivalent, cross-multiply to solve for the unknown variable x: a / b = c / d => a * d = b * c

Step-by-Step Worked Practice Problem

Exam Sample Problem:

A school cafeteria serves 180 lunches on Monday, of which 45 are vegetarian meals. What percentage of the lunches served are vegetarian?

Step-by-Step Solution:

Set up the fraction: Part / Whole = 45 / 180.
Simplify the fraction by dividing numerator and denominator by 45 (or successively by 9 and 5): 45 / 180 = 1 / 4.
Convert 1/4 to a percentage: 1/4 = 0.25 = 25%.
Answer: 25% of the lunches were vegetarian.