Workshop Calculation: Fractions, Decimals, Percentage and Ratio
Fractions, decimals, percentage and ratio
This domain tests fluent conversion and comparison of the numerical forms used on shopfloor paperwork: fraction-based stock sizes, decimal micrometer readings, percentage allowances and ratio mixes. Expect questions that combine two forms, such as a ratio mix expressed as a percentage.
Core rules
- Simplify a fraction by dividing numerator and denominator by their HCF; add or subtract using the LCM denominator.
- Decimal places show place value: 0.25 is 25/100, not 25/1000.
- Percent means ‘per hundred’: 37% = 37/100 = 0.37. To find a percentage of a quantity, multiply by the decimal.
- A ratio compares like quantities in a fixed order; simplify by dividing all terms by their HCF. The total number of parts is the sum of the terms.
- Percentage change = (change ÷ original) × 100; the original value is the base.
Worked example
A coolant is mixed concentrate:water = 1:20. A 42 L batch is required. Total parts = 1 + 20 = 21, so one part = 42/21 = 2 L. Concentrate = 2 L and water = 40 L. Concentrate percentage = (2/42) × 100 = 4.76% approximately. Check: water is 40/42 × 100 = 95.24%, and the two percentages sum to 100%.
Traps
- Adding denominators: 1/2 + 1/3 is not 2/5.
- Reversing ratio order: 1:20 is not 20:1.
- Using the new value instead of the original as the base for percentage change.
- Treating a percentage-point rise as a percentage rise.
- Rounding a ratio before finding the total parts.