Workplace Numeracy — Apprenticeship Support

• A percentage is a fraction out of 100. Find 15% of an amount by multiplying it by 0.15; a 15% discount leaves 85%, so multiply by 0.85.
• A ratio such as 2:3 describes five equal parts in total. Divide the total by five before multiplying by the number of parts for each share.
• Check what the question asks for: the discount is not the final price, and one ratio share is not the whole mixture.

Watch for: Giving the amount removed instead of the final price. Dividing by one side of a ratio instead of the total number of parts.

• One metre contains 100 centimetres and 1,000 millimetres. Converting metres to millimetres makes the number larger because the unit is smaller.
• The area of a rectangle is length × width. Convert both measurements to the same unit first and give the result in square units.
• A scale of 1:50 means every length on a drawing represents 50 times that length in reality. Area scale factors are different from length scale factors.

Watch for: Multiplying metres by centimetres without converting. Writing metres rather than square metres for an area.

• A rate compares a quantity with time: 24 items per hour means 24 items in each hour at a constant pace. Output = rate × working time.
• There are 60 minutes in one hour: 30 minutes is 0.5 hours, not 0.30 hours. Convert units before multiplying a rate.
• Elapsed time includes breaks; productive time may exclude them. State which time is being used and do not assume that real work always proceeds at a constant rate.

Watch for: Treating 45 minutes as 0.45 hours. Counting an unpaid break as productive time when the scenario excludes it.

• The mean is the total of the observations divided by their number. Include zero observations when they are part of the data.
• For a percentage rate, divide the part by the whole and multiply by 100. Comparing counts alone can be misleading when the totals differ.
• A rate calculated from a small sample describes that sample. It does not, by itself, prove which team or process will perform better in future.

Watch for: Dividing by the largest value instead of the number of observations. Calling the group with fewer errors better without checking how many tasks it completed.