Arithmetic
Terms & signs, multiplication/division, fractions & decimals, factors, weights & conversions, averages & percentages, areas & volumes, roots.
Fractions, Decimals & Percentages
Ratio & Proportion
Mean, Median, Mode & Range
Weights, Measures & Conversion
Arithmetic, summary notes
- Order of operations (BODMAS: Brackets, Orders, Division/Multiplication, Addition/Subtraction) decides the result of any mixed expression, get it wrong and every downstream calculation is wrong.
- Signs: like signs multiply to a positive, unlike signs to a negative. Subtracting a negative is the same as adding.
- A fraction, a decimal and a percentage are three ways of writing the same quantity, convert freely, because maintenance data mixes all three.
- Ratio and proportion govern gear trains, lever arms and mixture ratios. Direct proportion: one rises as the other rises. Inverse: one rises as the other falls.
- Averages (means) are used to smooth repeated measurements, e.g. taking several micrometer readings and averaging to reduce reading error.
- Unit conversion is a constant source of error in maintenance. Always carry the units through the calculation, not just the numbers.
- Percentage of a quantity
- x % of N = N × (x / 100)
- Percentage change
- % change = (change ÷ original) × 100
- Mean (average)
- mean = sum of values ÷ number of values
- Area of a rectangle
- A = length × width
- Volume of a cuboid
- V = length × width × height
- Metric length
- 1 m = 1000 mm, 1 cm = 10 mm, 1 km = 1000 m
- Metric mass / volume
- 1 kg = 1000 g, 1 litre = 1000 mL
A component is reworked from 250 mm to 244 mm. What is the percentage reduction?
Change = 250 − 244 = 6 mm. % change = (6 ÷ 250) × 100 = 2.4 % reduction.
A gearbox steps 3000 rpm down in the ratio 5 : 2. Find the output speed.
Output = 3000 × (2 ÷ 5) = 1200 rpm. The output turns slower, so the smaller number goes on top, a useful sanity check.
Four micrometer readings of a journal are 25.02, 25.04, 25.03 and 25.03 mm. What diameter should be recorded?
Mean = (25.02 + 25.04 + 25.03 + 25.03) ÷ 4 = 100.12 ÷ 4 = 25.03 mm. Averaging repeated readings reduces the effect of individual reading error.
Arithmetic concept map
Arithmetic
Arithmetic check
Arithmetic Check
1. What is −4 × −3?
12−12−72. What is −8 + 3?
−55−113. What is −6 − (−2)?
−4−844. What is 5 × (−2)?
−1010−75. What is −20 ÷ 4?
−55−166. The product of two numbers with unlike signs is:
NegativePositiveZero7. What is 12 × 8?
96104868. What is 144 ÷ 12?
1214119. What is 7 × 6?
42483610. A gearbox steps 3000 rpm down in the ratio 5 : 2. What is the output speed?
1200 rpm7500 rpm600 rpm11. What is 25 × 4?
1009012512. What is 156 ÷ 13?
12131113. Express 0.375 as a fraction in lowest terms.
3/81/45/814. What is 1/2 + 1/4?
3/42/61/315. Express 3/4 as a decimal.
0.750.340.43
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