Basic (Functional) Math Notes - Part 3

Number
Negative numbers e.g. -2, -8, -3.5 (say minus two, minus eight, minus three point five)
Put numbers in order from biggest to smallest eg 6, -1, 9, 10, -8, -10
Answer: 10, 9, 6, -1, -8, -10

Multiple – A multiple of a number can be divided exactly by that number
e.g. 18 is a multiple of 2, 3, 6 and 9

Factor – A factor of a number is something that divides exactly into it
e.g. 2, 3, 4 and 6 are all factors of 12

Prime Number – A prime number has only two factors – itself and one
e.g. 2, 5, 7 and 11 are all prime numbers

Estimate – buy 4 CDs at $7.98 each. How much approximately? $8 x 4 = $32
Ratio – e.g. Dilute 1 part orange juice to 4 parts water. (Dilute – add water) Written as a ratio is 1 : 4

Proportion – increase or decrease a quantity in proportion
e.g. to double the amount, multiply everything by 2
to make five times as much, multiply everything by 5
to make half the amount, divide everything by 2
to make a third of the amount, divide everything by 3

Using formulae (formula – singular; formulae – plural)
2a = 2 x a; a b = a x b; 2ab = 2 x a x b; 2 (a + b) = 2 x (a + b)
Perimeter = distance around the edge of a 2-D shape
Perimeter = 2 (l + w) l = length, w = width
Perimeter is measured in cm, metres, km, mm etc
Area = is the amount of surface covered by a 2-D shape (flat shape)
Area = lw
Area is measured in square units: m2, cm2, mm2, km2
Volume = is the space taken up by a 3-D shape (a solid) or liquid
Volume = lwh h = height
Volume is measured in cubic units: m³, cm³, mm³, km³

Fractions – 2/4 and ½ are equivalent fractions (equal)
In the fraction 2/3, 2 is the numerator and 3 is the denominator
Reduce a fraction to its simplest form – 24/30 = 12/15 = 4/5

Decimals
6.5 is a decimal number – say six point five
● = decimal point
Round 6.247 to 1 decimal place = 6.2
Round 6.268 to 1 dp = 6.3
Round 6.268 to 2 dp = 6.27
Round 47 to the nearest ten = 50
Round 438 to the nearest 100 = 400
VAT = Value Added Tax = 17.5%

Measures, Shape and Space
Convert between currencies – buying rate / selling rate.
E.g. If $1 = €1.3 How many Euros can you buy for $10?
10 x 1.3 = €13

Convert between different measures (conversions will be given)
12 inches in a foot; 3 feet in a yard;
1760 yards in a mile A foot is about 30 cm
16 ounces in a pound (lb); 14 pounds in a stone 1 lb is about 450 grams
20 fluid ounces in a pint; 8 pints in a gallon A gallon is about 4½ litres
1 litre = 1.76 pints A litre is a bit less than 2 pints
1 metre = 39.37 inches A metre is a bit more than a yard
1 kilogram = 2.205 pounds A kilogram is a bit more than 2 lb
1 inch = 2.54 cm An inch is about 2½ cm
1 ounce = 28.35 grams An ounce is about 30 grams
Temperature - measured in Celsius and Fahrenheit scales

Circles
Circumference – distance around a the edge of a circle
Diameter – distance across a circle
Radius – half the distance across a circle
Pi = 3.142 or 22/7 (said ‘twenty two over seven’)

3D Shapes (solid shapes)
Find volume of different shapes (formulae will be given)
Parallel lines – two lines that are the same distance apart at all times e.g. railway tracks.
Scale drawing – on a room plan, for example, 1cm = 2m so expressed as a ratio: 1:200.
Example: If the scale is 1:100 on a plan, what would one centimetre represent? (100 cm, which is 1 metre) What would 10cm represent? (1000 cm, which is 10 metres)

Data handling
Median
To find the median put the numbers in order and find the middle number.
Example: Find the median for 2, 5, 8, 2, 7, 5, 1.
First put them in order: 1, 2, 2, 5, 5, 7, 8. Median = 5

Mode
The mode is the most common number. (You can have more than one mode)
Example 1: Find the mode for 2, 5, 5, 8, 7, 4, 4, 7, 2, 7. Mode = 7
Example 2: Find the mode for 2, 5, 5, 8, 7, 5, 4, 7, 2, 7. Mode = 7 and 5