Review of Basic Mathematics

Notice that the answer given by most of your calculators (there may be small variations
here depending on the model calculator you have) is
1 ÷ 987654321 = 1.0125 −09
What this actually means is that the answer to the sum is 1.0125 × 10 −9 in other
words 0.0000000010125. Keep a watch out in that top right hand corner for this kind
of notation.
Distributive Law
Suppose you have four children and each child requires a pencil case ($2.50), a ruler
($1.25), an exercise book ($2.25) and a set of coloured pencils ($12) for school.
One way we can calculate the cost is by multiplying each item by 4 and adding
the result:
(4 × $2.50) + (4 × $1.25) + (4 × $2.25) + (4 × $12) = $10 + $5 + $9 + $48 = $72
This took quite a bit of effort so perhaps there might be a simpler method. Why not
work out how much it will cost for one child and then multiply by 4?
The fact that
($2.50 + $1.25 + $2.25 + $12) × 4 = $18 × 4 = $72
4 × (2.50 + 1.25 + 2.25 + 12) = 4 × 2.5+4×1.25 + 4 × 2.25 + 4 × 12
is called the distributive law in mathematics. When we do a calculation involving
brackets we generally do the calculation inside the brackets first. When that is
not possible, for example if you have an algebraic expression then you can use the
distributive law to expand the expression. Sometimes we leave out the times symbol
when multiplying a bracket by a quantity, this is another example of mathematical
shorthand, so the above could be written
OrderofOperations
4(2.5+1.25 + 2.25 + 12)
Consider the following situation. You have worked from 2 p.m. to 9 p.m. on a major
proposal. As you were required to complete it by the following day you can claim
overtime. The rates from 9 a.m. to 5 p.m. are $25 per hour and from 5 p.m. to
midnight rise to $37.50 per hour.
Mathematically, this can be expressed as 3 × $25 + 4 × $37.50. How much do you
think you earned? Which attempt below is most reasonable?
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