1203AFE Lecture Notes - Lecture 4: Multiplication Sign, Negative Number, Decimal Mark
30 May 2018
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Week 4 Money, Bank and Finance Lecture Notes
Numeracy 1- Maths refresher
Order of operations
• Order of Operations is very important when simplifying expressions and equations:
o Defines the order in which you should simplify different operations
o Without it, two different people may interpret an equation or expression in
different ways and come up with different answers.
• The order is as follows:
o 1. Brackets and Parentheses ( ) { } [ ] : Simplify the inside of parentheses and
brackets before you deal with the exponent (if any) of the set of parentheses
or remove the parentheses.
o 2. Orders (Exponents ( ), and Square Roots ( )): Simplify the exponent or
square root of a number or of a set of parentheses before you multiply,
divide, add, or subtract it.
o 3. Multiplication () and Division () : Simplify multiplication and division in
the order that they appear from left to right.
o 4. Addition (+) and Subtraction (-) : Simplify addition and subtraction in the
order that they appear from left to right.
• Solve the things inside brackets First:
o 2 × (4 + 6) = 2 × 10 = 20
o 2 × (4 + 6) = 8 + 6 = 14
• Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract:
o 4 × 32 = 4 × 9 = 36
o 4 × 32 = 122 = 144
• Multiply or Divide before you Add or Subtract:
o 4 + 5 × 6 = 4 + 30 = 34
o 4 + 5 × 6 = 9 × 6 = 54
• Otherwise just go left to right:
o 10 ÷ 2 × 5 = 5 × 5= 25
o 10 ÷ 2 × 5 = 10 ÷ 10 = 1
Fractions
• When we divide whole numbers we often end up with something less than a whole
uer = fratios.
• Understanding these is an essential skill which underpins all other algebraic
processes
• A fraction is some part of a whole. A fraction is written as:ଵ
ଶ
• The number below the line is the denominator and the number above it is the
numerator
• If the numerator of the fraction is smaller than the denominator then the
fraction is known as a proper fraction (the fraction has a value less than one):
• Where the numerator is larger than the denominator the fraction is known as
an improper fraction (the fraction has a value greater than or equal to one):
• A mixed number consists of fraction added to a whole number: 1
9
7
8
3
5
1
8
5
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• Can be converted to an improper fraction by first converting the whole number
(integer) to a fraction and then adding the two fractions.
• A fraction is in its lowest common terms if no number except one will divide without
remainder into both the denominator and the numerator.
Like Fractions
• Like fractions have the same number as the denominator (or a common
denominator).
• Add or subtract like fractions by adding or subtracting the numerator and placing the
result over the common denominator
Unlike Fractions
• Unlike fractions do not have the same denominator.
• To add or subtract unlike fractions it is first necessary to rewrite the
fractions so that they have a common denominator (e.g. 35 for the above)
• 35/5 = 7. Multiply 7 by the numerator 3. The numerator becomes 3 7 = 21
Multiplication of Fractions
• To multiply two fractions, multiply the two numerators together and the two
denominators together to form a new numerator and a new denominator:
• If there is a number that divides without remainder into the numerator use
cancellation:
Division of Fractions
• To divide one fraction into another, simply INVERT the second fraction (turn it upside
down) and then MULTIPLY the fractions together.
9
10
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39
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find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Week 4 money, bank and finance lecture notes. Brackets and parentheses ( ) { } [ ] : simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses: 2. Orders (exponents ( ), and square roots ( )): simplify the exponent or square root of a number or of a set of parentheses before you multiply, divide, add, or subtract it: 3. Multiplication ( ) and division ( ) : simplify multiplication and division in the order that they appear from left to right: 4. 4 32 = 4 9 = 36: 4 32 = 122 = 144, multiply or divide before you add or subtract, 4 + 5 6 = 4 + 30 = 34. 4 + 5 6 = 9 6 = 54: otherwise just go left to right, 10 2 5 = 5 5= 25, 10 2 5 = 10 10 = 1.
