Module 1 Order of Operations, Fractions and Decimals · PDF fileOrder of Operations, Fractions...

© Endeavour College of Natural Health endeavour.edu.au 1

Enabling Courses: Enabling Mathematics

Module 1

Order of Operations, Fractions and

Decimals


Module Plan

o General introduction• Welcome

• Module aims

• How to use these Modules

o Order of Operations

o Fractions• Proper fractions, improper fractions and mixed numbers

• Adding Fractions

• Subtracting Fractions

• Multiplying Fractions

• Dividing Fractions

o Decimals• Adding Decimals

• Subtracting Decimals

• Multiplying Decimals

• Dividing Decimals


General introduction

o Enabling subjects:

• Introductory level of knowledge

• Self-paced and flexible

o Mathematics is used everyday in medicine, cookery,

brewing and wine making, growing crops and animals,

architecture and building, and forensic science

o Aim: Provide a smooth transition into your introductory

courses such as chemistry.

o Structure: 4 modules

• Best to complete in order

o Use activities, and quizzes to help you learn


Order of Operations

o Order of Operations: Follow steps in a particular order to

get correct answer.

o Certain sums in mathematics must be done before

others.

o Six operations:

• Addition (+)

• Subtraction (–)

• Multiplication (x)

• Division (÷ or /)

• Brackets ( ) and

• Powers (also referred to as “of” or “to the order of”) (e.g. 32, 63).

Image:

http://europeansectionarcipreste.blogspot.com.au/2012/04/multiplying-and-

dividing-fractions.html


Order of Operations: BODMAS

o In mathematics we follow BODMAS rule for the order of

operations:

• Brackets ( )

• Of or Order 22, 34, 56

• Division ÷, or /

• Multiplication x

• Addition +

• Subtraction -

o Enable to compute in the correct order any mathematical

question put forward.

http://www.mentalstarters.co.uk/Key%20Stage%204

%20Foundation.htm


Order of Operations: BODMAS

o Example:

(3 – 5) + 6 ÷ 3 – 2

B first: (3 – 5) = -2

D next. 6 ÷ 3 = 2

o Therefore: -2 + 2 = 0 Here, A first (work out the

answer from left to right).

And: 0 – 2 = -2 Then complete the sum

Answer = -2 using S.


Fractions

o An essential tool:

• To make exact measurements and we often need to work with

parts or percentages of the whole

• When preparing a mixture for a natural medicine formulation; in

many mixtures, fractions of amounts need to be added,

subtracted, multiplied or even divided.

o Includes:

• Proper fractions, improper fractions and mixed numbers

• Adding Fractions

• Subtracting Fractions

• Multiplying Fractions

• Dividing Fractions

http://www.sweetcounter.co.uk/sc2-flip-flap-fractions-p-333.html


Proper Fractions

o Proper fraction: has a numerator less than its

denominator.

• Numerator as the top number and Denominator as the bottom

number. So a proper fraction is not a whole number, but a

fraction of it.

o Examples:¾ Or

𝟑

𝟒

-1/8 Or - 𝟏

𝟖

𝟏𝟏/𝟏𝟐 Or 𝟏𝟏

𝟏𝟐

http://memoryjoggers.com/2012/08/remembering-proper-

and-improper-fractions/

Proper Fraction Improper Fraction


Improper Fractions

o Improper fraction: has a numerator greater than its

denominator.

o Examples:

𝟓𝟑 Or

𝟓

𝟑

−𝟗𝟖 Or −

𝟗

𝟖

𝟏𝟓𝟏𝟐 Or

𝟏𝟓

𝟏𝟐


Mixed Numbers


Mixed Numbers

o Converting mixed numbers into improper fractions: The

whole number is first converted to a fraction. The

fractions are then added

o Example:

http://www.visualfractions.com/MixedtoFracC/mixedtofrCircles.html


Mixed Numbers

http://www.visualfractions.com/MixedCircles/imixedcircles.html


Adding Fractions

http://www2.potsdam.edu/abramovs/compenv310.htm


Adding Fractions

o Adding fractions with different denominators:

o Example:Multiples of 8 are 8, 16, 24, 32, 40, 48, and so on.

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, and so on.

The lowest common multiple of 8 and 3 is 24. The fraction needs to

be converted to a denominator of 24. Note that the numerator and

denominator of each fraction must be multiplied by the same

number.

Multiply the numerator and denominator of the first fraction by 3 to

make the denominator 24.

Multiply the numerator and denominator of the second fraction by 8

to make the denominator 24.

Now we can add the numerators.


Subtracting Fractions

http://www.buzzle.com/articles/subtracting-fractions-with-unlike-

denominators.html


Subtracting Fractions

The lowest common multiple of 6 and 5 is 30.

This fraction can be simplified by dividing the numerator and

denominator by a common number. All fractions can be simplified

if there is a common number you can divide the numerator and

denominator by.

o Subtracting fractions with different denominators:

o Example:


Multiplying Fractions

o Simply need to multiply the numerators and

denominators

o Best for the fractions to be in their simplest form when

multiplying them, so that the answer is not a large

fraction.

o Two methods:

• Multiplying fractions that are in their simplest form

• Multiplying fractions that need to be simplified first


Multiplying Fractions

http://testpreparations.com/help/learn-to-multiply-and-divide-with-fractions/


Multiplying fractions


Dividing Fractions

o To divide fractions, flip or invert the fraction that to be

dividing by (the second fraction).

o Then change the division sign to a multiplication sign

and treat it in the same way as multiplication of fractions

o Example:

3 2

4 7 Flip the second fraction.

= 3 7

4 2 Change the sign to x.

= 3 7

x 4 2

Multiply the numerators and denominators.

=

21

8

=

52

8

http://edtech2.boisestate.edu/robertsona/506/finalProject/DividingFractions.html


Decimals

http://www.mentalstarters.co.uk/Year%205.htm


Adding Decimals

o Place all decimals vertically keeping the decimal points

aligned.

o Example:

http://www.coolmath.com/prealgebra/02-decimals/06-decimals-adding-01.htm


Subtracting Decimals

o Same as adding decimals.

o Example:

http://www.coolmath.com/prealgebra/02-decimals/07-decimals-subtracting-01.htm


Multiplying Decimals

o Step 1: Multiply decimals by temporarily ignoring the

decimal point and multiply the digits.

o Step 2: The number of decimal places in the final answer

must be the same as the total number in the question.

So, insert the decimal point in the answer by counting to

the left for total number of decimals in question.

http://www.coolmath.com/prealgebra/02-decimals/08-decimals-multiplying-01.htm


Multiplying Decimals


Dividing Decimals

o Same method as multiplication of decimals.

o Complete the division of the two numbers first and then

include the position of the decimal point

o Example:

8.1 ÷ 9

= 81 ÷ 9

= 9

o Now, in the original question, 8.1 has one decimal place

and 9 has zero decimal places. So in total move one

decimal place to the left to arrive at the final answer of

0.9.

http://www.mahalo.com/how-to-

divide-decimals/


What Is Next

o In the Next module we will cover….

Percentages, Ratios and Indices (powers) and Logarithms


COMMONWEALTH OF AUSTRALIA

Copyright Regulations 1969

WARNING

This material has been reproduced and

communicated to you by or on behalf of

the Endeavour College of Natural Health pursuant to

Part VB of the Copyright Act 1968 (the Act).

The material in this communication may

be subject to copyright under the Act.

Any further reproduction or

communication of this material by you

may be the subject of copyright

protection under the Act.

Do not remove this notice.

Module 1 Order of Operations, Fractions and Decimals · PDF fileOrder of Operations, Fractions...

Documents

Transcript of Module 1 Order of Operations, Fractions and Decimals · PDF fileOrder of Operations, Fractions...