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Fractions Explained

- By Graeme Henchel

http//hench-maths.wikispaces.com

Index

- What is a fraction?
- Mixed Numbers method 1
- Mixed Numbers method 2
- Equivalent Fractions
- Special form of one Why
- Special form of one
- Finding equivalent fractions
- Simplifying Fractions
- Adding Common denominators
- Adding Different denominators
- Common denominators 1
- Common denominators 2
- ½1/3 with diagram
- 1/31/4 with diagram
- ½ 2/5 with diagram

- 3/72/3 No diagram
- Adding Mixed Numbers
- Multiplying Fractions
- Multiplying Mixed Numbers 1
- Multiplying Mixed numbers 2
- Multiplying Mixed diagram
- Dividing Fractions
- Fraction Flowchart .ppt
- Fraction Flowchart .doc (download)
- Decimal Fractions
- Fractionlt-gtDecimallt-gt
- 100 Heart (Percentages)

What is a Fraction?

A fraction is formed by dividing a whole into a

number of parts

Im the NUMERATOR. I tell you the number of parts

Im the DENOMINATOR. I tell you the name of part

Mixed numbers to improper fractions

Convert whole numbers to thirds

Mixed number

Improper fraction

Another Way to change Mixed Numbers to improper

fractions

In short 5x3217

Since 5/51 there are 5 fifths in each whole. So

3 wholes will have 3x515 fifths. Plus the 2

fifths already there makes a total of 15217

fifths

Equivalent fractions

An equivalent fraction is one that has the same

value and position on the number line but has a

different denominator

Equivalent fractions can be found by multiplying

by a special form of 1

Multiplying By a Special Form of One

Why does it work?

- Multiplying any number by 1 does not change the

value 4x14, 9x19 . - Any number divided by itself 1.

Multiplying a fraction by a special form of one

changes the numerator and the denominator but

DOES NOT CHANGE THE VALUE

1

Finding equivalent fractions

Convert 5ths to 20ths

Thats 4 so I must multiply by

What do we multiply 5 by to get a product of 20?

Special form of 1

Simplifying Fractions Cancelling

- Simplifying means finding an equivalent fraction

with the LOWEST denominator by making a special

form of 1 equal to 1

1

Another way of doing this

Adding Fractions with common denominators

Adding Fractions with different denominators

Problem You cant add fractions with different

denominators without getting them ready first.

They will be ready to add when they have common

denominators

Solution Turn fractions into equivalent

fractions with a common denominator that is find

the Lowest Common Multiple (LCM) of the two

denominators

Finding the Lowest Common Denominator

- The lowest common multiple of two numbers is the

lowest number in BOTH lists of multiples

Multiples of 2 are 2, 4, 6, 8, 10 Multiples of

3 are 3, 6, 9, 12, What is the lowest

common multiple?

Finding the Lowest Common Denominator

- The lowest common multiple of two numbers is the

lowest number they will BOTH divide into

2 divides into 2, 4, 6, 8.. 3 divides into 3, 6,

9. What is the lowest number 2 and 3 both

divide into?

You cant add fractions with different

denominators

The Lowest Common Multiple of 2 and 3 is 6 so

turn all fractions into sixths

Special form of 1

Lowest common denominator is 10 so make all

fractions tenths

Turn both fractions into twelfths

Finally the fractions are READY to add. I just

have to add the numerators 91423

It is 3/3 So I multiply 3/7 by 3/3

It is 7/7 So I multiply 2/3 by 7/7

What is the lowest number BOTH 3 and 7 divide

into? Hmmmmm??????

What special form of 1 will change 7 to 21.

Hmmmm?

What special form of 1 will change 3 to 21.

Hmmmm?

It is 21. So that is my common denominator

Now 3x39 and 2x714 Now I know the new numerators

Adding Mixed Numbers

- Separate the fraction and the whole number

sections, add them separately and recombine at

the end

Multiplying Fractions

Multiplying Fractions

Multiplying Mixed Numbers 1

Change to Improper fractions before multiplying

Multiplying Mixed numbers 2

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Division of Fractions

- By Graeme Henchel

http//hench-maths.wikispaces.com

The Traditional Way

- Turn the second fraction upside down and multiply

Division of fractions the short version

Invert the 2nd fraction and multiply

Division with numbers onlythe full story

An Alternative way

- Convert to equivalent fractions with a common

denominator and then you just divide the

numerators only

A visual representation

Form equivalent fractions with common denominators

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Fraction Flowchart

- Decisions and Actions in evaluating fraction

problems - Graeme Henchel
- http//hench-maths.wikispaces.com

FLOWCHART and Skill set

The following should be used with the Fraction

Flow chart word doc. Download from

http//hench-maths.wikispaces.com

Decision What is the operation?

What is the operation?

x,

, -

Decision Are there Mixed Numbers?

, -

For example is a mixed number

YES

Mixed Numbers?

NO

ACTION Evaluate Whole numbers

, -

Evaluate the whole number part and keep aside

till later

437

Decision Are there common Denominators?

, -

For example and have

the same (common) denominator

YES

Common Denominators?

NO

Action Find equivalent fractions

, -

Find equivalent fractions with common (the same)

denominators

Multiply by a special form of 1

Multiply by a special form of 1

Action Add or Subtract the numerators

, -

Add (or subtract) the numerators this is the

number of parts 235

Keep the Common Denominator. This is the name of

the fraction

Decision Is the numerator negative?

, -

YES

Is numerator negative?

NO

This numerator is negative

Action Borrow a whole unit

, -

Borrow 1 from the whole number part Write it as

an equivalent fraction Add this to your negative

fraction

Remember to adjust your whole number total

Action Add any whole number part

, -

Thats All Folks

, -

Decision Are there Mixed Numbers?

x,

For example is a mixed number

YES

Mixed Numbers?

NO

Action Change to improper fractions

x,

OR

4X520 and 20323

Decision Is this a X or a problem?

x,

x

X or ?

Action Invert the 2nd Fraction and replace

division with multiply x

x,

Invert the 2nd fraction and multiply

Decision Is cancelling Possible?

x,

- Do numbers in the numerators and the denominators

have common factors

Yes

Common factors in numerators and denominators

No

Action Simplify by cancelling

x,

1

1

3

5

3

5

2

2

ACTION Multiply the numerators AND the

denominators

x,

Decision Is the product improper (top heavy)

x,

Yes

Is the fraction improper ? (top heavy)

No

Action Change to a mixed Number

x,

Thats All Folks

x,

Representing Decimal Fractions

1

1

1

1

?

decimal point

?

Representing Decimal Fractions

1

3

5

2

?

decimal point

?

Converting Fractions to decimals and

- Graeme Henchel
- http//hench-maths.wikispaces.com

(No Transcript)

Conversions

Divide 2 by 5 Find ?25

Multiply by a special form of 1

Write as a decimal using place value

Write as a fraction with 10 as denominator

0.4

Multiply by a special form of 1

Multiply by special form of 1

40

Conversions

Divide numerator and denominator by a common

factor of 2

Write as a fraction with 100 as denominator then

divide numerator and denominator by common factor

of 20

0.4

Write as a fraction with 100 as denominator then

divide numerator and denominator by common factor

of 10

40

Conversions

0.4

Divide 40 by 100 ? Move decimal point 2 places

left

40

0

40

Percentages100 hearts

- Graeme Henchel
- http//hench-maths.wikispaces.com

Visual representations

- 100
- 1
- 5
- 10
- 20
- 25
- 33?
- 50

Percent per hundred

100100/100

11/100

55/1001/20

1010/1001/10

2020/1001/5

2525/1001/4

33?33?/100?

5050/100½