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Fractions Explained. By Graeme Henchel. http://hench-maths.wikispaces.com. 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

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Fractions explained l.jpg

Fractions Explained

By Graeme Henchel

http://hench-maths.wikispaces.com


Index l.jpg

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

½+1/3 with diagram

1/3+1/4 with diagram

½ +2/5 with diagram

3/7+2/3 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

Fraction<->Decimal<-> %

100 Heart (Percentages)

Index


What is a fraction l.jpg

A fraction is formed by dividing a whole into a number of parts

What is a Fraction?

I’m the NUMERATOR. I tell you the number of parts

I’m the DENOMINATOR. I tell you the name of part


Mixed numbers to improper fractions l.jpg
Mixed numbers to improper fractions parts

Convert whole numbers to thirds

Mixed number

Improper fraction


Another way to change mixed numbers to improper fractions l.jpg
Another Way to change Mixed Numbers to improper fractions parts

In short

5x3+2=17

Since 5/5=1 there are 5 fifths in each whole.

So 3 wholes will have 3x5=15 fifths.

Plus the 2 fifths already there makes a total of

15+2=17 fifths


Equivalent fractions l.jpg
Equivalent fractions parts

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 l.jpg
Multiplying By a Special Form of One parts

Why does it work?

  • Multiplying any number by 1 does not change the value 4x1=4, 9x1=9 ……….

  • 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


Slide8 l.jpg

1 parts


Finding equivalent fractions l.jpg
Finding equivalent fractions parts

Convert 5ths to 20ths

That’s 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 l.jpg
Simplifying Fractions: Cancelling parts

  • 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 different denominators l.jpg
Adding Fractions with different denominators parts

Problem:

You can’t 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 l.jpg
Finding the partsLowest 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 denominator14 l.jpg
Finding the partsLowest 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?


Slide15 l.jpg

You can’t add fractions with different denominators parts

+

The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths

Special form of 1




Slide18 l.jpg

Finally the fractions are READY to add. I just have to add the numerators 9+14=23

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 3x3=9 and 2x7=14

Now I know the new numerators


Adding mixed numbers l.jpg
Adding Mixed Numbers the numerators 9+14=23

  • Separate the fraction and the whole number sections, add them separately and recombine at the end


Multiplying fractions l.jpg
Multiplying Fractions the numerators 9+14=23


Multiplying fractions21 l.jpg
Multiplying Fractions the numerators 9+14=23


Multiplying mixed numbers 1 l.jpg
Multiplying Mixed Numbers 1 the numerators 9+14=23

Change to Improper fractions before multiplying


Multiplying mixed numbers 2 l.jpg
Multiplying Mixed numbers 2 the numerators 9+14=23


Division of fractions l.jpg

Division of Fractions the numerators 9+14=23

By Graeme Henchel

http://hench-maths.wikispaces.com


The traditional way l.jpg
The Traditional Way the numerators 9+14=23

  • Turn the second fraction upside down and multiply


Division of fractions the short version l.jpg
Division of fractions the short version the numerators 9+14=23

Invert the 2nd fraction and multiply


Division with numbers only the full story l.jpg
Division with numbers only the numerators 9+14=23the full story


An alternative way l.jpg
An Alternative way the numerators 9+14=23

  • Convert to equivalent fractions with a common denominator and then you just divide the numerators only


Slide30 l.jpg

A visual representation the numerators 9+14=23

Form equivalent fractions with common denominators


Fraction flowchart l.jpg

Fraction Flowchart the numerators 9+14=23

Decisions and Actions in evaluating fraction problems

Graeme Henchel

http://hench-maths.wikispaces.com


Flowchart and skill set l.jpg
FLOWCHART and Skill set the numerators 9+14=23

The following should be used with the Fraction Flow chart word doc. Download from http://hench-maths.wikispaces.com


Decision what is the operation l.jpg
Decision: What is the operation? the numerators 9+14=23

What is the operation?

x,÷

+ , -


Decision are there mixed numbers l.jpg
Decision: Are there Mixed Numbers? the numerators 9+14=23

+, -

For example is a mixed number

YES

Mixed Numbers?

NO


Action evaluate whole numbers l.jpg

+, - the numerators 9+14=23

ACTION: Evaluate Whole numbers

Evaluate the whole number part and

keep aside till later

4+3=7


Decision are there common denominators l.jpg
Decision: Are there common Denominators? the numerators 9+14=23

+, -

For example and have the same (common) denominator

Common Denominators?

YES

NO


Action find equivalent fractions l.jpg

+, - the numerators 9+14=23

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 l.jpg

+, - the numerators 9+14=23

Action: Add or Subtract the numerators

Add (or subtract) the numerators this is the number of parts 2+3=5

Keep the Common Denominator.

This is the name of the fraction


Decision is the numerator negative l.jpg

+, - the numerators 9+14=23

Decision: Is the numerator negative?

Is numerator negative?

YES

NO

This numerator is negative


Action borrow a whole unit l.jpg

+, - the numerators 9+14=23

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 l.jpg

+, - the numerators 9+14=23

Action: Add any whole number part


That s all folks l.jpg

+, - the numerators 9+14=23

That’s All Folks


Decision are there mixed numbers45 l.jpg

x, the numerators 9+14=23÷

Decision: Are there Mixed Numbers?

For example is a mixed number

YES

Mixed Numbers?

NO


Action change to improper fractions l.jpg

x, the numerators 9+14=23÷

Action: Change to improper fractions

OR

4X5=20

and 20+3=23


Decision is this a x or a problem l.jpg

x, the numerators 9+14=23÷

Decision: Is this a X or a ÷ problem?

x

X or ÷ ?

÷


Action invert the 2 nd fraction and replace division with multiply x l.jpg

x, the numerators 9+14=23÷

Action: Invert the 2nd Fraction and replace division ÷ with multiply x

Invert the 2nd fraction and multiply


Decision is cancelling possible l.jpg

x, the numerators 9+14=23÷

Decision : Is cancelling Possible?

  • Do numbers in the numerators and the denominators have common factors

Yes

Common factors

in numerators

and denominators

No


Action simplify by cancelling l.jpg

x, the numerators 9+14=23÷

Action Simplify by cancelling

1

1

÷ 3

÷ 5

÷ 3

÷ 5

2

2


Action multiply the numerators and the denominators l.jpg

x, the numerators 9+14=23÷

ACTION: Multiply the numerators AND the denominators


Decision is the product improper top heavy l.jpg

x, the numerators 9+14=23÷

Decision: Is the product improper (top heavy)

Yes

Is the fraction

improper ?

(top heavy)

No


Action change to a mixed number l.jpg

x, the numerators 9+14=23÷

Action: Change to a mixed Number


That s all folks54 l.jpg

x, the numerators 9+14=23÷

That’s All Folks


Representing decimal fractions l.jpg
Representing Decimal Fractions the numerators 9+14=23

1

1

1

1

decimal point


Representing decimal fractions56 l.jpg
Representing Decimal Fractions the numerators 9+14=23

1

3

5

2

decimal point


Converting fractions to decimals and l.jpg

Converting Fractions to decimals and % the numerators 9+14=23

Graeme Henchel

http://hench-maths.wikispaces.com


Slide59 l.jpg

Conversions the numerators 9+14=23

Divide 2 by 5

Find 2÷5

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%


Slide60 l.jpg

Conversions the numerators 9+14=23

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%


Slide61 l.jpg

Conversions the numerators 9+14=23

0.4

Divide 40 by 100

 Move decimal point 2 places left

%

40

0

40%


Percentages 100 hearts l.jpg

Percentages the numerators 9+14=23100 hearts

Graeme Henchel

http://hench-maths.wikispaces.com


Visual representations l.jpg
Visual representations the numerators 9+14=23

  • 100%

  • 1%

  • 5%

  • 10%

  • 20%

  • 25%

  • 33⅓%

  • 50%

Percent = per hundred


100 100 100 l.jpg
100%=100/100 the numerators 9+14=23


1 1 100 l.jpg
1%=1/100 the numerators 9+14=23


5 5 100 1 20 l.jpg
5%=5/100=1/20 the numerators 9+14=23


10 10 100 1 10 l.jpg
10%=10/100=1/10 the numerators 9+14=23


20 20 100 1 5 l.jpg
20%=20/100=1/5 the numerators 9+14=23


25 25 100 1 4 l.jpg
25%=25/100=1/4 the numerators 9+14=23


33 33 100 l.jpg
33 the numerators 9+14=23⅓%=33⅓/100=⅓


50 50 100 l.jpg
50%=50/100= the numerators 9+14=23½


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