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# Fractions Explained - PowerPoint PPT Presentation

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

By Graeme Henchel

http://hench-maths.wikispaces.com

Mixed Numbers method 1

Mixed Numbers method 2

Equivalent Fractions

Special form of one Why

Special form of one

Finding equivalent fractions

Simplifying Fractions

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

Multiplying Fractions

Multiplying Mixed Numbers 1

Multiplying Mixed numbers 2

Multiplying Mixed diagram

Dividing Fractions

Fraction Flowchart .ppt

Decimal Fractions

Fraction<->Decimal<-> %

100 Heart (Percentages)

Index

### 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

Convert whole numbers to thirds

Mixed number

Improper fraction

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 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

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

1 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 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

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 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 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?

+

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

Special form of 1

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 the numerators 9+14=23

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

Multiplying Fractions the numerators 9+14=23

Multiplying Fractions the numerators 9+14=23

Multiplying Mixed Numbers 1 the numerators 9+14=23

Change to Improper fractions before multiplying

Multiplying Mixed numbers 2 the numerators 9+14=23

### Division of Fractions the numerators 9+14=23

By Graeme Henchel

http://hench-maths.wikispaces.com

The Traditional Way the numerators 9+14=23

• Turn the second fraction upside down and multiply

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

Invert the 2nd fraction and multiply

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

An Alternative way the numerators 9+14=23

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

A visual representation the numerators 9+14=23

Form equivalent fractions with common denominators

### 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 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? the numerators 9+14=23

What is the operation?

x,÷

+ , -

Decision: Are there Mixed Numbers? the numerators 9+14=23

+, -

For example is a mixed number

YES

Mixed Numbers?

NO

+, - 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? the numerators 9+14=23

+, -

For example and have the same (common) denominator

Common Denominators?

YES

NO

+, - 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

+, - 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

+, - the numerators 9+14=23

Decision: Is the numerator negative?

Is numerator negative?

YES

NO

This numerator is negative

+, - the numerators 9+14=23

Action: Borrow a whole unit

Borrow 1 from the whole number part

Write it as an equivalent fraction

+, - the numerators 9+14=23

Action: Add any whole number part

+, - the numerators 9+14=23

That’s All Folks

x, the numerators 9+14=23÷

Decision: Are there Mixed Numbers?

For example is a mixed number

YES

Mixed Numbers?

NO

x, the numerators 9+14=23÷

Action: Change to improper fractions

OR

4X5=20

and 20+3=23

x, the numerators 9+14=23÷

Decision: Is this a X or a ÷ problem?

x

X or ÷ ?

÷

x, the numerators 9+14=23÷

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

Invert the 2nd fraction and multiply

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

x, the numerators 9+14=23÷

Action Simplify by cancelling

1

1

÷ 3

÷ 5

÷ 3

÷ 5

2

2

x, the numerators 9+14=23÷

ACTION: Multiply the numerators AND the denominators

x, the numerators 9+14=23÷

Decision: Is the product improper (top heavy)

Yes

Is the fraction

improper ?

(top heavy)

No

x, the numerators 9+14=23÷

Action: Change to a mixed Number

x, the numerators 9+14=23÷

That’s All Folks

Representing Decimal Fractions the numerators 9+14=23

1

1

1

1

decimal point

Representing Decimal Fractions the numerators 9+14=23

1

3

5

2

decimal point

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

Graeme Henchel

http://hench-maths.wikispaces.com

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%

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%

Conversions the numerators 9+14=23

0.4

Divide 40 by 100

 Move decimal point 2 places left

%

40

0

40%

### Percentages the numerators 9+14=23100 hearts

Graeme Henchel

http://hench-maths.wikispaces.com

Visual representations the numerators 9+14=23

• 100%

• 1%

• 5%

• 10%

• 20%

• 25%

• 33⅓%

• 50%

Percent = per hundred

100%=100/100 the numerators 9+14=23

1%=1/100 the numerators 9+14=23

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

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

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

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

33 the numerators 9+14=23⅓%=33⅓/100=⅓

50%=50/100= the numerators 9+14=23½