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### What is a Fraction?

### Fraction Flowchart the numerators 9+14=23

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

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)

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

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 parts

Convert whole numbers to thirds

Mixed number

Improper fraction

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 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 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

1 parts

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 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 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 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?

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

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 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

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

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: 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 numbersEvaluate 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 fractionsFind 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 numeratorsAdd (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 unitBorrow 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

+, - the numerators 9+14=23

Action: Add any whole number part+, - the numerators 9+14=23

That’s All Folksx, 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: Invert the 2nd Fraction and replace division ÷ with multiply xInvert 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: Multiply the numerators AND the denominatorsx, 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 Numberx, the numerators 9+14=23÷

That’s All FolksGraeme 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%

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

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