 # Fractions Explained By Graeme Henchel

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Fractions Explained By Graeme Henchel

Index 3/7+2/3 No diagram Adding Mixed Numbers Multiplying Fractions
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)

What is a Fraction? A 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
Convert whole numbers to thirds Mixed number Improper fraction

Another Way to change Mixed Numbers to improper fractions
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 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 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

Finding equivalent fractions
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
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 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
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 can’t 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

What is the lowest number BOTH 3 and 7 divide into?
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 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

Division of Fractions By Graeme Henchel

Turn the second fraction upside down and multiply
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 only the full story

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

Form equivalent fractions with common denominators
A visual representation Form equivalent fractions with common denominators

Decisions and Actions in evaluating fraction problems
Fraction Flowchart Decisions and Actions in evaluating fraction problems Graeme Henchel

FLOWCHART and Skill set
The following should be used with the Fraction Flow chart word doc. Download from

Decision: What is the operation?
x,÷ + , -

Decision: Are there Mixed Numbers?
+, - 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 4+3=7

Decision: Are there common Denominators?
+, - For example and have the same (common) denominator Common Denominators? YES 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 2+3=5 Keep the Common Denominator. This is the name of the fraction

Decision: Is the numerator negative?
+, - Decision: Is the numerator negative? Is numerator negative? YES NO This numerator is negative

Action: Borrow a whole unit
+, - 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
+, - Action: Add any whole number part

+, - That’s All Folks

Decision: Are there Mixed Numbers?
For example is a mixed number YES NO Mixed Numbers?

Action: Change to improper fractions
x,÷ Action: Change to improper fractions OR 4X5=20 and 20+3=23

Decision: Is this a X or a ÷ problem?

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

Decision : Is cancelling Possible?
x,÷ Decision : Is cancelling Possible? Do numbers in the numerators and the denominators have common factors Yes No Common factors in numerators and denominators

Action Simplify by cancelling
x,÷ Action Simplify by cancelling 1 1 ÷ 3 ÷ 5 ÷ 3 ÷ 5 2 2

ACTION: Multiply the numerators AND the denominators
x,÷ ACTION: Multiply the numerators AND the denominators

Decision: Is the product improper (top heavy)
x,÷ Decision: Is the product improper (top heavy) Yes No Is the fraction improper ? (top heavy)

Action: Change to a mixed Number

x,÷ That’s All Folks

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

Conversions 0.4 40% Multiply by a special form of 1 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%

Divide numerator and denominator by a common factor of 2
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%

 Move decimal point 2 places left
Conversions 0.4 Divide 40 by 100  Move decimal point 2 places left 40 % 40%

Graeme Henchel http://hench-maths.wikispaces.com
Percentages 100 hearts Graeme Henchel

Visual representations
100% 1% 5% 10% 20% 25% 33⅓% 50% Percent = per hundred

100%=100/100

1%=1/100

5%=5/100=1/20

10%=10/100=1/10

20%=20/100=1/5

25%=25/100=1/4

33⅓%=33⅓/100=⅓

50%=50/100=½

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