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**Fractions Explained By Graeme Henchel**

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**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)

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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

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**Mixed numbers to improper fractions**

Convert whole numbers to thirds Mixed number Improper fraction

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**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

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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

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**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

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1

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**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

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**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

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**Adding Fractions with common denominators**

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**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

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**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?

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**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?

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**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

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**Lowest common denominator is 10 so make all fractions tenths**

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**Turn both fractions into twelfths**

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**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

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Adding Mixed Numbers Separate the fraction and the whole number sections, add them separately and recombine at the end

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**Multiplying Fractions**

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**Multiplying Fractions**

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**Multiplying Mixed Numbers 1**

Change to Improper fractions before multiplying

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**Multiplying Mixed numbers 2**

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**Division of Fractions By Graeme Henchel**

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**Turn the second fraction upside down and multiply**

The Traditional Way Turn the second fraction upside down and multiply

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**Division of fractions the short version**

Invert the 2nd fraction and multiply

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**Division with numbers only the full story**

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

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**Form equivalent fractions with common denominators**

A visual representation Form equivalent fractions with common denominators

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**Decisions and Actions in evaluating fraction problems**

Fraction Flowchart Decisions and Actions in evaluating fraction problems Graeme Henchel

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**FLOWCHART and Skill set**

The following should be used with the Fraction Flow chart word doc. Download from

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**Decision: What is the operation?**

x,÷ + , -

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**Decision: Are there Mixed Numbers?**

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

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**ACTION: Evaluate Whole numbers**

+, - Evaluate the whole number part and keep aside till later 4+3=7

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**Decision: Are there common Denominators?**

+, - For example and have the same (common) denominator Common Denominators? YES NO

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**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

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**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

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**Decision: Is the numerator negative?**

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

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**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

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**Action: Add any whole number part**

+, - Action: Add any whole number part

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+, - That’s All Folks

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**Decision: Are there Mixed Numbers?**

For example is a mixed number YES NO Mixed Numbers?

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**Action: Change to improper fractions**

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

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**Decision: Is this a X or a ÷ problem?**

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

Invert the 2nd fraction and multiply

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**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

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**Action Simplify by cancelling**

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

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**ACTION: Multiply the numerators AND the denominators**

x,÷ ACTION: Multiply the numerators AND the denominators

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**Decision: Is the product improper (top heavy)**

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

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**Action: Change to a mixed Number**

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x,÷ That’s All Folks

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**Representing Decimal Fractions**

1 1 1 1 ● decimal point ●

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**Representing Decimal Fractions**

1 3 5 2 ● decimal point ●

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**Converting Fractions to decimals and %**

Graeme Henchel

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**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%

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**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%

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** Move decimal point 2 places left**

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

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

Percentages 100 hearts Graeme Henchel

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**Visual representations**

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

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100%=100/100

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1%=1/100

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5%=5/100=1/20

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10%=10/100=1/10

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20%=20/100=1/5

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25%=25/100=1/4

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33⅓%=33⅓/100=⅓

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50%=50/100=½

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