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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

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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 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**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**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**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 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****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 Mixed Numbers 1**Change to Improper fractions before multiplying**Division of Fractions**By Graeme Henchel http://hench-maths.wikispaces.com**The Traditional Way**• Turn the second fraction upside down and multiply**Division of fractions the short version**Invert the 2nd fraction and multiply**An Alternative way**• Convert to equivalent fractions with a common denominator and then you just divide the numerators only**A visual representation**Form equivalent fractions with common denominators**Fraction Flowchart**Decisions and Actions in evaluating fraction problems Graeme Henchel http://hench-maths.wikispaces.com**FLOWCHART and Skill set**The following should be used with the Fraction Flow chart word doc. Download from http://hench-maths.wikispaces.com**Decision: What is the operation?**What is the operation? x,÷ + , -**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? Is numerator negative? YES NO This numerator is negative**+, -**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**+, -**That’s All Folks**x,÷**Decision: Are there Mixed Numbers? For example is a mixed number YES Mixed Numbers? NO**x,÷**Action: Change to improper fractions OR 4X5=20 and 20+3=23**x,÷**Decision: Is this a X or a ÷ problem? x X or ÷ ? ÷**x,÷**Action: Invert the 2nd Fraction and replace division ÷ with multiply x Invert the 2nd fraction and multiply**x,÷**Decision : Is cancelling Possible? • Do numbers in the numerators and the denominators have common factors Yes Common factors in numerators and denominators No**x,÷**Action Simplify by cancelling 1 1 ÷ 3 ÷ 5 ÷ 3 ÷ 5 2 2

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