S2_Level_F_Ch31_Fractions - Fractions Level F...

Unformatted text preview: Fractions Level F www.mathsrevision.com Reminder and Mixed Fractions Add & Subtract basic Fractions Add & Sub Harder Fractions Multiplying Fractions 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Level F Starter Level F 1. Solve t he inequalit y 3x - 6 =12 Calculat e (- 29) + (- 11) + 9 W hat f ract ion is x: Simplif y t he f ract ion www.mathsrevision.com 2. 3. 4. 5. X 25 200 W hat is t he coordinat e C(- 2,- 2) ref lect ed in t he x - axis? 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Mixed Fractions Level F Learning Intention Success Criteria 1. To know what the terms fraction, topheavy and mixed fraction are. 2. Convert between topheavy and mixed fraction. 3. Solve problems involving fractions. www.mathsrevision.com 1. To understand the term Fraction and Mixed Fraction. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fraction Reminder Level F A Fraction consists of 2 parts. www.mathsrevision.com Top number called the NUMERATOR 3 5 Bottom number called the DENOMINATOR 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fractions Level F We can sometimes `simplify' a fraction by dividing by the HCF of the numerator and denominator www.mathsrevision.com F15 1 and 15 3 and 5 15 27 13 Feb 2012 15 27 F27 1 and 27 3 and 9 5 = 9 3 3 Compiled by Mr. Lafferty Maths Dept. Fractions Level F 7 A fraction, like, where the numerator is bigger 3 www.mathsrevision.com than the denominator is called a `TopHeavy' fraction. 3 5 A number,like, consisting of 4 a `whole number' part and a `fraction' part is called a Mixed fraction 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Top Heavy to Mixed Level F 7 3 means seven thirds www.mathsrevision.com 7 1 1 1 1 1 1 1 = + + + + + + 3 3 3 3 3 3 3 3 7 3 3 1 = + + 3 3 3 3 7 1 =2 3 3 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Top Heavy to Mixed Level F NUMERATOR DENOMINATOR www.mathsrevision.com 7 can be written as 7 3 3 2 3 7 remainder 1 1 =2 3 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Top Heavy to Mixed Level F NUMERATOR DENOMINATOR www.mathsrevision.com 17 can be written as 17 5 5 3 5 17 remainder 2 2 =3 5 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Mixed to Top Heavy Level F www.mathsrevision.com WHOLE NUMBER DENOMINATOR then add NUMERATOR Changing a mixed fraction to a topheavy. 5 3 4 5 4 3 7 5 2 23 quarters = 23 4 2 7 5 13 Feb 2012 37 fifths Compiled by Mr. Lafferty Maths Dept. 37 = 5 Mixed Fractions Level F www.mathsrevision.com Now try Exercise 1 Ch31 (page 128) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Level F Starter Questions Level F 1. Calculat e t he perimet er of Simplif y 5cm 7cm www.mathsrevision.com 2. 3. 4. 5. 12 ? 84 W rit e 2% as a decimal List t he prime numbers bet ween 20 and 30 Calculat e 7 5 + 2 2 Compiled by Mr. Lafferty Maths Dept. 13 Feb 2012 Add / Sub Fractions Level F Learning Intention Success Criteria 1. To know that to add and subtract fractions the denominators must be the same. 2. To be able to do simple fraction calculations. www.mathsrevision.com 1. To understand how to add and subtract basic fractions. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Add / Sub Fractions Level F You can only add or subtract fractions if: www.mathsrevision.com DENOMINATORS ARE THE SAME NUMBER Example 1 3 2 5 + = 7 7 7 Example 2 7 1 6 3 - = = 8 8 8 4 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Add Fractions Level F When dealing with mixed fractions deal with `whole' part first then the fraction part www.mathsrevision.com 3 4 3 4 2 +1 = 2 +1 + + 5 5 5 5 =3 + 2 =4 5 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. 7 5 Subtract Fractions Level F When dealing with mixed fractions deal with `whole' part first then the fraction part www.mathsrevision.com 5 1 5 1 7 - 4 = 7 - 4 + - 6 6 6 6 4 =3 + 6 2 =3 3 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Add / Sub Fractions Level F www.mathsrevision.com Now try Exercise 2 Ch31 (page 131) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Level F Starter Questions 1. Calculat e www.mathsrevision.com 4 14 + 9 9 2. 3. 4. 5. 13 Feb 2012 Expand y(2 y + 3x + 4) W rit e 72% as a decimal Find t he LCM of 2 and 3 2. 5% of 600 Compiled by Mr. Lafferty Maths Dept. Harder Fractions Level F Learning Intention Success Criteria 1. Apply ` kiss and smile' method. 2. Convert top heavy fractions to mixed fractions. 3. Simplify fractions. www.mathsrevision.com 1. To understand how to add and subtract fractions with different denominators. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Level F We are going to use Harder the kiss and smile method Fractions How can we add /subtract fractions that have different denominators www.mathsrevision.com Step 1 : Do the smile Step 2 : Do the kiss Step 3 : Add/Subtract the numerator and simplify 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Harder Fractions Level F www.mathsrevision.com Step 1 : Do the smile Step 2 : Do the kiss Example 1 Step 3 : Add/Subtract the numerator and simplify 1 1 + 2 4 4 +2 8 6 2 = 2 8 3 = 4 Compiled by Mr. Lafferty Maths Dept. 13 Feb 2012 Harder Fractions 5 1 - 6 5 25 6 30 19 = 30 www.mathsrevision.com 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Harder Fractions Level F www.mathsrevision.com 5 3 + 6 4 20 + 18 24 38 = 24 14 14 2 7 =1 =1 =1 2 24 24 12 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Harder Fractions Level F www.mathsrevision.com Now try Exercise 3 Ch31 (page 133) Q1 and Q2 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Harder Fractions Level F How can we add /subtract mixed fractions that have different denominators www.mathsrevision.com Simple ! When dealing with mixed fractions deal with `whole' part first then the fraction part 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Harder Fractions Level F www.mathsrevision.com 1 2 1 2 2 +3 = 2 +3 + + 2 3 2 3 1 2 =5 + + 2 3 1 = 5 +1 6 1 =6 6 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. 3 +4 6 7 = 6 1 =1 6 Harder Fractions Level F www.mathsrevision.com 7 2 7 2 7 -4 =7 -4 + - 8 3 8 3 7 2 =3 + - 8 3 5 =3 + 24 5 =3 24 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. 21 16 24 5 = 24 Harder Fractions Level F www.mathsrevision.com 3 5 3 5 4 + =4 + + 4 6 4 6 7 = 4 +1 12 7 =5 12 18 + 20 24 38 = 24 14 7 =1 =1 24 12 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Harder Fractions Level F www.mathsrevision.com Now try Exercise 3 Ch31 (page 134) Q4 to Q8 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Level F Most Difficult Fractions 1 2 1 2 6 -2 = 6 -2 + - 4 3 4 3 =4 + =4 + 12 5 =3 + - 12 12 13 Feb 2012 www.mathsrevision.com 1 2 - 4 3 -5 12 3 8 12 -5 = 12 7 =3 12 Compiled by Mr. Lafferty Maths Dept. Level F Most Difficult Fractions 1 2 1 2 7 -1 = 7 -1 + - 5 3 5 3 1 2 =6 + - 5 3 -7 =6 + 15 8 =5 15 Compiled by Mr. Lafferty Maths Dept. www.mathsrevision.com 3 10 15 -7 = 15 =5 + 15 7 - 15 15 13 Feb 2012 Harder Fractions Level F www.mathsrevision.com Now try Exercise 3 Ch31 (page 134) Q9 to Q15 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Level F Starter Questions Level F 1. 3 1 Calculat e + 4 3 I f x = 4 , y = 3 and z = 2. Find z 2 (2 z + xy) Calculat e 60% of 360 www.mathsrevision.com 2. 3. 4. 13 Feb 2012 5 Make t he f ollowing t op- heavy 5 6 Compiled by Mr. Lafferty Maths Dept. Multiplying Fractions Level F Learning Intention Success Criteria 1. To know the simply rules for multiplying basic and mixed fractions. 2. Calculate fractions. www.mathsrevision.com 1. To show how to multiply basic and mixed fractions. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Multiplying Fractions Level F Multiply basic fractions 1. Multiply the numerators 2. Multiply the denominators Example 1 3 4 13 Feb 2012 www.mathsrevision.com Example 2 4 5 Compiled by Mr. Lafferty Maths Dept. 3 3 3 9 = = 5 4 5 20 5 4 5 20 2 = = = 6 5 6 30 3 Multiplying Fractions Level F www.mathsrevision.com Now try Exercise 4 Ch31 (page 136) Q1 to Q4 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Multiplying Fractions Level F Multiplying Mixed Fractions www.mathsrevision.com 1. Make fractions topheavy 2. Multiply the numerators 3. Multiply the denominators 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Multiplying Fractions Level F Example 1 1 1 3 1 2 3 = 7 2 4 3 www.mathsrevision.com 7 4 = 2 3 28 4 2 = = 4 =2 6 6 3 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Multiplying Fractions Level F Example 2 3 4 4 = 19 4 1 1 5 6 5 www.mathsrevision.com 19 6 = 4 5 114 14 7 = =5 =5 20 20 10 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Multiplying Fractions Level F www.mathsrevision.com Now try Exercise 4 Ch31 (page 136) Q5 to Q10 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Level F Starter Questions Level F www.mathsrevision.com 1. 2. 3. 13 Feb 2012 1 1 Calculat e 1 + 3 2 3 Simplif y 3a(4a -3b) - 12ab 2 3 Mult iply 3 2 Compiled by Mr. Lafferty Maths Dept. Dividing Fractions Level F www.mathsrevision.com Now try Exercise 5 Ch31 (page 138) Q1 to Q4 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Dividing Fractions Level F www.mathsrevision.com Now try Exercise 5 Ch31 (page 138) Q5 to Q10 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. ...
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