S3_General_Chapter11_TJ_Fractions

S3_General_Chapter11_TJ_Fractions - Fractions General...

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Unformatted text preview: Fractions General Simplifying Fractions www.mathsrevision.com Fractions of a quantity Finding (Simple) Percentages More Simple Percentages Reminder of Mixed Fractions Add & Subtract Fractions Multiplying Fractions 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions General 1. 3 ? Find t he missing value = 4 20 I f you know t he lengt h of t he side of a square describe in words how t o calculat e t he perimet er. 4x + 10 = 46 www.mathsrevision.com 2. 3. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fractions General Learning Intention Success Criteria 1. To know what the terms fraction. www.mathsrevision.com 1. To understand the term Fraction and be able to simplify fraction. 2. Be able to simply fractions. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fractions General A Fraction consists of 2 parts. www.mathsrevision.com 3 5 Top number is called the numerator Bottom number is called the denominator The denominator tells us the type of fraction we have The numerator tells us the how many we have 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fractions General www.mathsrevision.com 2 4 Write down the fraction that is shaded in light blue. 3 6 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fractions General www.mathsrevision.com It is possible to find a fraction equivalent to any fraction that you have by multiplying the numerator and the denominator by any number. Find a fraction equivalent to : 2 4 13 Feb 2012 x3 6 = x3 12 Compiled by Mr. Lafferty Maths Dept. 1 5 x2 2 x2 = 10 Fractions General www.mathsrevision.com We can sometimes simplify a fraction by finding a HCF between the numerator and denominator. Simplify the fractions below : 2 2 4 2 1 = 2 1 3 = 3 4 12 3 Compiled by Mr. Lafferty Maths Dept. 13 Feb 2012 Fractions General www.mathsrevision.com Now try Ex 1 Ch11(page 126) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions General 1. Calculat e t he perimet er www.mathsrevision.com 6cm 10cm 2. 3. 4. 13 Feb 2012 25 Simplif y 150 8. 52 + 4. 6 1 of 235 5 Compiled by Mr. Lafferty Maths Dept. Fractions of a quantity General Learning Intention Success Criteria 1. To know the 2 step for finding a fraction of a quantity. 2. Be able to calculate the fraction of a quantity. www.mathsrevision.com 1. To explain the 2 step process of finding a fraction of a quantity. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fractions of a quantity General Q. Do the calculations below. www.mathsrevision.com 1 2 of 120 60 2 12 0 1 4 of 120 30 4 12 0 Simply divide by the bottom number 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fractions of a quantity General Q. Do the calculation below. www.mathsrevision.com 2 3 of 24 Simply divide by the bottom number Then multiply the answer by top number Step 1: 13 Feb 2012 8 3 24 Step 2: Compiled by Mr. Lafferty Maths Dept. 8 x 2 = 16 Fractions of a quantity General Q. Do the calculation below. www.mathsrevision.com 5 8 of 360 Simply divide by the bottom number Then multiply the answer by top number Step 1: 13 Feb 2012 45 8 360 Step 2: Compiled by Mr. Lafferty Maths Dept. 4 5 x 5 = 2 2 5 Fractions of a quantity General www.mathsrevision.com Now try Ex 2 Ch11 (page 126) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions General 1. Find t he LCM of 2 and 3 Find HCF of 4 and 1 Find www.mathsrevision.com 2. 3. 4 o f 12 0 5 4. 13 Feb 2012 85 Simplif y 200 Compiled by Mr. Lafferty Maths Dept. Simple Percentages General Learning Intention Success Criteria 1. Calculate basic simple percentages. 2. Show all working. www.mathsrevision.com 1. To understand how to calculate simple percentages without a calculator. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Simple Percentages General Copy down and learn the following basic percentages www.mathsrevision.com 10 0 % 5 0 % 33 1 % 3 2 5 % 2 0 % 10 % 5 % 1% 1 4 1 5 1 1 2 1 3 1 10 1 1 2 0 10 0 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Percentages General Q. Find 25% of 40 www.mathsrevision.com 1 4 0 4 4 0 4 = 10 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Percentages General Q. Find 5% of 300 www.mathsrevision.com 1 3 0 0 20 3 0 0 2 0 = 15 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Percentages General www.mathsrevision.com Now try Ex 3 Ch11 (page 128) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions General 1. www.mathsrevision.com Calculat e 1200 Simplif y 300 2. 3. 4. 13 Feb 2012 75 200 Find 10% of 65 Find LCM and HCF f or 7 and 35 Compiled by Mr. Lafferty Maths Dept. Extended Percentages General Learning Intention Success Criteria 1. To know the basic percentages. www.mathsrevision.com 1. To explain some more basic percentages. 2. Calculate basic percentage without a calculator. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Extended Percentages General Copy down and learn the following basic percentages www.mathsrevision.com 10 0 % 50% 1 2 1 33 % 3 2 66 % 20% 3 40% 60% 80% 2 5 1 1 3 2 3 1 5 3 5 7 10 4 5 90% 9 10 10 % 3 0 % 7 0 % 1 10 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. 3 10 Extended Percentages General Q. Find 30% of 40 www.mathsrevision.com 3 4 0 10 4 0 10 x 3 = 12 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Extended Percentages General Q. Find 75% of 600 www.mathsrevision.com 3 6 0 0 4 6 0 0 4 x 3 = 4 5 0 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Extended Percentages General www.mathsrevision.com Now try Ex 4 Ch11 (page 129) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions General 1. www.mathsrevision.com Solve t he inequalit y 4x +5>29 Calculat e 3 + (- 10) + (- 7) 2. 3. 13 Feb 2012 4 Simplif y t he f ract ion 200 Compiled by Mr. Lafferty Maths Dept. Add / Sub Fractions General 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. Fractions General 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 General 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 General 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 General 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 General 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 Top Heavy to Mixed General Examples www.mathsrevision.com 1 3 4 + = 7 7 7 8 7 1 - = 9 9 9 13 Feb 2012 3 1 5 +3 = 7 7 4 8 7 2 3 1 15 - 4 = 11 7 7 7 Compiled by Mr. Lafferty Maths Dept. Top Heavy to Mixed General Examples www.mathsrevision.com 2 6 3 9 + = = 1 7 7 7 7 16 5 9 7 15 + = 15 = 16 11 11 11 11 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Add / Sub Fractions General 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 General 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 General 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. Mixed Fractions General www.mathsrevision.com Now try Extension Booklet Ex 5E (page 46) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions General 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 Starter Questions General 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 General 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. General 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 General 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 General www.mathsrevision.com 5 1 - 6 5 25 6 30 19 = 30 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Harder Fractions General 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 General 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 General 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 General 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 General Most Difficult Fractions 3 5 3 5 4 + =4 + + 4 6 4 6 7 = 5 +1 12 7 =6 12 18 + 20 24 38 = 24 14 7 =1 =1 24 12 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. www.mathsrevision.com Subtracting Fractions General www.mathsrevision.com 1 2 1 2 6 -2 = 6 -2 + - 4 3 4 3 =4 + =4 + 12 5 =3 + - 12 12 13 Feb 2012 1 2 - 4 3 -5 12 3 8 12 -5 = 12 7 =3 12 Compiled by Mr. Lafferty Maths Dept. General Most Difficult Fractions 1 1 1 1 7 -1 = 7 -1 + - 5 6 5 6 1 1 =6 + - 5 6 1 =6 + 30 1 =6 30 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. www.mathsrevision.com 6 5 30 1 = 30 Subtract Fractions General When dealing with mixed fractions deal with `whole' part first then the fraction part www.mathsrevision.com 1 6 1 1- = - 6 6 6 5 = 6 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Multiplying Fractions General www.mathsrevision.com Now try Extension Booklet Ex 6E (page 48) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Starter Questions General 1. www.mathsrevision.com 3 1 Calculat e + 4 3 I f x = 4 , y = 3 and z = 2. Find 2 z + xy Calculat e 60% of 360 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 General Learning Intention Success Criteria 1. To know the simply rule for multiplying basic fractions. 2. Calculate fractions. www.mathsrevision.com 1. To show how to multiply basic fractions. 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Fractions General A Fraction consists of 2 parts. www.mathsrevision.com 3 5 Top number is called the numerator Bottom number is called the denominator The denominator tells us the type of fraction we have The numerator tells us the how many we have 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Multiplying Fractions General Multiplying basic fractions www.mathsrevision.com 1. Multiply the numerators 2. Multiply the denominators Example 1 3 4 13 Feb 2012 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 General Multiplying basic fractions www.mathsrevision.com Example 3 2 3 2 = 5 1 3 6 5 = =1 5 5 6 Example 4 4 2 4 = 3 1 2 8 2 = =2 3 3 3 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. Multiplying Fractions General www.mathsrevision.com Now try Extension Booklet Ex 7E (page 50) 13 Feb 2012 Compiled by Mr. Lafferty Maths Dept. ...
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