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Numeric Reasoning 1.1

Numeric Reasoning 1.1. Year 11. Note 4 : Fractions (Revision). To reduce fractions to their simplest form : find the highest common factor in the numerator and denominator and divide by this factor. Examples: 12 = 3 15 = 3 16 4 40 8. IWB Ex 2.01 pg 47.

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Numeric Reasoning 1.1

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  1. Numeric Reasoning 1.1 Year 11

  2. Note 4: Fractions (Revision) To reduce fractions to their simplest form: find the highest common factor in the numerator and denominator and divide by this factor. Examples: 12 = 315 = 3 16 4 40 8 IWB Ex2.01pg47

  3. Note 4: Fractions (Revision) Rules for multiplying two fractions: • multiply the two numerators • multiply the two denominators • simplify if possible Examples: x = x = =

  4. Note 4: Fractions (Revision) To get the reciprocal of a fraction, turn it upside down Examples: The reciprocal of is The reciprocal of 5 ( ) is To divide by a fraction we multiply by the reciprocal of the second fraction. IWB Ex2.03pg51 Ex2.04 pg 54 = × = Examples: ÷

  5. Note 4: Fractions (Revision) • To add/subtract fractions with different denominators • change to equivalent fractions with the same denominator • add/subtract the equivalent fractions • simplify if possible Examples: + = + IWB Ex2.02pg49-50 =

  6. StarterFractions (Applications) Let x represent the capacity of the tank ×x = 64 L 96 × = 84 L x = 64 × 84 L – 64 L = 20 L should be added x = 96 L

  7. Note 5: Decimals -> Fractions -> % To convert a decimal and fraction to a percentage multiply by 100%. Examples: 0.6 = 0.6 x 100% 0.348 = 0.348 x 100% = 60 % = 34.8 % = x 100% = x 100% = 32.5 % = 20 %

  8. Note 5: Decimals -> Fractions -> % To convert a percentage to a decimal or fraction, divide by 100 ( and simplify if a fraction is required). Examples: 75% 64 % = = = = 0.75 IWB Ex3.01 pg64-65

  9. Note 5: Decimals -> Fractions -> % Last season = x 100 % = 36.2% This season = x 100 % IWB Ex3.02 pg68-72 = 46.3%

  10. Note 5: Decimals -> Fractions -> % White Chocolate = 200 g x 0.21 = 42 + 42 x 100% = 42 g 350 = 24 % Dark Chocolate = 150 g x 0.28 IWB Ex3.02 pg68 = 42 g

  11. Note 6: Calculating Percentages and Fractions of Quantities To calculate a percentage/fraction of a given quantity, multiply the quantity by the percentage (as a fraction or a decimal). Examples: 24% of 70 30% of the Year 11 pupils at JMC (90 pupils) are left handed. How many Year 11 pupils are left handed? = x 70 = 16.8 30% of 90 = 0.3 x 90 = 27 IWB Ex3.02 pg69

  12. Note 7: Calculating ‘Original’ Quantities To calculate the original quantity we reverse the process of working out percentages of quantities. We express the percentage as a decimal and write an algebraic equation to solve. Examples: 30 is 20% of some amount. What is this amount? 20% of x = 30 0.2 x x= 30 = 150

  13. Note 7: Calculating ‘Original’ Quantities Examples: 15% of the students in a class are left handed. If there are 6 students who are left handed, how many students are in the class? 15% of x = 6 0.15 x x= 6 x = IWB Ex3.02 pg68-72 x = 40 students

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