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Comprehensive Guide to Fractions, Decimals, and Percentages for Year 11 Students

This resource provides an essential revision guide for Year 11 students covering key concepts in fractions, decimals, and percentages. It includes methods for simplifying fractions, rules for multiplication and division, and guidance on converting between decimals, fractions, and percentages. Students will learn to calculate percentages of quantities, determine original amounts from given percentages, and solve practical problems involving fractions. Clear examples and step-by-step methods ensure a solid understanding of these critical mathematical concepts.

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Comprehensive Guide to Fractions, Decimals, and Percentages for Year 11 Students

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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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