Percentages Objectives D Grade Express one quantity as

Percentages Objectives: D Grade Express one quantity as a percentage of another Prior knowledge: Understand how to: Convert fractions to equivalent fractions Convert fractions to decimals Convert decimals to percentages

Percentages What is a percentage? percent out of hundred So we can think of percentages also as fractions with a denominator of 100: This helps us to understand that e. g. 65 percent finding a percentage of a quantity 65 is the same as finding a fraction of a per 000 0 quantity cent

Percentages Expressing one quantity as a percentage of another Compare one quantity with the other. e. g. compare 20 with 25 Write: compare with 20 25 Write as an equivalent fraction with the denomination 100 20 25 80 ≡ 100 This is now 80% because 80 is the same as 80% 100

Percentages Sometimes you might need to have an intermediate equivalent fraction e. g. compare 4 with 40 4 compare with 40 Simplify as an equivalent fraction Write: 4 40 1 ≡ 10 Now write as an equivalent fraction with the denominator of 100 1 10 ≡ 10 100 This is now 10% because 10 is the same as 10% 100

Percentages Now do these: 1. Write 4 as a percentage of 20 2. Write 50 as a percentage of 200 3. Write 14 as a percentage of 28 4. Write 4 as a percentage of 25 5. Write 18 as a percentage of 45 4 ≡ 20 50 ≡ 200 21 ≡ 28 4 ≡ 25 18 ≡ 45 20 100 25 100 3 10 ≡ 4 100 16 100 2 40 ≡ 5 100

Percentages Harder percentages of quantities can be found using a calculator. compare with 24 34 can be read as ÷ Convert from a fraction to a decimal: Using a calculator: 24 ÷ 34 = 0. 7059 Convert from a decimal to a percentage: 0. 7059 × 100 = 70. 59 %

Percentages Now do these: 1. 2. 3. 4. 5. 3 ÷ 72 = 0. 04167 × 100 = 4. 167 % 42 ÷ 76 = 0. 5526 Write 42 as a percentage of 76 0. 5526 × 100 = 55. 26 % 45 ÷ 135 = 0. 3333 Write 45 as a percentage of 135 0. 3333 × 100 = 33. 33 % 37 ÷ 52 = 0. 7115 Write 37 as a percentage of 52 0. 7115 × 100 = 71. 15 % 92 ÷ 56 = 1. 6429 Write 92 as a percentage of 56 1. 6429 × 100 = 164. 29 % Write 3 as a percentage of 72