Grade DE Expressing one quantity as a percentage

Grade D/E Expressing one quantity as a percentage of another Understand that a percentage means "parts per hundred", and express one quantity as a percentage of another, including percentages greater than 100% If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk

Key Vocabulary Per hundred Percentages Quantity

How to express one quantity as a percentage of another 1) Express 6 g as a percentage of 20 g. 6 20 6 x 100 = 30% 20 We know percentage means ‘per hundred’

How to express one quantity as a percentage of another 2) Express 650 g as a percentage of 2 kg. 650 2000 650 x 100 = 32. 5% 2000 First, we need to change 2 kg to grams so we have common units

How to express one quantity as a percentage of another 3) It rained for 18 days last January. What percentage of the month was it dry? January has 31 days. 31 – 18 = 13 13 31 13 x 100 = 42% 31

Express one quantity as a fraction of another – Now you try … 1) Express each of the following as percentage (1 dp) a) 30 p of a pound b) 18 days of April c) 55 p of £ 2 d) 1 kg of 220 g e) 20 minutes of 2 hours 2) In a class of 28 pupils, 16 are girls. What percentage of the class are boys? 3) A car journey took 7 hours to complete. What percentage of the day was spent on the journey? 4) The number of trees in a forest increased from 80 to 125 from 2001 to 2016. What percentage had the number of trees increased?

Express one quantity as a fraction of another – Now you try … 1) Express each of the following as percentage (1 dp) a) 30% a) 30 p of a pound b) 60% b) 18 days of April c) 27. 5% c) 55 p of £ 2 d) 454. 5% d) 1 kg of 220 g e) 20 minutes of 2 hours e) 16. 7% 2) In a class of 28, 16 pupils are girls. What percentage of the class are boys? 2) 42. 9% 3) A car journey took 7 hours to complete. What percentage of the day was spent on the journey? 3) 29. 2% 4) The number of trees in a forest increased from 80 to 125 from 2001 to 2016. What percentage had the number of trees 4) 64% increased?

Problem Solving and Reasoning Daisy and Callum need to get an average score of 68% in their maths test to get a Grade A. Daisy gets 53 marks in the first test and 49 in the second test. Callum answers all questions and gets 2/7 of the answers wrong. Both tests are out of 85. Did either Daisy or Callum get a grade A?

Problem Solving and Reasoning Daisy and Callum need to get an average score of 68% in their maths test to get a Grade A. Daisy gets 53 marks in the first test and 49 in the second test. Callum answers all questions and gets 2/7 of the answers wrong. Both tests are out of 85. Did either Daisy or Callum get a grade A? Daisy’s total marks: 53 + 49 = 102 Total number of marks: 85 + 85 = 170 Daisy’s percentage: 102 / 170 = 0. 6 x 100 = 60% Daisy did not get A. Callum’s mark for correct answers: 7/7 – 2/7 = 5/7 of total number of marks: 5/7 x 170 = 121. 4 Callum’s percentage: 121. 4 / 170 = 0. 71 x 100 = 71% Callum got A.

Reason and explain What is the relationship between fractions and percentages? Which is a greater reduction- 1/3 off or 33% off? Calculate the pre-VAT price of a phone costing £ 230. What does 130% mean for the price of an item?