How do I answer questions involving ratios along with fractions and/or percentages ?

• In harder ratio questions, the information you are given may also involve fractions and/or percentages
• In most of these questions the key is to remember that ratios can also be turned into fractions (or vice versa)
  • For example, the ratio of staff to students in a school may be 3:37
    • That means the ratio divides the school into 3+37=40 parts
    • Staff members represent 3 of those parts, so of the people in the school are staff members
    • And students represent 37 of those parts, so of the people in the school are students
  • Note that you don’t need to know how many people are in the school to determine those fractions!
• Another key concept is the fact that you can use multiplication to find fractions or percentages of something
  • This includes finding something like a fraction of a fraction, or a percentage of a percentage, or a fraction of a percentage, or a percentage of a fraction
  • For example, of the of the people in the school who are members of staff, of them wore Christmas jumpers on a particular day
    • That means of the people in the school that day were members of staff wearing Christmas jumpers
    • , so this means 5% of the people in the school that day were members of staff wearing Christmas jumpers
  • And of the of the people in the school who are students, 88% of them wore Christmas jumpers on that same day
    • To find 88% of something, you can multiply it by 0.88
    • , so this means 81.4% of the people in the school that day were students wearing Christmas jumpers
  • Adding those percentages together tells us that 5+81.4=86.4% of the people in the school that day were wearing Christmas jumpers
  • Notice again that you don’t need to know how many people are in the school to determine all of that
• There is another method that can be used if you don’t really like dealing with ‘abstract’ fractions and percentages
  • You can pick a number for the total number of things in the question
    • So in the example above, you might assume that there are 1000 people in total in the school
    • This doesn’t mean there are really 1000 people in the school (and it doesn’t matter if there actually aren’t 1000 people in the school)
    • It just gives you a ‘real number’ to work with, instead of abstract fractions and percentages 
  • Then do all the rest of the workings on that number, using your usual techniques for fractions, ratios, and percentages
    • For example if you assumed there were 1000 people in the school described above, you would find to start that there were 75 members of staff and 925 students
    • And then you would find that 50 members of staff and 814 students wore Christmas jumpers on that day
    • So of people in the school were wearing Christmas jumpers
  • You just need to make sure at the end that you turn your answer back into the form (fraction, ratio, or percentage) that the question asks for!
  • The only problem with this method is you might pick a number that doesn’t ‘play nicely’ with the ratios, fractions, and percentages in the question
    • With the question above, for example, you might find that the number was dividing up into numbers of staff members and students that weren’t whole numbers
    • If this happens you might have to pick a new number and start over
    • For many questions, big numbers like 100 or 120, or 1000 or 1200, might be a good bet
  • See the Worked Example below for an example of this method being used