Care needs to be taken when talking in percentages. In newspapers, it is not always clear what quoted percentages are percentages of. Politicians too can give misleading statements. To avoid this confusion some people use the term percentage points, when they are comparing the percentages of different quantities.
In elections the percentage of the vote at one election for a given party is often compared with the percentage of the vote at the previous election. In a local election votes are cast for the Purple party out of a total of votes.
At the previous election What is the swing to the Purple party in percentage points? In the election in Example 11 the Average party gets votes. Find the swing. Does it make any difference to what you have to pay if the VAT is added first then the service charge or vice versa? Does it make a difference to the amount of VAT paid? In the first case 1.
The total bill is the same. The order does not matter from the customer's point of view. However, it does from the VAT collector's point of view and indeed from that of the restaurant management, who receive a bigger service charge if it is calculated last. Hence legally VAT must be added last! Does it make any difference to the customer whether the VAT is added first then the discount subtracted, or vice versa? Give a reason for your answer. In practice this would be rounded to the nearest penny, i.
If the discount is taken first you get 1. Thus it makes no difference to the final price whether you take the discount or the VAT first. The train company announces an increase of 7. How much will the season ticket cost after the increase? Discount can be calculated in the same way as an increase by a percentage. What would the same Chinese rug be sold for now?
Give your answer as minutes and seconds. The population of a small town is What is the population likely to be after a one year, b two years? The number of casualties this year was Make a prediction for the number of casualties handled a next year, b in two years' time.
This gives 1. In an election votes out of are cast for the Gold party. What is this as a percentage? If in the previous election What would the new fares be for these trips after the increases? Now try the quiz , and see if there are any areas you need to work on.
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Printable page generated Friday, 12 Nov , Ratio, proportion and percentages Introduction The topics in this free course, Ratio, proportion and percentages , are concerned with dividing something into parts. Learning outcomes After studying this course, you should be able to: work with simple ratios convert between fractions, decimals and percentages explain the meaning of ratio, proportion and percentage find percentages of different quantities calculate percentage increases and decreases.
Example 1 At the time of writing the ratio of prices in pounds sterling to prices in euros is two to three 2 : 3. Answer 3 euros are equivalent to 2 pounds. This means that. Answer An area of 9 m 2 requires 2 litres of paint. Activity 2 If the ratio of distance measured in miles to the same distance measured in kilometres is five to eight, which is the higher speed limit, 70 miles per hour or kilometres per hour?
Example 2 Adam's grandfather ran a mile in minutes. Answer To compare the prices it would be best to compare the ratio of prices to amounts measuring amounts in the same units i.
The three tins are 15 p cheaper per kg. So the three-tin pack is the better bargain. Answer In order to compare the prices of the two cereal packs it is best to work out the price per gram for each. Example 4 The ratio of the circumference of a circle to its diameter is a constant denoted by the Greek letter p pronounced pi, it has been approximated by a number of different fractions. Example 5 Suppose you had been told that the ratio between a distance measured in miles and the same distance measured in kilometres is about 0.
Activity 6 Convert each of the following decimal ratios to fraction ratios. Answer a 0. Activity 7 A recipe for a casserole involves soaking dried beans.
Answer You need to multiply by. The units are given as: unit of distance per unit of time. Example 6 In , Hicham El Guerrouj held the record for running a mile. Work out: a his average speed in miles per hour for the 1 mile race; b his average speed in kilometres per hour for the metre race; c compare a and b. Answer a To find the speed in miles per hour, you need the ratio of the distance in miles to time in hours. Activity 9 Answer the following questions: a A cheetah is the fastest land animal over short distances.
Answer a Speed is the ratio of distance travelled to time taken, which in the cheetah's case is metres to 15 seconds. To determine this speed in kilometres per hour, both units need changing. Activity 10 Which is longer, 11 minutes or 0. To convert this to a decimal, divide 11 by 60 to get 0.
This is greater than 0. Alternatively, 0. Activity 11 A van driver averages 50 km per hour travelling on ordinary roads and 70 km per hour on motorways. Estimate: i how far the van will travel in hours; ii how long it will take to travel km; when travelling on a ordinary roads and b motorways.
Example 7 John lives with three cats. Answer There are several ways to do this. Here is one. Example 8 Debbie is checking her phone bill. Answer a 1 minute cost 30 p.
Answer For one person you need teaspoons. So almost 2 teaspoons of mustard are needed. Activity 13 The length of time it takes to cook a Christmas pudding in a pressure cooker depends on the weight of the pudding. How long will it take to cook a 2 kg pudding? Example 9 A team of five people can deliver leaflets to every house on a housing estate in three hours.
Answer Take the same approach as in Examples 7 and 8 , and first work out how long it would take one person to deliver leaflets to the estate. As a check: you would expect two people to take longer than five. A 1 year 3 months B 9 months C 1 year 4 months.
Answer C: 4 programmers take 1 year. So 1 programmer would take 4 years. Activity 15 A 10 kg bag of potatoes lasts for a week when used in catering for 7 people. Answer a First work out how long it would last one person, remembering that it will last longer for one person: it lasts 1 week for 7 people, so it lasts 7 weeks for 1 person. Activity 16 Two workers in the Open University warehouse take 20 minutes to stick labels on packages for an MU mailing.
Answer One worker should take twice as long as two. Here the ratio is also 3 blue squares to 1 yellow square, even though there are more squares. To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by So for every 2 inches, meters, whatever of height there should be 3 of width. If we made the flag 40 cm high, it should be 60 cm wide which is still in the ratio A ratio table is a list containing the equivalent ratios of any given ratio in a structured manner.
The following ratio table gives the relation between the ratio and four of its equivalent ratios. The equivalent ratios are related to each other by the multiplication of a number.
Equivalent ratios are obtained by multiplying or dividing the two terms of a ratio by the same number. In the example shown in the figure, let us take the ratio and find four equivalent ratios, by multiplying both the terms of the ratio by 2, 3, 6, and 9.
As a result, we get , , , and Example 1: There are 49 boys and 28 girls in school. Express the ratio of the number of boys to that of girls. The GCF of 49 and 28 is 7. Now, to simplify, divide the two terms by their GCF which is 7. Example 2: A music class has 30 students. Out of the 10 of them were adults and the rest were children. What is the ratio of the number of children to the total number of students in the music class?
The GCF of 87 and 75 is 3. We divide each term in the ratio by 3. Thus, the ratio in the simplest form is Ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. For example, if the number of marks scored in a test is 7 out of 10, then the ratio of marks obtained to the total number of marks is written as A ratio can be written by separating the two quantities using a colon : or it can be written in the fractional form.
Two ratios are said to be equivalent if a relationship can be established either by multiplying the first ratio's two terms by a number or dividing the first ratio's two terms with a number. Similarly, the ratio 10, when divided by 10, gives the ratio as Sometimes there may be a need wherein we have to compare the total number of values in an ordered interval. The interval of values in a ratio scale is equally distributed. It helps us to find out the total number in each interval and find the ratio between them.
The ratio scale does not support negative values. For example, to find out the total number of customers who visit a shop in a day can be found by taking a ratio scale of , , , Ratio tables are a list of equivalent ratios which are obtained either by multiplying or dividing both the quantities by the same value.
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