Here are some everyday examples of times when you could use ratios:
When you convert your Pounds to Dollars or Euros when you go on holiday When you calculate your winnings on a bet When you work out how many bottles of beer you need for a party When you share a packet of sweets fairly among your friends When you calculate how much tax you must pay on your income
Ratios are usually used to compare two numbers, though they can also be used to compare multiple quantities. Ratios are often included in numerical reasoning tests, where they can be presented in a number of different ways. It is therefore important that you are able to recognize and manipulate ratios however they are presented. However, they can also be shown in a number of other ways; the three examples below are all different expressions of the same ratio. Scaling is also helpful for increasing or decreasing the amount of ingredients in a recipe or chemical reaction. Ratios can be scaled up or down by multiplying both parts of the ratio by the same number. For example: What quantity of the ingredients will she need to use? Pancake recipe (serves 3)
100g flour 300ml milk 2 large eggs
For example, if a farmer has seven chickens and together they lay 56 eggs every day, this would be represented by the ratio 7:56 (or presented as a fraction this would be shown as 7/56). Reducing a ratio means converting the ratio to its simplest form, and this makes it easier to use. This is done by dividing both numbers in of the ratio by the largest number that they can both be divided by (this is just the same as reducing a fraction to its simplest form). So, for example: We know from the ratio that each chicken lays 8 eggs, therefore, if the farmer wants 96 eggs he must divide 96 by 8 to calculate the number of chickens required: 96/8 = 12 chickens Similarly, if one of the farmer’s chickens stopped laying eggs, he could use the ratio to work out how much that would reduce his total number of eggs to; for example, 56 – 8 = 48. You will get access to three PrepPacks of your choice, from a database that covers all the major test providers and employers and tailored profession packs. For example, there are four rings and seven bracelets in the jewellery box. If this ratio were maintained, how many necklaces would there be if there were 28 bracelets?
Question 3: Finding Unknown Quantities From Existing Equivalent Ratios
How much wine do they need in total? How much fuel will he need? How much chocolate does Claudia get? For example, if you have to split 20 sweets into a ratio of 3:1, you add the ratio figures up to find the total. In this case, that’s 3 + 1 = 4. The second step is to divide the number of sweets you are working with by the total you found. So 20 sweets divided by 4 equals 5. That 5 is then used in the third and final step to create the answer. The first number in the ratio is 3 so you multiply the 5 by 3. This gives 15. The second number in the ratio is 1 so you multiply the 5 by 1 to get 5. That gives you a final ratio of 15:5 or 20 sweets split into a pile of 15 and a pile of 5. Another common mistake in ratio questions is misreading the information, so always take care to read thoroughly before rushing to answer. A third common mistake in ratio questions is being thrown off by units or decimals. The principles of ratios remain the same regardless – but do convert km to meters, for example, so that you’re working in the same size unit for both sides of the ratio. Once you work out which type of question it is you can get an answer in minutes. A scaling question almost always just involves multiplying or dividing the original ratio numbers. Reducing a ratio requires working in fractions and might just require dividing the original ratio by half or another number. The last type of ratio question, which requires finding an unknown quantity, can require cross-multiplication or simple algebra. In terms of tricks, it helps to remember that the main property of ratios is that they need to exist between like quantities (for example, the same units and type, so that you’re comparing kg to kg or lbs to lbs). The other main property of ratios to remember is that all parts of it must be multiplied or divided by the same quantity. So if you are doubling a recipe, for example, all parts of it must be increased by a factor of two. This is an example of a ratio reduction. An example of a scaling question could be: “If 10 liters of fuel are needed to drive 50 miles, how much is needed to drive 200 miles?” In this case, you can see that the mileage has increased 4 times, therefore the fuel amount also needs to be multiplied by 4, – giving an answer of 40 liters. For example, if we are talking about how many smokers there are in an office you could say that the ratio is 1:10. That would mean there is one smoker to every 10 non-smokers – and this ratio is the most simplified way to look at the numbers. As a proportion, that same concept would be expressed as 1/10. If the office was bigger, you might say that the proportion is 10/100. Each of these two fractions (1/10 and 10/100) is equivalent to the same proportion. Ratios are also used when traveling. For example, if you needed to convert British Sterling from US Dollars it might help you to know that the ratio is 1:1.4 when shopping. That way you can work out what you’re spending in your home currency versus just the travel currency. Another everyday use of ratios can happen if you are planning a party and you predict most people will drink 3 beverages. You could then use ratios to work out how much to buy. If 15 people are coming, for example, you would then use ratios and multiply by 3 to buy 45 beverages. For example, a 1:2 ratio could be expressed as 1/2 or with the words ‘1 to 2’. In terms of basic rules, you need to treat each side of the ratio the same way. For example, if you’re tripling one side of a ratio, you would do the same to the other side. Another rule is that ratios should exist between quantities of the same kind, such as mm to mm or kg to kg. You can always adjust the units to match – for example, if you were given two items, one in grams and one in kg you can multiply the latter by 1,000 to turn both items into gram measurements. For example, you might be asked to work out the ratio of white sand beaches to black sand beaches in the world, so being able to manipulate data in these simple ways is a useful skill to have. Also, when it comes to applying for jobs or internships as a student, you will need to prepare for assessment tests. These often include numerical reasoning tests, where ratios and proportions can be presented in several different ways. As a student, it is therefore important that you can recognize and work with data to make the best of the next steps in your career. If you have previously studied fractions or algebra then the concept of ratios is easier to grasp. Even basic human constructs such as sharing food fairly between people can be helpful to give ratios a context that is relatable. For example, the knowledge of how to share a box of chocolates between five people can be useful to understand ratios. If there are 30 chocolates in the box you can describe the distribution of them in a ratio of 6:1 – so 6 chocolates are given per person. Giving as many examples as possible from real life will make it more straightforward to teach a student about ratios. Simple examples will make it easier for them to understand ratios and you can also relate ratios to the concept of fairness – as students often care a lot about this. For example, you could say that in the school next door the teacher-to-student ratio is 1:10. You could compare this to the school you are in and ask them whether it’s fair that the ratio is different in one learning environment versus another. If you wanted to make double the amount of shortbread you were originally making, you would then use 8 cups of flour, 4 cups of sugar and 2 cups of butter. Therefore just doubling the initial measurements is a way of using ratios. Using ratios this way removes the need to remember exact weights or measurements, which is helpful when you don’t have a scale to hand. Learning commonly-used ratios like the amount of flour to liquid when making bread or fritters, can result in more powerful and intuitive cooking skills than slavishly following a recipe each time would.
