Ratios - Revision Notes

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4.1Ratios


In these revision notes for Ratios, we cover the following key points:

  • What are ratios? Why ratios are called so?
  • How many quantities can be present in a ratio?
  • Why it is better to use a ratio rather than subtraction to compare two quantities?
  • What is the procedure used to calculate a ratio?
  • How to express ratios R in a number line?
  • How to calculate the inverse ratio 1:R?
  • How to calculate the fraction of a quantity out of a total?
  • How to scale up ratios?
  • How to calculate the part of a whole?
  • How to calculate part of another part.
  • How to find the new ratio when one of quantities changes?
  • How to divide in a given ratio?

Ratios Revision Notes

We use two methods for comparison of two quantities:

  1. By subtraction; for example, when we calculate how much taller a child is compared to one year ago, so that we can calculate the increase in height of that child; and
  2. By division; for example, when we calculate how many times more fruits a large box has compared to a small box so that we can calculate the number of boxes.

By definition, a ratio is a comparison of two or more numbers by means of division.

Since rational numbers are all those numbers that can be expressed as fractions, the term "rational number" therefore derives from the word "ratio".

We represent ratios through the colon (:) symbol. Ratios are nothing more than divisions of the same type of quantity. Hence, a ratio has no unit.

We calculate the value of quantities expressed as a ratio by using their GCF. We denote this GCF as k and everything is expressed in terms of k. First, we calculate k and eventually, each of the quantities involved in the ratio.

We can use the help of number line to express ratios. We need at least two number lines to represent each quantity involved in a ratio. The units are not the same but they correspond to the quantities they represent when viewed vertically.

Sometimes, it is more appropriate to express two quantities as ratios of type 1:R. In other words, we may want to calculate how much from the quantity b is needed for every a.

In other situations, we need to calculate what part of the total is one component involved in the ratio. In such cases, we first calculate in how many parts the total is made and then, we find the fraction that shows what part of the total is the quantity required.

Scaling up ratios means expressing the two quantities in two perpendicular axis. The advantage of this method is that we can obtain a larger number of possible combinations between the quantities involved, which follow the rule given in the ratio. However, it also has a disadvantage: we cannot include more than three quantities in the calculations, as the maximum number of axes we can use is three (the space is 3D). The relationship is linear, so the graph obtained is a straight line.

We can also add or subtract a quantity from a given ratio to obtain a new ratio. This procedure is carried out by applying the known rules.

Ratios can be used to divide a given quantity into unequal amounts according the numbers of the ratio.

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  3. Ratio and Proportion Practice Questions: Ratios. Test and improve your knowledge of Ratios with example questins and answers
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  5. Continuing learning ratio and proportion - read our next math tutorial: Rates. Applications of Ratios and Rates in Practice

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