Ratios

Understanding Ratios

  • Ratio is a method of comparing quantities. It shows how much of one thing there is compared to another thing.

  • Ratios can be written in several ways: for instance, 2 to 3, 2:3 or 2/3.

  • The order in which quantities are represented in a ratio is significant. The ratio 2:3 is not the same as the ratio 3:2.

Simplifying Ratios

  • Simplifying a ratio involves making it as simple as possible, similarly to simplifying fractions.

  • To simplify a ratio, find the highest factor that divides exactly into both quantities, and then divide both sides by this number.

  • For example, if the ratio is 10:15, you can simplify it by dividing both quantities by their highest common factor, which is 5. Hence, it simplifies to 2:3.

Ratios in Real-Life Scenarios

  • Ratios are often used in real-life scenarios, such as following a recipe, sharing treats or comparing quantities of different things.

  • For instance, if you are sharing sweets in the ratio 2:1, and there are 15 sweets, you can divide the total number by the sum of the parts of the ratio, in this case, 2 + 1 = 3. Then you multiply the result by each part to find out how many each person gets.

Ratio Problems

  • A common type of maths problem involving ratios is finding out the total quantity, such as ‘if 2 parts represent 10, what does 5 parts represent?’

  • To solve such a problem, first figure out how much one part represents (by dividing the given total by the given number of parts), and then multiply this by the number of parts you need to find.

Ratios and Fractions

  • Ratios are closely related to fractions. A ratio of 2:3 can be represented as the fraction 2/3. This shows that for every 2 parts of one quantity, there are 3 parts of another.

  • To convert a fraction to a ratio, simply take the numerator and the denominator as the two components of the ratio. For example, the fraction 1/4 converts to the ratio 1:4.

Ratios involving Three Quantities

  • Ratios can also involve more than two quantities. For instance, a ratio might compare the quantities of three types of sweets in a bag: 2:3:5.

  • Solving problems with three-part ratios involves the same principles as those with two parts: adding up the parts, dividing the total by this number and then multiplying by each part.