Proportion

• Proportion is a mathematical concept that reflects the relationship between two quantities. There are two main types: direct and inverse.
• Direct proportion occurs when two quantities increase or decrease in tandem. For example, if the distance travelled depends on speed, the greater the speed, the greater the distance travelled.
• To solve problems in direct proportionality, you use a formula, e.g., y = kx, where ‘k’ is the constant of proportionality. If you are given two proportional quantities (x,y), you can find the value of ‘k’ by rearranging the formula to k = y/x.
• Inverse proportionality describes cases where as one quantity increases, the other decreases. For example, the more workmen there are to do a job, the quicker the job is completed.
• For inverse proportions, the formula for calculation is xy = k. Here, ‘k’ is a constant of proportionality. If you are given two inversely proportional quantities (x,y), you can find the value of ‘k’ by multiplying them: k = xy.
• To solve a proportion problem, first, identify if it is a case of direct or inverse proportion, then use the appropriate formula.
• When drawing graphs of proportional relationships, a direct proportion will result in a straight line going through the origin, while an inversely proportional relationship will appear as a hyperbola with the x and y-axes as asymptotes.
• Proportional reasoning involves gauging whether the quantities are proportionate by comparing their ratios. It’s used for estimating, predicting, and solving problems.
• Beware of non-proportional quantities where an increase or decrease in one does not cause a similar change in the other. Recognising these cases is crucial.
• Practicing proportion problems regularly will improve your ability to solve them quickly and accurately. Always make sure to check your answers with the original problem.