Proportional Thinking

Proportional Thinking is comparing 2 ratios in different situations and drawing conclusions. It is the most sophisticated mode of multiplicative thinking.

Situations where 2 ratios are equal are important in life situations. Such ratios are said to be in proportion and can lead to conclusions relevant to the context.

Similarity

The idea of similarity of figures & objects in geometry & life is related to a situation of equal ratios.

Two triangles are similar in shape if the ratio of each of their corresponding sides is in the same ratio. The size of the triangles can be different. One could have dimensions 2, 3 & 4 and the other could have dimensions 4, 6 & 8 so that for each set of corresponding sides the ratio is 1:2. Two similar triangles are said to be in proportion.

The similarity of 2 shapes enables us to predict the ratio of their areas, surface areas and volumes. It also helps us understand the biological logic of the shapes of many of our internal organs.

Equivalent Fractions

We have seen equivalent fractions earlier. We can now see that equivalent fractions are an example of equal ratios.

Enlargement of photos

When a small photograph is enlarged, the larger photo would “look same” only if the ratios of both the height & width of the smaller & enlarged photo are in the same ratio. The 2 photographs are said to be in proportion.

Recipes

Take a common recipe for making rotis. Whatever be the number of rotis that are to be made the ingredients; quantities of flour, salt and water have to be mixed in quantities that are related to each other. For example it may be 2 cups of water for every cup of flour and 1 teaspoon of salt for every cup of flour. If the ratios are not maintained the same, the quality of the rotis, in terms of taste will change.

Price & Speed

In situations related to price & speed, ratios being same implies that the price of a product has not changed or the speed of the vehicle has remained same.

From the above examples, we can also get a sense of what happens when the ratios are not same or not proportionate.