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Ideas of multiplicative thinking develop much later than additive thinking. It is a more sophisticated way of thinking. The following example would clarify the situation.
Multiplicative Vs Additive
Imagine a situation where in the first math test Ram & Govind have scored 50 & 70. In the 2ndtest their scores are 55 & 76. Both have improved their scores. But whose improvement is better?
An additive thinker could say that Ram’s improvement is 5 & Govind’s is 6 and hence Govind’s improvement is better. We can call this comparison as absolute comparison.
A multiplicative thinker could say that their improvement has to be seen relative to their previous score. Ram’s improvement can be denoted as and Govind’s can be denoted as . The first fraction (or ratio) is bigger. Hence Ram’s improvement is better.
Most adults & educators would agree that multiplicative thinking is more in tune with human reasoning.
Types of Multiplicative Thinking
Multiplicative thinking is the identification of life situations where 2 changing parameters have a relation of the following kinds.
Constant Ratio – the ratio (as a result of division) of the (changing) values is always the same. This can also be called a “directly proportional” situation.
Constant Product – the (multiplied) product of the (changing) values is always same. This is also called “inversely proportional” situation.
Multiplicative thinking can also be extended to “proportional thinking” where 2 ratios from 2 different situations are compared and conclusions drawn.
Roughly the three types of thinking have been arranged in order of increasing difficulty.
We will study the ratio & product situations in this and the next chapter. We will deal with “proportional thinking” after we get a good understanding of ratios.
Constant Ratio situations
In these situations, when one of the parameters changes in its value, the other parameter also changes in such a way that their ratio always remains same. A few examples would clarify this idea.
Shopping
We buy certain daily needs from a shop and pay a certain cost for the purchase. Let us assume that we buy 3 kgs of oranges for Rs 120. We can also say that for buying 4 kgs we would have to pay Rs 160. This is because the cost per kg of oranges, which is the ratio between the total cost and the quantity purchased, would remain same at Rs 40 per kg.
This kind of life experience is so common in our lives that this ratio has been given a special name “price”, which is stated as price in Rs per Kg or Rs/Kg.
The cost we would have to pay depends on the quantity we purchase. It increases or decreases as the quantity increases or decreases. Hence we can say that the cost is “directly proportional” to the quantity. Hence, such situations are also called “direct variation”.
Travel
Imagine that we are travelling from Chennai to Tirupati by car. The more hours we drive, the more distance we will cover. The ratio of the distance to the time taken is called speed which is expressed as kms/hour. If the speed of the car is the same, we can say that in twice the time, we will cover twice the distance.
Price & Speed are 2 ratios which we come across frequently in our life and hence have got special names.
In the next chapter we will study events where the product of changing parameters in constant.
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