Division Metaphors 2

< 10.1 Division Metaphors 1 | Topic Index | 10.3 Origins of Multiplication 1 >

Ratio

In &ldquo;comparison&rdquo; situation in Subtraction, we saw additive comparison. Ratio is the multiplicative comparison which we referred to there. Let us take the same example.

&ldquo;Ram got 50 marks in Math and Shyam got 25 marks. Who got more marks and how much more?&rdquo;

We can describe the situation in several ways.

In ratio the order in which the numbers are written is very important. For example, Shyam&rsquo;s and Ram&rsquo;s marks are in the ratio 1:2.
 * 1) Ram&rsquo;s &amp; Shyam&rsquo;s marks are in the ratio 2:1.
 * 2) Ram got twice as many marks as Shyam
 * 3) Shyam got &frac12; the marks that Ram got.

Ratio is always taken between two quantities expressed in the same units of measurement. In the above example both quantities compared were measures in marks. Hence Ratio is just a number. It has no units.

Ratio is the concept which leads to the idea of Proportion which in Geometry leads to the idea of Similarity.

&ldquo;Ratio&rdquo; is also the reverse of &ldquo;Scaling&rdquo; in multiplication.

Ratio is a very important concept in math. We will deal with it in detail, in a subsequent chapter.

Rate

Rate is similar in spirit to Ratio but is used to compare the relation of 2 quantities expressed in different units of measurement. It is an indication of the rate at which one of the quantities changes with respect to the other. Common examples are price and speed.

Price is expressed as Rupees per kg or Rupees per Litre etc. Speed is expressed as Kms per Hour or Meters per Second.

Rate is a very important concept which is necessary to understand, compare and evaluate many phenomena in real life.

&ldquo;Rate&rdquo; is the reverse of &ldquo;Product&rdquo; situation in multiplication.

< 10.1 Division Metaphors 1 | Topic Index | 10.3 Origins of Multiplication 1 >