Many mathematical algorithms are performed so routinely that we sometimes do not think about why we do them or why the method works. One example of such routine algorithm is reducing fractions to lowest terms. Why do we always perform this procedure? What is really happening when we reduce fraction to lowest terms?
One of the basic reasons why we reduce fraction to lowest terms is to lessen the burden of calculating large numbers. Of course, we would rather add or multiply and than and . So you see, the effort of multiplying the same fraction is lessen when they are reduced to lowest terms.
But what really happens when we reduce fraction to lowest terms? Why is it possible and why does it work? » Read more
Two weeks ago, I discussed the basic concepts of domain and range which I presented in an ‘algebraic way.’ In this post, I would like to discuss these concepts from a graphical perspective.
The domain of a function is the set of points on the x-axis where if a vertical line is drawn, it will hit a point on the graph. Take for instance, in the linear function , we are sure that we can always hit a point wherever we draw a vertical line. In algebraic explanation, we can always find an for every . Therefore, we can conclude the that domain of is the set of real numbers. On the other hand, if we draw a horizontal line and it hits the graph, then it is part of the range of the graph. Clearly, the range of the is also the set of real numbers.
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