Using Ratio method To Solve the Difficulties of World Problems involving (direct or indirect/inverse) Proportion of Junior high school Pupils.

Using Ratio method To Solve  the Difficulties of World Problems involving (direct or indirect/inverse) Proportion of Junior high school Pupils.

 

            Proportion problems are word problems where the items in the question are proportional to each other.  There are two main types of proportional problems: Directly Proportional Problems and Inversely Proportional Problems.(1)  The problem usually will not present to you that the items are directly proportional.  Instead, it will tell you the importance of two items which are related and then press you to find out what will be the value of one of the item if the value of the other item changes. 

            Proportional problems are most of the times in this form:

                  If B then C.  If b is change to d then what will be the value of c?

            For example,

                  If two notebooks cost .50, how many notebooks can you buy with .00?

The main dilemma with this type of question is to figure out which values to divide and which values to multiply.

           The following technique is useful:

           Change the world problem into the form:

                   If B then C.  If B is changed to D

                   Then what will be the value of C?

           Which can then be repeated as:

                   B  >C

                   D>D BC

                        C

For example,

You can think of the following:

If two notebooks cost $ 2.50, how many notebooks can you buy with $ 8.00?

As if $ 2.50 then two notebooks.  If $ 8.00, then how many notebooks?

Follow the similar proportional relationship:

                  2.5 > 2

                  8 > 8 b2 =12

                        2.5     

 

Inversely Proportional Problems—are similar to directly proportional problems, but the disparity is that when B increase C will decrease and by an amount such that  BC remains the same. (2)  When two variables are indirectly proportional to each other ( also known as inversely proportional), they are related by an equation of the following form:

                B C = G

Where G is a constant and B and C are variables.

This equation may be illustrated in this form:

               C =G/B or B = G/C.

It now becomes more clarified in illustrating that in an inversely proportional relationship, as one of the variable increases, the other decreases.

             Knowing that the product does not change also allows you to form an equation to find the value of an unknown variable.  For example:

             It takes 5 men 8 hours to repair a bridge.  How long will it take 10 men to do the job if they work at the same rate? 

             The number of men is inversely proportional to the time taken to do the jobs.

             5×8 = 10xt = 10xt =40 = t = 4 hours.

Usually, one will be able to choose from the question whether the values are Directly proportional or Indirectly/inversely Proportional.            

 

Footnotes:

1.    Online Math learning. Com

2.    Math Central

 

                       

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