Unitary method

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The unitary method is an algebraic technique for solving a problem by first finding the value of a single unit, i.e., 1, (by dividing) and then finding the necessary value by multiplying the single unit value. In essence, the unitary method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple. With the unitary method, it is not always necessary to find the value of single unit; let us study it with the help of examples below.


For example, to solve the problem: "A man walks 7 miles in 2 hours. How far does he walk in 7 hours?", one would first calculate how far the man walks in 1 hour. One can safely assume that he would walk half the distance in half the time. Therefore, dividing by 2, the man walks 3.5 miles in 1 hour. Multiplying by 7 for 7 hours, the man walks 7x3.5=24.5 miles, or let us consider the distance travelled by the man be X, then divide it given distance that is 7 (x/7). It is equal to the time taken to travel X distance that is 7 hours divided by the time taken to travel 7 miles, that is 2 hours (7/2), therefore x/7=7/2, hence X=24.5 miles.

The same method can be applied to the problem: "A man walks at 4 miles per hour. How long would it take him to cover 5 miles?". Dividing by 4 shows that the man covers 1 mile in a quarter (0.25) of an hour. Multiplying by 5 shows that the man therefore takes 1 hour and a quarter (1.25 hours) to cover 5 miles. Similarly, by the second method, we can find the value of time taken to cover 5 miles. The 1st method is more preferable and easier.


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