Finding What Percent One Number is of Another

Particular problems involving division with whole numbers and with common fractions can now be solved by using decimals. The use of decimals often makes the problems more realistic. However, certain aspect of percent cannot be treated effectively until the pupil understands divisions involving decimals. Use problems whose answers are readily apparent to introduce how to find what percent one number is of another. Do oral work. Have each pupil identify the number to be compared and the number with which it is compared. Then have them write a number sentence for the situation. The following problems illustrate the procedure:

1.  5 is what percent of 100?

     5  =  n%  of  100

     5  =  is compared with 100, or     5/100  =  5% 

 

2.  3 is what percent of 10?

     3  =  n%  of  10

     3  =  is compared with 10, or     3/10 =     3/100=  30% 

 

3.  What percent of 10 is 7?

     7  =  n%  of  10

     7  =  is compared with 10, or      =    70/100  =  70% 

 

Solving such easy problems enable the pupils to discover the pattern for writing the number sentence in problems of this type. Then they are ready for problem in which the ratio is not so readily determined as a percent.

 

For example, the class knows how to express           as the decimal .625. To find what percent 5 of 8, rename .625 as 62.5%.  To find what percent one number is of another, one simple divides on number by another (or write a common fraction) and expresses the quotient as a percent.  Because the division is not commutative. It is vital to know which number to use as the divisor (denominator). This process compares two numbers. One of them, the base, represents 100%. The number compared with the base is the percentage. There is no single rule standard form, r% of b = p, the base follows “of”.

 

The terms “percent” and “percentage” of ten confuse pupils. The percent is a rate. The percentage is a number obtained by multiplying the base by the rate.

 

Exercises >>> then “Standard Percent Situations”

“Estimation and Percent”

The Proportion Method

 

The percent formula, as described in the previous section, has been traditional method for solving problems in the percent. In the 1960s, the proportion method became popular, and is still widely used. A proportion has two equal quotients.

 

The formula p = br can be restated, by applying the multiplication/ division relation, as the proportion          =             . Therefore, the three problems discussed in the previous section can now be restarted as proportions: