FINDING A PERCENT GIVEN A PART AND A WHOLE

For the purpose of comparison, in our day to day life, often we need to find percent for the given part and whole.

We can use the following two methods to find percent for the given part and whole.

They are

1.  Proportional reasoning

2.  Multiplication 

The formula to find percent using proportional reasoning is given by 

The formula to find percent using multiplication is given by 

Examples 

Example 1 : 

The school principal spent $2,000 to buy some new computer equipment. Of this money, $120 was used to buy some new keyboards. What percent of the money was spent on keyboards ?

Solution :

Step 1 :

Since we want to know the part of the money spent on keyboards, compare the part to the whole.

Step 2 :

Write a proportion comparing the percent to the ratio of part to whole.

Step 3 :

Find the multiplication factor.

Since 100 · 20 = 2,000, find what number times 20 equals 120.

Step 4 :

Find the numerator.

6/100  =  120/2000

(Since 20 · 6 = 120, the percent is 6%)

So, the principal spent 6% of the money on keyboards.

Example 2 : 

Out of the 25 students in Mrs. Green’s class, 19 have a pet. What percent of the students in Mrs. Green’s class have a pet ?

Solution :

Let us use multiplication method to find percentage.

Step 1 :

In multiplication method, the formula is

Percent  =  (Part / Whole) x 100 % -----(1)

Step 2 :

Since we want to find percent of the students in Mrs. Green’s class have a pet, the part is 19 and the whole is 25.

Then, we have

(1)------------ > Percent  =  (19/25) x 100 %

Percent  =  19 x 4 %  =  36 %

So, 36 percent of the students in Mrs. Green’s class have a pet.

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