FINDING A WHOLE GIVEN A PART AND A PERCENT

We can use proportional reasoning and multiplication to solve problems in which we know a part and a percent and need to find the whole.

The formula to find the whole using proportional reasoning is given by 

The formula to find the whole using multiplication is given by 

Examples 

Example 1 : 

Twelve of the students in the school choir like to sing solos. These 12 students make up 24% of the choir. How many students are in the choir ?

Solution :

Step 1 :

Since we want to know the total number of students in the choir, compare the part to the whole.

Step 2 :

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

We know that 12 students represent 24%.

Step 3 :

Find the multiplication factor.

Since 12 x 2 = 24, find what number times 2 is equal to 100.

Step 4 :

Find the denominator.

12/50  =  24/100

(Since 50 · 2  =  100, the denominator is 50)

Hence, there are 50 students in the choir.

Example 2 : 

240 televisions of a store are are high definition. These 240 televisions make up 80% of the televisions. How many televisions are in the store ?

Solution :

Let us use multiplication method to find the whole.

Step 1 :

In multiplication method, the formula is

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

Step 2 :

From the given information, the part is 240 and the percent is 80.

Then, we have

(1)------------ > Whole  =  (240/80) x 100 %

Whole  =  300

Hence, there are 300 televisions in the store in total. 

Example 3 : 

There are 12 girls in a class and these girls make up 40% of the total students. How many students are in the class in total ?

Solution :

Let us use multiplication method to find the whole.

Step 1 :

In multiplication method, the formula is

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

Step 2 :

From the given information, the part is 12 and the percent is 40.

Then, we have

(1)------------ > Whole  =  (12/40) x 100 %

Whole  =  30

Hence, there are 30 students in the class in total. 

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