**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

**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.

After having gone through the stuff given above, we hope that the students would have understood "How to find a whole given a part and a percent".

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