Finding the Whole Quantity Given a Part and a Percent

Introduction:

You can display percent in several ways, such as 0.01 or 0.1 and also in fractional form.  

You have heard the word percent on a broader level. In this session, you will learn how to find the whole quantity when a part and a percent is given. 

To determine totals from a percent in the future, multiply the given percentage value by 100 and divide that product by the percent. This method works in any instance where a percentage and its value are given.  

We can use this equation to find the unknown value, 

PartWhole= Percent100PartWhole= Percent100

Double line diagram 

Using Equation 

Let’s use a double line diagram and Equation to find the Unknown Whole.  

Method 1: Double line diagram 

Example 1: Joe scores 104 marks in his entrance test, which is 80% of total marks. Find  the total marks.  

104 ÷8 = 13 

So, 13 × 10 = 130 

Therefore, 80% of 130 is 104. 

Method 2: Use Equation 

Example 1:  You spent $10 or 20% of your pocket money in the first three days of the month. Find the total pocket money you got. 

Solution: Here we have, part = $10, percent = 20%, whole = ? 

Now, using the equation,  

Example2: Jose got 8 questions right on his test. If his grade was 80%, how many questions were on the test? 

Solution: Here we have, part = 8 questions, percent = 80%, whole =? 

Now, using the equation,  

More Word Problems: Understand Percent 

Example: Two of the pets at the pet store are birds. If it is 10% of the pets at the store. How many pets are at the store?  

Solution:  

Here we have, part = 2, percent = 10% 

Whole =? 

Using an equation, 

Concept Map: