Understanding Percent Problems

All calculations involving percent can fall into one of the three basic types of problems. These three are related to all percent problems that arise in business, technology, or the trades. By learning these three types of problems you will be able to solve any percent problem, and we examine each of the three types of problems. All percent problems involve three quantities:
• the base ( B ) or whole or total amount, a standard used for comparison
• the portion ( P ) or part being compared with the base
• the rate ( R ) or percent, a percent number
Identify the Parameters:

To solve any percent problem, you need to identify which of the quantities given in the problem is P, which is B, and which is R. The percent number R is easy to identify because it always has the % symbol attached to it. If you have trouble distinguishing the part P from the base B, notice that B usually follows the word “of” and P usually follows the word “is”.

Example: What is 20% of 280?

• is indicates the portion (or percent) P to be found.
• % indicate the percent rate R, here R = 30%
• of indicates the base B which is equal to 280.
Finding the percent of a number
Calculating the percent of a number is done in 2 steps:
1. Change the rate (percent form) to a decimal and
2. Multiply the base amount by this decimal
EXAMPLE
The next three questions are all forms of the same problem. They are all asking you to find the portion P. In fact the percent is given (R = 40%), and the base is known (B = 70). The only unknown information is the portion P.
• What is 40% of 70?
• Find 40% of 70.
• 40% of 70 is what number?
SOLUTION
1. Change 40% into decimal:
40% = 0.40
2. Multiply the number by the decimal:
70 x 0.40 = 28
28 represents 40% of 70 ### A Short Review

Example:
What is 25% of 80? (Or what portion is a quarter of 80?)

SOLUTION
1. Change 25% into decimal:
20% = 0.25
2. Multiply the number by the decimal:
80 x 0.25 = 20
20 represents 25% of 80 ### Worksheet: Level 1

The operations used are clearly specified. Only one type of mathematical operation is used in a task.

### Worksheet: Level 1 Sample Question

Example:
The 10 x 10 box below represents 1 whole or 1.00
Write a fraction, a percent and a decimal to represent the amounts in the boxes. ### Worksheet: Level 1 Answer Key

27/100
27%
0.27 ### Worksheet: Level 2

Tasks involve one or two types of mathematical operation. Few steps of calculation are required.

### Worksheet: Level 2 Sample Question

Example:
Convert to a decimal:
25% =

### Worksheet: Level 2 Sample Answer

25% = 0.25 ### Worksheet: Level 3

Tasks require a combination of operations. Several steps of calculation are required.

### Worksheet: Level 3 Sample Question

Example:
Calculate 32% of 55.

### Worksheet: Level 3 Sample Answer

32% of 55 = 17.6 Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.

Math in real life does not often happen in a ready-to-calculate pre-printed format. The math is very often hidden in word  problems. The following word  problems are all based on the math in this lesson. Here  is how to deal  with word  problems:

1. Read the word problem and  write down the numbers from the word problems in the order they appear with their units  of measure. For example:

5 m
18%
72 hrs
21 lbs 2 oz

2. Write the  meaning of or label  the  copied out  numbers with their  units  of measure.  For example:

Part  = 3.8 carton
Width = 5 m or w = 5 m
Taxes = 18%  or VAT = 18%
Work in Pay Period = 72 hrs or Labour = 72 hrs
Weight  = 21 lbs 2 oz or w = 21 lbs 2 oz

3. Identify what  exactly needs to be calculated and  write it down. For example:

Volume = ? or V = ?
Density = ? or ρ = ?
Angle = ? or = ?
Length = ? or L = ?

4. Read all the words of a word  problem. The math is hidden, only the words indicate math.

For example:

- Stretching out, adding to, making more, growing, getting bigger, heavier, and building anew almost always means addition
- cutting, shortening, getting less, loss or losing all imply subtraction
- "of” or "at" following or near numbers means multiplication, many  pieces of uniform  units  (boxes, crates, loads, lifts, nights, hours) can  also  be multiplied
- chopping, sharing, splitting, slicing, or breaking up unto identical groups means division, so does the word "per", such as per student, per box, per room.

5. Based on the clues in the text, choose the applicable math procedure that  will answer the problem. In this  case, you don’t  have to do this.  The word problems in this lesson are solved with math shown in this lesson.
6. Recall steps of the calculation to get the answer or review and follow the steps in a sample calculation.
7. Calculate the final answer and write it down with its correct unit of measure. Tasks involve multiple steps of calculation. Advanced mathematical techniques may be required.

What is 14% of $170? Another way to get the answer, using division and multiplication: 1. First off, recognize that “portion” can be calculated given a percent rate and a base. 170 is the “base”. A portion of, or 14% of this base, 170, is to be calculated. The biggest number without the % sign is usually the base. 2. Set up the problem: percent ÷ 100 x base = portion This 100 comes from the fact that percents always have an invisible “divided by 100” concept with them. The % sign is actually short for “out of or divided into 100”. 3. Calculate: 14 ÷ 100 x 170 = 23.8 4. Take a pencil and write down 23.8 5. Write the$ symbol before the 23.8 Now you`re done with the math.