# Solve Problems Involving Percentages: TEAS

## Basic Terms and Terminology Relating to Solving Problems Involving Percentages

- Percentages are a number with a % sign that represent numbers in comparison to 100.

### Percentages and Their Meaning

Percentages are a number with a % sign that represent numbers in comparison to 100. As shown in the picture below, of all of the persons using a web browser to access Wikipedia, 20.03 %, or 20.03 people out of every hundred people, used Chrome and 19.26% of all of the persons using a web browser to access Wikipedia, 19.26%, or 19.26 people out of every hundred people, used Firefox, etc.

100% is the whole and it is equal to 1. Percentages less than 100% are less than 1 or the whole and percentages more than 100% are more than one or the whole; and percentages less than 1% are also possible.

**Some examples of percentages less than 100% that are less than 1 and less than the whole are:**

- 16%
- 25%
- 76%
- 89%
- 99%

**Some examples of percentages more than 100% that are more than 1 and more than the whole are:**

- 123%
- 167%
- 200%
- 399%
- 546%

**Some examples of percentages less than 1% that are less than the whole AND less than 1 out of every hundred are:**

- 3/4%
- 1/25%
- 007%
- 1%
- 009%

## Converting Among Fractions, Decimals, Ratios and Percentages

Percentages have equivalents in terms of a fraction, a decimal point number and as a ratio.

You may have noticed a pattern in the chart above suggesting how to convert among fractions, decimals and percentages.

The conversion of percentages into fractions is done by simply placing the percentage number over 100. Regardless of whether or not the percentage number is less than or greater than 100, the denominator of the fraction is always 100

**Here are some examples:**

- 12% = 12/100
- 120% = 120/100
- 220% = 220/100
- 2222% = 2222/100

The conversion of percentages into decimal numbers is done by moving the percentage number's decimal place 2 places to the left. As previously discussed, dividing by 100 can be done simply by moving the decimal place two places to the left.

**Here are some examples:**

- 12% = 0.12
- 120% = 1.20
- 220% = 2.20
- 2222% = 22

The conversion of percentages into ratios is done by placing the percentage number and then : (colon) and then 100. A ratio is read as 12 is to 100 when you see 12 : 100. There are 12 per hundred.

**Here are some examples:**

- 12% = 12 : 100
- 120% = 120 : 100
- 220% = 220 : 100
- 2222% = 2222 : 100

## Calculating Problems Involving Percentages

In your everyday life, you use and calculate with percentages more than you think.

**Here are some of the everyday percentages that you use on a daily or regular basis:**

- BOGO or Buy 1 and Get 1 Free
- 30% off men's shirts
- Your weight goal is to lose 5% of your weight every 6 months
- You financial goal is to save 3% of your annual salary each year

**Example 1: Calculating Problems Involving Percentages**

Your local grocery store is having a huge BOGO sale this week. You will be purchasing 1 of each of these BOGO items this week and your store does NOT require that you take 2 to get the BOGO discount:

**Cereal (usual price is $5.39 per box)**

50% of $5.39

1/2 x $5.39 **OR** 0.5 x $5.39 **OR** 50% : !00% = x : $5.39

1/2 x $5.39 = $5.29/2 = $2.70 rounded off to the nearest penny

**OR**

0.5 x $5.39 = $2.70 rounded off to the nearest penny

**OR**

50% : !00% = x : $5.39

50/100 = x / $5.39

x=$2.70 rounded off to the nearest penny

In this example, you have paid $2.70 per box of cereal and you have also saved $2.69 per box of cereal.

**Example 2: Calculating Problems Involving Percentages**

You will be purchasing each of these shirts during the 30% off sale. How much will you save with the purchase of these 4 shirts?

- Blue shirt (Regular price is $19.99)

When shirts are discounted by 30%, you will be paying only 70% of the regular price for the shirt. So, in order to find out what you are saving per shirt, you would have to calculate 30% of the regular price; and, in order to determine what you will be spending for each discounted shirt, you would have to calculate 70% of the regular price.

1/3 x $19.99 **OR** 0.33 x $19.99 **OR** 30% : 100% = x : $19.99

1/3 x $19.99 = $19.99/3 = $6.66 rounded off to the nearest penny

**OR**

0.33 x $19.99 = $6.66 rounder off the nearest penny

**OR**

30% : 100% = x : $19.99

30/100 = x / $19.99

x = $6.66 rounded off to the nearest penny

In this example, you have saved $6.66 for this blue shirt.

**Example 3: Calculating Problems Involving Percentages**

When your weight goal is to lose 5% of your weight every 6 months, how much weight should you lose every 6 months when your weight is as follows:

- Your weight: 160 pounds

5/100 x 160 pounds **OR** 0.05 x 160 pounds **OR** 5% : 100% = x : 160 pounds

5 /100 **OR** 1/20 x 160 pounds = 8 pounds

**OR**

0.05 x 160 pounds = 8 pounds

**OR**

5% : 100% = x : 160 pounds

5/100 = x/160

x = 8 pounds

In this example, you should lose 8 pounds every 6 months.

**Example 4: Calculating Problems Involving Percentages**

When your weight goal is to lose 5% of your weight every 6 months, how much weight should you lose every 6 months when your weight is as follows:

- Your weight: 65 kilograms

5/100 x 65 kg **OR** 0.05 x 65 kg **OR** 5% : 100% = x : 65 kg

5/100 **OR** 1/20 x 65 kg = 3.25 kg

**OR**

0.05 x 65 kg = 3.25 kg

**OR**

5% : 100% = x : 65 kg

5/100 = x/65

x = 3.25 kg

In this example, you should lose 3.25 kg every 6 months.

**Example 5: Calculating Problems Involving Percentages**

When your weight goal is to lose 5% of your weight every 6 months, how much weight should you lose every 6 months when your weight is as follows:

- Your weight: 89 kilograms

5/100 x 89 kg **OR** 0.05 x 89 kg **OR** 5% : 100% = x : 89 kg

5/100 **OR** 1/20 x 89 kg = 4.45 kg

**OR**

0.05 x 89 kg = 4.45 kg

**OR**

5% : 100% = x : 89 kg

5/100 = x/89

x = 4.45 kg

In this example, you should lose 4.45 kg every 6 months.

**RELATED TEAS NUMBERS & ALGEBRA CONTENT**:

- Converting Among Non Negative Fractions, Decimals, and Percentages
- Arithmetic Operations with Rational Numbers
- Comparing and Ordering Rational Numbers
- Solve Equations with One Variable
- Solve One or Multi-Step Problems with Rational Numbers
**Solve Problems Involving Percentages (Currently here)**- Applying Estimation Strategies and Rounding Rules for Real-World Problems
- Solve Problems Involving Proportions
- Solve Problems Involving Ratios and Rates of Change
- Translating Phrases and Sentences into Expressions, Equations and Inequalities