# 8.4 Self-Check

## 8.4.1 Self-Check on Percentages

In this unit, you might have struggled with certain activities, and that’s okay! We all get stumped from time to time. Remember that there are plenty of resources that can provide guidance and advice, such as family, friends, teachers, old textbooks, and the Internet.

It’s important for you to reflect on the material you have studied and consider the development of your skills. Your confidence will continue to increase the more you practice. You can do this by working through the exercises for each section. Here are some activities to help you perform a self-check.

### Exercise 1: Fractions, Decimals, and Percentages

Copy the table below into your notebook. Then, fill in the columns to show which fractions, decimals, and percentages are equivalent to each other. The first column has been filled in for you. You have worked out some of these calculations already earlier in this unit.

#### Equivalent fractions, decimals and percentages

Percentage | Decimal | Fraction |
---|---|---|

5% | 0.05 | |

10% | ||

0.2 | ||

0.5 | ||

75% | ||

1 |

#### Comment

To change a fraction or decimal to a percentage, multiply it by 100%.

For example, and .

To change a percentage to a fraction or decimal, interpret the % symbol to mean “divided by 100”.

For example, and .

To change a fraction to a decimal, divide the numerator by the denominator.

For example: .

#### Answer

##### Equivalent fractions, decimals, and percentages

Percentage | Decimal | Fraction |
---|---|---|

5% | 0.05 | |

10% | 0.1 | |

20% | 0.2 | |

25% | 0.25 | |

30% | 0.3 | |

50% | 0.5 | |

64% | 0.64 | |

75% | 0.75 | |

100% | 1 | 1 |

Note: Converting a decimal into percent means moving the decimal point two places to the right and including the percent symbol.

Note: In your conversion from a fraction to a percent you can also go through the decimal, i.e. work out the quotient and then move the decimal point two places to the right and include the percent symbol.

### Exercise 2a: Motel Room

A motel in Delaware rents a room for $56.80 for one night. Delaware has no sales tax. If the motel applies a service charge of 10%, what is the total cost of this motel room for one night?

#### Answer

10% of $56.80 is $5.68. Then, add the service charge to the room cost, . The total cost of the room is $62.48.

### Exercise 2b: Sales Figures

In January, a company sells $8,500 worth of goods. However, the sales fall by 8% in February. How much is sold in February?

#### Answer

8% of $8500 is .

The total sales in February are .

Alternatively, 92% of $8500 is .

### Exercise 2c: Sales Tax

An item costs $35.49, plus sales tax. If the sales tax rate is 6%, what is the total price?

#### Answer

6% of $35.49 is in sales tax. Together it is .

The item costs $37.62 after sales tax.

Alternatively, .

### Exercise 3: A Clerical Error

A mail order company offers a 15% reduction on its prices to new customers. Unfortunately, a clerical error has been made and some existing customers have also been given the discount. One existing customer has been charged $144.50, including the discount. What should the customer have been charged? How can you check your answer?

#### Answer

The reduction is 15%, so eligible customers are charged 85% of the original cost.

85% of the cost is $144.50.

1% of the cost is and 100% of the cost is .

The existing customer should have been charged $170.

You can check this answer by calculating the reduced price.

15% of $170 is .

So, the reduced price is .

### Exercise 4: Large Group at a Restaurant

In 2010, you went on a trip to visit some friends in Montana, which charged no sales tax at the time. You and six friends went out to dinner together—a party of seven in all. The restaurant’s policy stated that groups of six people or more will have 18% gratuity (tip) added to their bill. If your food and drinks totaled $176.23, how much was the bill? If you had split the bill evenly seven ways, how much was your share?

#### Answer

18% of 176.23 is and the total bill was .

Divide by seven and is what you and each other person in the party owed.

### Exercise 5: “Of” versus “Off”

(a) What percentage of the original price do you pay if an ad promises “20% off everything?”

#### Answer

(a) You pay 80% of the original price.

(b) What percentage of the original price do you pay if “the sale price is 40% of the original price?”

#### Answer

(b) You pay 40% of the original price.

### Exercise 6: Discount

Find the sale price of a $340 television that is on sale for 25% off.

#### Answer

25% of $340 is . With a discount of $85, the sales price of the television is .

### Exercise 7: Time for That New Television

The price of a 55-inch flat-screen television is $1,897.22, which includes 8.25% California sales tax. How much did the television cost before sales tax?

#### Answer

$1,897.22 is 108.25% of the original price. Dividing the after sales tax amount by 108.25% gives you 1% of the original price: . Multiply this result by 100 to create 100%, and thus the original price, which is (rounded to the nearest cent).

The pretax price of the television was $1,752.63. You can check your answer by finding out what a television of $1,752.63 would cost after 8.25% of sales tax is applied.

### Exercise 8: Spending

The consumer expenditure survey (Graph: Where the Money Goes) shows how much the average household spent on different categories in 2009. The percentages displayed in the picture were calculated based on the total money spent (average household expenditure).

If based on a different number, these percentages will be different. According to the numbers in this picture, what percent of the average household’s income** before taxes ...**

(a) ... is spent on food away from home?

#### Answer

(a) Food away from home: .

(b) ... is spent on housing?

#### Answer

(b) Housing: .

(c) ... is not spent?

#### Answer

(c) Money not spent is taxes, savings, etc. This is the income before taxes minus average annual expenditure, . As a percent of the income before taxes, this is .

8.3.7 Sweet or Savory?