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.

Tick iconExercise 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

PercentageDecimalFraction
5%0.05
one divided by 20
10%
0.2
one divided by four
three divided by 10
0.5
16 divided by 25
75%
1
Hint icon

Comment

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

For example, 0.05 equals 0.05 multiplication 100 percent equals five percent and one divided by 20 multiplication 100 percent equals five percent.

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

For example, 30 percent equation sequence equals 30 cubed divided by 100 super 10 equals three divided by 10 and 30 percent equation sequence equals 30 division 100 equals 0.3.

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

For example: equation sequence three divided by four equals three division four equals 0.75 full stop.

Solutions icon

Answer

Equivalent fractions, decimals, and percentages
PercentageDecimalFraction
5%0.05
one divided by 20
10%0.1
one divided by 10
20%0.2
one divided by five
25%0.25
one divided by four
30%0.3
three divided by 10
50%0.5
one divided by two
64%0.64
16 divided by 25
75%0.75
three divided by four
100%11

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.

Tick iconExercise 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?

Solutions icon

Answer

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

Tick iconExercise 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?

Solutions icon

Answer

8% of $8500 is equation left hand side 0.08 multiplication dollar times 8500 equals right hand side dollar times 680.

The total sales in February are equation left hand side dollar times 8500 minus dollar times 680 equals right hand side dollar times 7820.

Alternatively, 92% of $8500 is equation left hand side 0.92 multiplication dollar times 8500 equals right hand side dollar times 7820.

Tick iconExercise 2c: Sales Tax

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

Solutions icon

Answer

6% of $35.49 is equation left hand side 0.06 multiplication dollar times 35.49 almost equals right hand side dollar times 2.13 in sales tax. Together it is dollar 35.49 postfix plus dollar 2.13 equals dollar 37.62.

The item costs $37.62 after sales tax.

Alternatively, equation left hand side 1.06 multiplication dollar times 35.49 almost equals right hand side dollar times 37.62.

Tick iconExercise 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?

Solutions icon

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 dollar times 144.50 division 85 and 100% of the cost is equation left hand side 100 multiplication dollar times 144.50 division 85 equals right hand side dollar times 170.

The existing customer should have been charged $170.

You can check this answer by calculating the reduced price.

15% of $170 is equation left hand side 0.15 multiplication dollar times 170 equals right hand side dollar times 25.50.

So, the reduced price is equation left hand side dollar times 170 minus dollar times 25.50 equals right hand side dollar times 144.50.

Tick iconExercise 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?

Solutions icon

Answer

18% of 176.23 is 0.18 postfix multiplication dollar 176.23 almost equals dollar 31.72 and the total bill was dollar 176.23 postfix plus dollar 31.72 equals dollar 207.95.

Divide by seven and equation left hand side dollar times 207.95 divided by seven almost equals right hand side dollar times 29.71 is what you and each other person in the party owed.

Tick iconExercise 5: “Of” versus “Off”

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

Solutions icon

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?”

Solutions icon

Answer

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

Tick iconExercise 6: Discount

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

Solutions icon

Answer

25% of $340 is equation left hand side 0.25 multiplication dollar times 340 equals right hand side dollar times 85. With a discount of $85, the sales price of the television is dollar 340 postfix minus dollar 85 equals dollar 255.

Tick iconExercise 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?

Solutions icon

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: equation left hand side dollar times 1897.22 divided by 108.25 almost equals right hand side dollar times 17.52628. Multiply this result by 100 to create 100%, and thus the original price, which is equation left hand side 100 multiplication dollar times 17.52628 almost equals right hand side dollar times 1752.63(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.

Tick iconExercise 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?

Solutions icon

Answer

(a) Food away from home: multirelation dollar times two comma 619 divided by dollar times 62 comma 857 almost equals 0.042 equals 4.2 percent.

(b) ... is spent on housing?

Solutions icon

Answer

(b) Housing: multirelation dollar times 16 comma 895 divided by dollar times 62 comma 857 almost equals 0.269 equals 26.9 percent.

(c) ... is not spent?

Solutions icon

Answer

(c) Money not spent is taxes, savings, etc. This is the income before taxes minus average annual expenditure, dollar 62 comma 857 postfix minus dollar 49 comma 067 equals dollar 13 comma 790. As a percent of the income before taxes, this is multirelation dollar times 13 comma 790 divided by dollar times 62 comma 857 almost equals 0.219 equals 21.9 percent.

8.3.7 Sweet or Savory?

8.4.2 Self-Check on Ratios