## Understanding Ratios and Percents

In mathematics, a

It is often denoted using the percent sign, “%”, or the abbreviation “pct.”

A

**percentage**is a number or ratio as a fraction of 100.It is often denoted using the percent sign, “%”, or the abbreviation “pct.”

A

**ratio**is a comparison of 2 quantities. The focus of this article is writing a ratio.## Percents

Multiply a number by 1 in the form of 100% to change a number to a percent.
For a shortcut, move the decimal two places to the right. |
## Classwork/Practice
1) If 4/5 of the telephone workers in a city are female, what percent are female?
2) Change 7/8 to a percent equivalent. 3) Change 0.008 to a percent equivalent. 4) Change 4.0125 to a percent equivalent. 5) Change 7 3/5 to a percent equivalent. Answers:
1) 80% 2) 87.5% 3) 8% 4) 401.25 5) 760% |

Solve percent problems using the percentage formula

Use key words to identify the known elements and the missing element. Then select the appropriate percentage formula.

Use key words to identify the known elements and the missing element. Then select the appropriate percentage formula.

What amount is 15% of $300?

The percent or rate is 15%. The missing element is the portion.

What percent of 9 is 3?

*Of*identifies $300 as the base.The percent or rate is 15%. The missing element is the portion.

*P = RB*Select the appropriate percentage formula and substitute given amounts.*P =*15%($300) Change 15% to a fraction or decimal equivalent by dividing by 100%.*P =*(0.15)(300) Multiply.*P =*$45 Portion.What percent of 9 is 3?

*Is*suggests 3 is the portion.*Of*identifies 9 as the base. The rate is missing.25 is 10% of what number?

The rate is 10%. 25 is the part or portion and is suggested by

The rate is 10%. 25 is the part or portion and is suggested by

*is*.*Of*identifies “what number” as the missing base.
## Identify the portion, base, and rate in percent problemsUse the key words for rate (
percent or %), base ( total, original, associated with the word of), and portion ( part, associated with the word is).Identify the rate ( R), base (B), and portion (P).Answers: 1-a-3.75 2-c-7 3-b-65 4-c-85 5-b-15 |
## Classwork/Practice
1) What is 15% of 25?
a-3.75 b-37.5 c-1.67 d-16.7 2) What is 20% of 35? a-1.75 b-17.5 c-7 d-70 3) 16.25 is 25% of what number? a-75 b-65 c-55 d-45 4) 29.75 is 35% of what number? a-105 b-95 c-85 d-75 5) 17.25 is what percent of 115? a-5% b-15% c-25% d-35% |

## Solve percent problems using the percentage proportion

To solve a proportion, multiply diagonally across the equal sign to find the cross products. Then divide the cross product of the two known factors by the number factor of the other cross product.

40 is 16% of what number?

The rate is 16%. 40 is the part or portion and is suggested by

40 is 16% of what number?

The rate is 16%. 40 is the part or portion and is suggested by

*is*.*Of*identifies “what number” as the missing base.
## Classwork/Practice
1) Find the value of the letter in the proportion 5/b = 2/6 a-0.6 b-60 c-15 d-10 2) Find the value of the letter in the proportion 4/9 = c/3 a-2 b-1 1/3 c-1.3 d-0.75 3) What number is 0.4% of 78? a-3.12 b-31.2 c-0.0312 d-0.312 |
4) What percent of 48 is 32?
a-2/3% b-66 2/3% c-150% d-1.5% 5) 43% of what number is 105.565? a-2.45 b-24.5 c-245.5 d-2,455 1) c- 15 2) b-1 1/3 3) a-3.12 4) b-66.66 5) c-245.5 |

Answers
1) d |
## Classwork/Practice
1) California requires a 6% sales tax on all purchases on California residents even if purchased on the Internet. Sue lives in California and purchased a small computer system for $505 from an Internet source. How much sales tax did she pay?
a-$511 b-$535.30 c-$6.00 d-$30.30 George makes a monthly gross income of $4,288.45. His net salary is $3,096.26. What percent of his salary is the total of the deductions, rounding to the nearest whole percent? 39% 28% 72% 15% A worker had 6.4% deducted from his weekly pay check of $432.75 for social security. Find the tax on the gross earning, rounded to the nearest cent. $460.45 $405.05 $27.70 $426.35 An employee had a monthly gross income of $2,100. She had a total of $331.80 deducted from her gross. What percent of the gross was deducted, rounded to the nearest tenth of a percent? 84.2% 15.8% 67.1% 32.4% The local sales tax rate is . A trip to the lumberyard cost $78.57 before tax. How much of the total bill was tax? $73.95 $4.91 $12.57 $4.62 A 3% discount is given if you pay cash at the gas pump. The pump showed a charge of $14.78 before the discount. How much is saved with the discount? $14.34 $0.44 $14.78 $0.43 A real estate agent makes a 3.5% commission. What does the agent make on a $129,900 home? $4,546.50 $45,465 $454.65 $3,711.42 What is the rate of discount given if the original item cost $59.49 and is sold at a discount of $44.62? 75% 33.3% 7.5% 25% A salesperson is paid a salary of $210 per week and a 6% commission on all sales over $4,500 per week. The sales for the week were $8,765. What is the salesperson's salary for the week? $465.90 $255.90 $210 $735.90 A used car salesman makes $100 per week plus a 15% commission on all sales. He sold $24,000 in used cars one week. What was his salary? $3,600 $3,700 $3,500 $36,100 Find the simple interest on a loan of $4,350 at 11% per year for 3 years, 6 months. $1,722.60 $478.50 $1,674.75 $2,675.25 A credit-card service charges a finance charge of per month on the average daily balance of the account. If the average daily balance on an account is $236.78, what is the finance charge for the month? $3.55 $2.84 $35.50 $28.40 If $2,875 is invested for 6 months at an interest rate of per year, find the simple interest earned. $265.94 $132.97 $797.81 $159.56 A business earned $4.67 in interest on an account balance of $346.88. What is the monthly rate of interest? 13.5% 1.35% 16.2% 0.1125% If $8,000 is invested for 4 months at 12% per year, how much interest is earned? $3,840 $32 $38.40 $320 |