KU122 Unit 4 Seminar Percent Notation KU Introduction to Math Skills and Strategies Seminars: Wednesdays at 8:00 PM ET Instructor: Tammy Mata Office Hours: By appointment AIM: tammymataku The seminar will begin at the top of the hour. Audio will be available when the seminar begins.

Percent Notation Chapter and Section 4.1, Ratio and Proportion Percent Notation is a fractional value that indicates a ratio that is “per 100.” Percent means “per 100.” Thus 50% means 50 per 100 while 17% means 17 per 100 and 93% means 93 per 100. Percent Notation is a ratio: 50:100 or “50 out of every 100.” This is more commonly expressed as 50/100 in a fraction notation. A ratio is the quotient of TWO quantities. When a ratio is used to compare two different kinds of measure, we call it a rate. Proportions are compared by finding translating into ratios with common denominators. So to compare 3/6 and 2/4, they must be translated into ratios with common denominators. Both translate to 6/12. Since the two pairs of numbers match, they are “proportional.”

Percent Notation Chapter and Section 4.2, Percent Notation Percent notation, n%, can be expressed as (1) n%, a ratio of n to 100 (n: 100 or n/100) (2) n/100, a fraction notation (n x 1/100) (3) 0.nn, a decimal notation (n x 0.01) Converting from percent notation to decimal notation: (a) replace the percent symbol with x 0.01 (b) multiply by 0.01, which means moving the decimal point two places to the left Example: 36.5% (a) 36.5 x 0.01 (b) 36.5 x 0.01 = move decimal two places to the left =.365 Conversion: 36.5% = Converting from decimal notation to percent notation (a) multiply by 100%, which means moving the decimal point two places to the right (b) write a percent symbol Example: (a) x 100% = move decimal to places to the right = (b) write a percent symbol and drop the beginning 0 = 67.5% Conversion: = 67.5%

Percent Notation Chapter and Section 4.3, Percent and Fraction Notation Converting from Fraction Notation to Percent Notation (a) Find decimal notation by division (b) Convert the decimal notation to percent notation (per steps in 4.2) Example: 3/5 (a) 3/5 = 3 divided by 5: ) (b) 0.6 x 100% = moving decimal two places to right = (c) Write the percent symbol and drop the unnecessary zeros Conversion: 3/5 = 60%

Percent Notation Converting from Percent Notation to Fraction Notation (a) Use the definition of percent as a ratio (b) simplify, if possible Example: 30% (a) change to its ratio definition = 30/100 (b) simplify, if possible: 30/100 = 3/10 Conversion: 30% = 3/10

Percent Notation Chapter and Section 4.4, Solving Percent Problem Using Percent Equations Key words in Percent-to-Equation Translation “of” translates to multiple “is” translates to equals “what” translates to any variable (letter) “%” translates to “multiply by 1/100” OR “multiply by 0.01” Example: What is 11% of 49? Translation: x = 11% * 49 Now the equation can be solved for x. REMEMBER to always include the percent symbol in the answer when the question asks “what percent.”

Percent Notation Chapter and Section 4.5, Solving Percent Problems Using Proportions Remember that a percent is a ratio of some number to 100. Solving a percent problem using a proportion (a) translate to a “Number to 100” and an “Amount to a Base” N a = b (b) it is “part is to a whole” as “part is to a whole” Example: 60% of 25 is 15 (a) 60/100 = 15/25 (b) the proportion of 60/100 is the same as the proportion 15/25 (c) notice that 60% * 25 = 15 solves for the proportion

Percent Notation Chapter and Section 4.6, Applications of Percent Applied problems (word problems) involving percents use the same steps as always: 1. Familiarize 2. Translate 3. Solve 4. Check 5. State (including unit of measurement – remember that percent symbol) The application problems require understanding the operations for percent notation discussed in this unit

Percent Notation Chapter and Section 4.7, Sales Tax, Commission, Discount, and Interest “Sales tax” is the extra amount tagged onto the purchase price that goes to the government. To solve for the sales tax, multiply the sales tax rate to the purchase price. To solve for total price, add purchase price and sales tax. “Commission” is a certain percentage of total sales; certain professions (such as a real estate agent or a car salesman) might be paid by commission instead of by hour or by salary. To solve for commission, multiply the commission rate by sales amount. “Discount” is a reduced amount off an original purchase price, such as a sales discount. To solve for discount, multiply the rate of discount by original price. To solve for sales price, subtract the discount from the original price.

Percent Notation Simple Interest “Simple Interest” is how much money earns when it is invested, loaned, or borrowed. “Principal” is the amount of the original money invested, loaned, or borrowed. “Rate” is the percentage amount that is used to calculate the interest. “Time” is the period in which the money is invested, loaned, or borrowed. The Simple Interest Formula is as follows: I = P * R * T Key: I, interest P, principal r, rate t, time

Percent Notation Compound Interest “Compound Interest” is when interest is paid on interest. “Compounded annually” is when interest is computed each year on the previous year’s interest. Compound interest formula is as follows: A = P * (1 + r/n)^n*t (See pages 313 and 314 in textbook.)

Percent Notation Chapter and Section 4.8, Interest Rates on Credit Cards and Loans Annual Percentage Rate (APR) the amount of interest charged on borrowed money Minimum monthly payment (often 2%) that is required for payment each month Work through example 1 on page 321. See chart on page 322, 323, 325

Unit 4 Practice Problems See example B at top of page 251 See example 16 on page 255 PRACTICE: 53, 57 58, page 262; 7, page 330 See example 1, page 271 PRACTICE: 4, 5, and 6, margin, page 273 See example 1, page 307 PRACTICE: 1 and 2, margin, page 307 See example 8 on page 282 PRACTICE: 8, 9, and 10, margin, page 282 See examples 1 and 2 on page 288 PRACTICE: 1, 2, 3 margin, page 288 (DO NOT SOLVE) To find miles per hour (mph, also known as “rate”), divide distance by time. Formula: MPH = Distance / Time Other formulas: Time = Distance / MPH OR Distance = Time * MPH NOTE: For the Unit 4 MML Quiz, if an answer needs to be rounded, rounded up OR down to the nearest hundredths.