Bell Work: Write a conjunction that designates the numbers that are greater than or equal to -2 and less than 5.

Answer: -2 ≤ x < 5

Lesson 47: Percents Less than 100, Percents Greater than 100

We have been working problems about fractional and decimal parts of numbers by using one of the following equation: (F) x (of) = is (D) x (of) = is

The percent equation is exactly the same as (a) except that the fraction has a denominator of 100. Centum is the Latin word for 100, and thus percent literally means “by the 100.” we often use the symbol % to represent the word percent.

The percent equation is c) P/100 x of = is Which can also be written as d) P/100 = is/of

The part identified by the word of is often called the base, and the part identified by the word is called the percentage. If we use these words, we get equation (e). In equation (f) P/100 is called the rate. e) P/100 x base = percentage f) Rate x base = percentage

All four equations produce the same result All four equations produce the same result. To solve word problems about percent, it is necessary to be able to visualize the problem. We will begin to work on achieving this visualization by drawing diagrams of percent problems after we work the problems. Learning to draw these diagrams is very important.

Example: Twenty percent of what number is 15 Example: Twenty percent of what number is 15? Work the problem and then draw a diagram of the problem.

Answer: P/100 x of = is 20/100 x WN = 15 WN = 15 x 100/20 WN = 1500/20 = 75 The “before” diagram is 75, which represents 100 percent. The “after” diagram shows that 15 is 20 percent. Thus the other part must be 60, which is 80 percent. Of 75 60 is 80% 15 is 20% Before 100% After

Example: What percent of 140 is 98 Example: What percent of 140 is 98? Work the problem and then draw a diagram of the problem.

Answer: P/100 x of = is WP/100 x 140 = 98 98 x 100/140 = WP = 70% Before, 100% After

Example: Fifteen percent of 300 is what number Example: Fifteen percent of 300 is what number? Work the problem and then draw a diagram of the problem.

Answer: P/100 x of = is 15/100 x (300) = WN = 45 Before, 100% After

When a problem discusses a quantity that increases, the final quantity is greater than the initial quantity. If we let the initial quantity represent 100 percent, the final percent will be greater than 100. this means that the “after” diagram representing the final quantity will be larger than the “before” diagram. The “after” diagrams in this book will no be drawn to scale.

To demonstrate, we will work problems of this type To demonstrate, we will work problems of this type. We will finish each problem by drawing diagrams that give a visual representation of the problem.

Example: What number is 160 percent of 60 Example: What number is 160 percent of 60? Work the problem and then draw a diagram of the problem.

Answer: P/100 x of = is 160/100 x (60) = WN = 96 Before, 100% After

Example: If 75 is increased by 150 percent, what is the result Example: If 75 is increased by 150 percent, what is the result? Work the problem and then draw a diagram of the problem.

Answer: 250 percent of 75 is what number Answer: 250 percent of 75 is what number? P/100 x of = is 250/100 x 75 = WN 2.5 x 75 = WN = 187.5

Example: What percent of 90 is 306 Example: What percent of 90 is 306? Work the problem and then draw a diagram of the problem.

Answer: P/100 x of = is WP/100 x 90 = 306 WP = 306 x 100/90 = 340%

HW: Lesson 47 #1-30