Percentages by itself means divided by one hundred. For example, 15% means 15 / 100. A percentage shows what portion of 100 a given number constitutes. For example, if an individual had 100 plants and gave away 20, that would mean he gave away 20/100 or .20. To determine the % of plants given away, we would simply multiply .20 by 100, giving us 20%. Let's look at another problem and determine the percentages involved. (Divide the number of correct answers by the total number of questions and multiply by 100 Number of questions 21. Number of correct answers 19. 19/21 x 100 = .90476 x 100 = 90.48% A
Ratios is simply two items compared by division. Gear ratios have implications toward mechanical advantage or speed depending on the ratio involved. However, a proportion is an equation that shows that two ratios are equal. One of the more common types of questions seen on past exams cancel speed and distance proportions. For example, if a car can travel S miles in 6 minutes, how far can it travel in 30 minutes, assuming the same speed is maintained? This kind of a problem would first be set up as two separate ratios and then placed in a proportion to determine the distance traveled. RATIO 1 5 miles in 6 minutes Ratio 2 How many (X) miles is traveled in 30 minutes? In proportional form we then have: 5 miles/ 6minutes = X miles/30 minutes Once the proportion is established, you can cross multiply the proportion figures and obtain this: 6X = 5 x 30. To solve for X, one of two basic algebraic laws needs to be applied. The addition law for equations states that the same value can be added or subtracted from both sides of an equation without altering the solution. The second basic law is the multiplication law for equations. This states that both sides of an equation can be multiplied or divided by the same number without changing the final solution. These two laws are used to solve equations that have only one variable. In the case of 6X = 5 x 30, we will implement the multiplication division law to determine X. If we divide both sides of the equation by 6, we can then figure how many miles the car would travel in 30 minutes. 6X 5x30( = 5 x 5 = 25) = 6 6 1
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