RATES, RATIOS AND PROPORTIONS NOTES

DEFINITIONS A ratio is a relationship between two numbers of the same kind. A proportion is a name given to two ratios that are equal. Rate refers to a ratio between two measurements, often with different units.

PROBLEMS WITH MONEY EXAMPLE: Jamal is a great couponer and realizes that he can buy crackers that are originally $4.00 for 25% off. What is the cost of the crackers? To solve this we create a proportion to solve! We know that 100% of the price is $4.00 and that we are getting a 25% discount. We want to know how much that discount is = xTo solve this we used a method call 10025CROSS MULTIPLY To Cross multiply we multiply the items that are across from each other and then set them equal to one another 4.00 x 25 = 100 x = 100x x = 1.00, so that means we get a $1.00 off; the crackers will cost $3.00

PROBLEMS WITH GEOMETRY These two triangles are similar, which means the ratios of the sides are the same. 6What is the length of the side xthat is labeled x? 10First, we set up our proportion 20x = Then we cross multiply to get 10x = 20 x 6 10x = 120, so x = 12

RATES The rate a car can travel is measured in distance/time. The equation we use is r = D/t where r = rate, d = distance and t = time Sometimes we will see this solved for distance and in that case the equation is D = rt EXAMPLE: What is Marcy’s rate of speed if she has traveled 300 miles in 5 hours? r = D/t or r = 300miles/5 hours, so r = 60 miles/hour If Marcy travels 50 miles/hour, how long will it take her to travel the same distance? (300 miles?) D = rt 300 miles = 50t t = 6 hours

TRAVELLING We can also use a proportion when dealing with travelling: EXAMPLE: If it takes Juan 4 hours to travel 200 miles, how long will it take him to travel 300 miles? 4 = x(notice that the same units are across from one another) Cross multiply to get 4 x 300 = 200x 1200 = 200x x = 6 hours

DEALING WITH MAPS Maps have something called a scale. Scales are used as part of the proportion when dealing with distances from one place to another. EXAMPLE: On a map, Concord and Charlotte are 2.5 inches apart. The scale tells us that one inch equals 10 miles. How far apart are these two cities? To solve this we set up a proportion: 1 inch = 2.5 inches 10 miles x Cross multiplying, we get 1x = 25, therefore x = 25 miles