RATES, R

ATIO

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PROPO

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NO

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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.

4.00 = x To solve this we used a method call

100 25 CROSS 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

100.00 = 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.

6 What is the length of the side

xthat is labeled x?

10 First, we set up our proportion

20 x = 6

20 10

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

200 300 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