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RATES, R
ATIO
S AND
PROPO
RTIO
NS
NO
TE
S
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
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