Math 215
I
Notes 7.1 – Meanings of Ratio, Rate and & Proportion
Ratio: A ratio describes a specific type of relationship between two quantities.
Example: To make lemonade we use 4 tablespoons of concentrate for every quart
of water. If we want to make 3 quarts of lemonade, how many
tablespoons of concentrate should we use?
II
Rate: A ratio between two quantities that are measured in different units. For
example speed is the ratio of distance traveled to time elapsed.
Joe’s speed is 60 miles per hour. Rate is the same as speed.
III
Ways to express a ratio:
4 to 6 or 4: 6 or 4/6
IV
Ratio Problems: Solve using a strip diagram.
Example: Suppose a certain shade of green paint is made by mixing blue paint
with yellow paint in a ratio of 2 to 3.
a.
If you use 40 pails of blue paint how many pails of yellow paint will you
need?
V
b.
If you use 48 pails of yellow paint, how many pails of blue paint will you
need?
c.
If you want to make 100 pails of green paint, how many pails of blue paint
and how many pails of yellow paint will you need?
d.
At lunch, there was a choice of pizza or a hot dog. Three times as many
students chose pizza as hot dogs. All together 160 got lunch. How many
students got pizza and how many students got a hot dog?
When two equivalent ratios are set equal to each other we have a proportion.
Example:
2 = 4
5
10
VI
Solving Proportions with Multiplication, Division & Simple Logical Reasoning
Problem: Sam used 4 gallons of gas to drive 120 miles. Assuming Sam can get
the same gas mileage per gallon, how far can he drive with 24 gallons of
gasoline?
“Direct” Solution Method:
“Going Through One” Solution Method
VII
Solving Proportions by Cross Multiplying Fractions
Problem: Sam used 4 gallons of gas to drive 120 miles. Assuming Sam can get
the same gas mileage per gallon, how far can he drive with 24 gallons of
gasoline?