Transcript Section 2.6
Section 2.6
RATIOS, RATES, AND
CONVERSIONS
Ratio
Compares two numbers by division
Can be written in 3 ways:
a
a:b
a to b
b
Must always be simplified!!
Meaning – for every a units of one quantity, you have b
units of another quantity
Example: the number of boys to girls in class is 2 to 1
Rate
A ratio that compares quantities measured in
different units
A rate with a denominator of 1 unit is called a
unit rate
Comparing Unit Rates
Write each ratio as a unit rate THEN compare
Example:
You are shopping for T-shirts. Which store offers the better
deal?
Store A: $25 for 2 shirts
Store B: $45 for 4 shirts
Store C: $30 for 3 shirts
Converting Units
To convert from one unit to another, such as feet to
inches, you multiply the original unit by a conversion
factor that produces the desired unit.
Conversion
factor – a ratio of two equivalent measures in
different units
Conversion factors ALWAYS equal to 1
ALWAYS
place the given conversion on the bottom on
the conversion factor
Example:
1 ft
12 in
**** PAGE 723 has Conversions
Example
Convert the given amount to the given unit
330 min; hours
● 15 kg; grams
330 min · 1 h
60 min
● 5 ft 3in; inches
Converting Rates with 2 Different Units
You must multiply by two conversion factors in order
to change both of the units.
Example:
A student ran the 50-yard dash in 5.8 seconds. At what speed
did the student run in miles per hour? Round your answer to
the nearest tenth.
50 yards
5.8 sec