RATIOS, RATES, AND CONVERSIONS

Section 2.6

Ratio

Compares two numbers by division

Can be written in 3 ways:a a : b a to bb

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 ft12 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 yards5.8 sec