2.6 Ratios, Rates and Conversions:

Unit Rate: A rate with 1 in the denominator.

Rate: A ratio that compares quantities measured in different units.

Ratio: a comparison of two numbers using division.

Conversion Factor: A ratio of two equivalent measures in different units.

Unit Analysis (Dimension Analysis): The process of including the units of quantities in a conversion to obtain the desired units.

GOAL:

REAL-WORLD:

Justin runs for 25 minutes and does 8 laps around the track. What is the time he takes to do a lap?

Justin runs 25 minutesSolution:

Justin does 8 laps

The unit rate is:

25𝑚𝑖𝑛𝑢𝑡𝑒𝑠8 𝑙𝑎𝑝𝑠 by 8

3.125𝑚𝑖𝑛𝑢𝑡𝑒𝑠1𝑙𝑎𝑝

Justin takes an average of 3.125 minutes per lap.

We can use unit rates to compare quantities:

Store A: $25 for 2 shirts

Ex: There are three stores that sell the same shirt. Use the info to tell which stores is the most affordable?

Store B: $45 for 4 shirts

Store C: $30 for 3 shirts

In order to compare the prices, we must find out the price of a single shirt.

A: $25 for 2 shirts

SOLUTION:To find the price per shirt we must find the ratio of price to one shirt.

B: $45 for 4 shirts

C: $30 for 3 shirts

Looking at the price per shirt, Store C is the most affordable.

= =

=

When we are given units different from the ones we want to work with, therefore we must use the conversion factor (a ratio of two equivalent measures in different units).

Converting Units:

125cm ∙Ex: What is 125 cm in meters?

Here x represents thenumber of cm that makeup a meter, that is x = 100

∙ = = 1.25 m

Hence: 125cm is equivalent to 1.25 m.

NOTICE: By now you must have a knowledge of the conversions we use in everyday life, such as:

ALSO: This is the on that will be given to you on the baselines, interims and EOCs.

YOU TRY IT:

Convert 5 kg to milligrams?

YOU TRY IT: (Solution)Here we must start by relating kilograms to milligrams:

We must know that: 1 kg = 1000 grams

and 1 gram = 100 milligrams

Using this info we set up the conversion as:

∙ ∙Then: ¿𝟏 ,𝟎𝟎𝟎 ,𝟎𝟎𝟎𝒎𝒍

YOU TRY IT:

What is 9 yards in meters?

Solution:Here we must start by relating yards to meters.

We must know that: 1 yrd = 3ft

and 1 ft = 12 inand 1 in = 2.54 cm and 100 cm = 1 meter.

Using this info we set up the conversion as: ∙ ∙ ∙ ∙

Then: ¿𝟖 .𝟐𝟑𝐦

YOU TRY IT:

Copy and complete the statement.

2.5 days = ____ sec.

Solution: Relate days to minutes:

1 day = 24 hrsand 1 hr = 24 minand 1 min = 60 sec.

Using this info we set up the conversion as: ∙ ∙ ∙

Then: ¿𝟐𝟏𝟔 ,𝟎𝟎𝟎 𝒔𝒆𝒄

VIDEOS: Unit Conversion

https://www.khanacademy.org/math/arithmetic/rates-and-ratios/unit_conversion/v/converting-gallons-to-quarts-pints-and-cups

https://www.khanacademy.org/math/arithmetic/rates-and-ratios/unit_conversion/v/converting-yards-into-inches

https://www.khanacademy.org/math/arithmetic/rates-and-ratios/unit_conversion/v/converting-pounds-to-ounces

CLASS WORK:

Pages: 121 – 123

Problems: As many as it takes to master the concept.