Download Lesson 2-6

Lesson 2 – 6: Ratios, Rates and Conversions
Vocabulary:
Ratio – A comparison of two numbers by division
Rate – A ratio of two quantities with different units
Unit Rate – A rate with the second quantity of 1 unit
Conversion Factor – A ratio of two equivalent measures in different units
A ratio compares two numbers by using division. The ratio of two numbers 𝑎 𝑎𝑛𝑑 𝑏 can be written in three
𝑎
ways: 𝑏 , 𝑎: 𝑏 𝑜𝑟 𝑎 𝑡𝑜 𝑏. So, if we had a class of 10 girls and 7 boys we could write the ratio of girls to boys as
10
7
, 10: 7 𝑜𝑟 10 𝑡𝑜 7. Being that ratios are written as division they can be reduce if possible.
2-6.1 – Unit Rates
One of the main uses for rates are to compare similar situations. We can to this by using unit rates. To find a
unit rate we need to get our second unit equal to one.
Example:
If John can eat 53.5 hot dogs in 12 minutes, how many can he eat in one minute.
53.5/12 = 4.46 hot dogs per minute
We can then use this to evenly compare items. Such as:
Example: You are shopping for T-shirts. Which of the following stores has the best offer.
Store A
$25 for 2 shirts
25/2 = $12.50 per shirt
Store B
$45 for 4 shirts
45/4 = $11.25 per shirt
Store C
$30 for 3 shirts
30/3 = $10 per shirt
So Store C is the best deal.
2-6.2 – Converting Units
To convert from one unit of measure to another we use a conversion factor. This is a ratio with equivalent units
so that it is equal to 1 that we multiply the original unit by to change it.
Example:
Convert 330 minutes to hours
330 𝑚𝑖𝑛
1
1 ℎ𝑟
∗ 60 𝑚𝑖𝑛 =
330 ℎ𝑟
60
= 5.5 ℎ𝑟𝑠
Convert 3 miles to feet
3 𝑚𝑖
We can also convert between systems
Convert 1815 feet to meters (1 𝑚 ≈ 3.28 𝑓𝑡)
1815 𝑓𝑡
1
1𝑚
∗ 3.28 𝑓𝑡 ≈ 553 𝑚
1
∗
5280 𝑓𝑡
1 𝑚𝑖
= 15840 𝑓𝑡
2-6.3 – Converting Rates
Sometimes we have to convert rates with 2 different measurements. To do this we just have to use multiple
conversion factors.
Examples:
A student ran the 50 yard dash in 5.8 seconds. At what speed did the runner run in miles per hour?
50 𝑦𝑑
1 𝑚𝑖
5.8 𝑠𝑒𝑐
60 𝑠𝑒𝑐
∗ 1760 𝑦𝑑 ∗ 1 𝑚𝑖𝑛 ∗
60 𝑚𝑖𝑛
1 ℎ𝑟
=
180000 𝑚𝑖
10208 ℎ𝑟
≈ 17.63 𝑚/ℎ
The janitor at school found that a sink was leaking at a rate of 4 oz. per minute. How many gallons per hour
would this be?
4 𝑜𝑧
1 𝑚𝑖𝑛
∗
60 𝑚𝑖𝑛
1 ℎ𝑟
1 𝑔𝑎𝑙
∗ 128 𝑜𝑧 =
240 𝑔𝑎𝑙
128 ℎ𝑟
7
= 1 8 𝑔𝑎𝑙/ℎ𝑟