Introduction to Ratios and Rates
First, what is a ratio and what is a rate?
Leonardo da Vinci's drawings of the human body emphasized its proportion. It is an example of the use of the Golden Ratio.
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A RATIO is....
A ratio is the comparison of two numbers which have the same units of measure. Since the units are the same, they are not written after the numbers.
For example: There are 27 students in grade 2, and 6 of them are left handed.
Number of left handed
6:27
Total students
6:27 is read: “6 is compared to 27” or “6 to 27”.
6 and 27 are the terms of the ratio.
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Ratio Symbols
Ratios can be symbolized using 3 different notations:
1.
6:27 This is a common notation
2.
6/27 This is the fraction notation
3.
(6,27) This is the ordered pair notation
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Equivalent Ratios
The order of the numbers in a ratio is important.
Equivalent ratio: represents the same comparison
A statement that 2 ratios are equal, such as 2/3 = 4/6, is called a proportion.
e.g. 6:6:4 and 3: __ : ___ e.g. 3:5:7 and ___:___:14 4
Rates are....
A RATE is a comparison of 2 numbers with different units e.g. km/h, breaths/min
Types of Rates
A unit price is the cost of one item or unit e.g. 94 cents/ litre
A unit rate has 1 as its second term e.g. 90 km/h
There are also units that are different, so we don't want to mix them up with rates! For Example:
Units ­ (2 different units ­ ie. Km/h, g/mL)
What's the difference?
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Also, you can express the UNIT RATE:
$30 for 5 h work
30/5 = 6/1
saved $480 in 4 months
480/4 = 120/month
lost 48kg/96 weeks
0.5 kg/week
An example:
Natalie skated 1000m in 1 min 45.46 sec.
How many m did she skate per second?
Convert her total time to seconds: 105.46
1000m/105.46s = 9.48m/x (USE CALCULATOR)
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Name:
Let's apply ratios:
Tamara has a recipe for fruit punch that calls for three cans of frozen orange juice concentrate, two cans of raspberry juice concentrate, and one can of lime juice concentrate. For each can of juice concentrate, the directions say to add three cans of water. All the cans are the same size. Tamara makes one recipe of fruit punch.
Questions:
1. What is the ratio of orange juice to lime juice concentrate?
Express the ratio two different ways.
2. What is the ratio of lime to orange to raspberry juice concentrate? 3. What is the ratio of water to juice concentrate?
4. How many cans of punch does the recipe make?
5. What is the ratio of orange, raspberry, and lime juice concentrate to total punch? Express the ratio as a fraction, a decimal, and a percent.
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Solution:
Orange
Raspberry
Lime
Total
Juice Concentrate (cans)
Water (cans)
Total Punch (cans)
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Answers to #1­5
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Applying Rate
Three apples cost 1.35 dollars. What do 5 apples cost?
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http://www.youtube.com/watch?v=M4eoMxGDEJA
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