1. Unit Rates and Proportional Reasoning
LESSON 5-2
Problem of the Day
Solve using distributive property
1) 8y -(2y -3) = 9
2) 6(x + 4) -2x = -8
1) y = 1
2) X = -8
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2. Unit Rates and Proportional Reasoning
LESSON 5-2
Recall
(For help, go to Lesson 5-1.)
What is a ratio?
- Compares two quantities measured in the same unit
- It can be written as a fraction
- It has no units
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3. Unit Rates and Proportional Reasoning
LESSON 5-2
What are you going to learn?
(For help, go to Lesson 5-1.)
3 main concepts –
Finding unit rate
Finding total cost using unit cost
Using unit cost to compare and find out better buy
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4. Unit Rates and Proportional Reasoning
LESSON 5-2
RATE?
Rate compares two quantities measured in different units
It is a form of ratio in which the two terms are in different units
Unit Rate – Rate for one unit of a given quantity. Simply put, rate which has denominator of 1.
Examples?
mi/hr, $/kg, m/s
To find the unit rate, simply divide the first quantity by the second.
Unit Cost – A unit rate that gives cost per unit.
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5. Unit Rates and Proportional Reasoning
LESSON 5-2
Additional Examples
Find the unit rate: earn $33 for 4 hours of work.
dollars 33
hours 4
= 8.25
Divide the first quantity by the second
quantity.
The unit rate is , or $8.25 per hour.
$8.25
1 hour
Quick Check
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6. Unit Rates and Proportional Reasoning
LESSON 5-2
Additional Examples
Use the unit price to find the total price: 7 yd of ribbon at $.39 per yard.
= $ unit price • number of units = total price
$.39 • 7
The total price of 7 yd of ribbon is $2.73.
Quick Check
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7. Unit Rates and Proportional Reasoning
LESSON 5-2
Additional Examples
Find each unit price. Then determine the better buy.
3 lb of potatoes for $.89
5 lb of potatoes for $1.59
Remember:
Better buy has the smallest price / unit
Divide to find the unit price of each size.
price
number of lb
$.30/lb
$.89 3
price
number of lb
$.32/lb
$1.59 5
Since $.30 < $.32, 3 lb of potatoes for $.89 is the better buy.
Quick Check
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8. Unit Rates and Proportional Reasoning
LESSON 5-2
Using conversion factors
We are going to use ratios to convert a measurement from one system to another.
Conversion factor is a rate that equals 1.
Note: This method of canceling units is quite useful especially in Science. This technique is called ‘unit analysis’ or ‘dimensional analysis’ – I’ve introduced this to you as “multiplying by a fraction equal to 1”
Main principle – multiplying / dividing something by 1 doesn’t change the value.
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9. Unit Rates and Proportional Reasoning
LESSON 5-2
Lesson Quiz
1. It took Anthony 5 h 45 min to complete a 25-mi walkathon. What was his average speed in miles per hour? Round your answer to the nearest hundredth.
2. A 20-lb bag of dog food costs $ A 30-lb bag of the same dog food costs $ Find each unit price. Then determine the better buy.
4.35 mi/h
$1.08/lb; $1.10/lb; 20 lb for $21.50.
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10. Unit Rates and Proportional Reasoning
LESSON 5-2
Lesson Quiz
1. If a car travels 45 miles in 30 min, what is the rate at which the car is travelling?
If John bought 2.5 kg of rice for $7.5, what is the unit price of rice?
It takes 30 min for a tap to fill one bucket, how much time (in hrs) would it take to fill 6 buckets?
You can buy 28 fl oz of fruit juice for $1.69 or 64 fl oz for $3.19. Which size is a better buy?
90 mi/hr or 1.5 mi/min
$3/kg
Total 3 hrs
64 fl oz for $3.19
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11. HOMEWORK
Homework:
Lesson 5-2: p : 1, 6 – 28 e, 29
p. 236: # 1-9 all – This should be review. Show all work.