Ratio, Rates and proportions

Ratio, Rates and proportions

Use the mini lesson notes as part of this lesson.

Ratios

• A ratio is a comparison of two numbers or quantities by division.

• Ratios can be written three different ways:

• As a fraction:

   $\frac{2}{3}$  

• As a comparison:   2:3

• As a sentence: 2 to three

• All have the same meaning.

Rates

• A rate is a ration that compare two quantities with different types of units such as $5 for 2 pounds or 130 miles in 2 hours. When a rate is simplified to have a denominator of 1, it is called a unit rate.

• Rate: 150 miles in 5 hours Unit rate: 30 miles in 1 hour.

Proportion

• Proportions express a pair of equivalent or equal ratios

• Example:

   $\frac{1}{3}\ =\ \frac{4}{12}$  

• Cross-multiplication:  method used to determine if a proportion is a true proportion.

Open Ended

Mary has a bag of MMs. IN the bag there are 5 yellow , 4 blue , 6 green, 2 brown and 3 red.

Multiple Choice

Scott had to run for 18 minutes, ride his bike for 20 minutes, and lifted weights for 15 minutes. What is the ratio of the time he rode his bike to the total amount of time he exercised?

• 18:20

• 20:33

• 53:20

• 20:53

Multiple Choice

What is the ratio of shaded squares to not shaded squares?

• 10:5

• 10:6

• 6:10

• 10:18

Multiple Choice

Express the ratio as a fraction in simplest form:
18 ounces to 3 cups

• 6 to 1
• 1/6
• 18/3
• 3/18

Multiple Choice

What is the cost of 1 gallon of gas if you pay $31.20 for 15 gallons of gas? Hint: What is the unit rate?

• $1.95

• $0.15

• $2.08

• $10.00

Multiple Choice

What is the unite rate of 680 calories in 6 muffins?

• 674

• 113.3

• 4,080

• 156.2

Multiple Choice

What is the unit rate for 476 miles in 8 hours

• 59.5

• 0.01

• 3808

Multiple Choice

You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?

• $8 per pound

• $35 per pound

• $5 per pound

• $0.125 per pound

Multiple Choice

15 minutes to drive 21 miles; 25 minutes to drive 35 miles

• yes, equivalent
• no

Multiple Choice

20 out of 45 students attended the concert; 12 out of 25 students attend the concert

• yes, equivalent
• no

Multiple Choice

18 vocab words learned in 2 hours; 27 vocab words learned in 3 hours

• yes, equivalent
• no, not equivalent

Multiple Choice

20 out of 45 students attended the concert; 12 out of 25 students attend the concert

• yes, equivalent
• no

Multiple Choice

$15 for 5 pairs of socks; $25 for 10 pairs of socks

• yes, equivalent
• no, not equivalent

Multiple Choice

A proportion is a number sentence that relates two ratios that are equivalent .

• True

• False

Multiple Choice

You go to the grocery store to buy dog food. The store has three sizes available:

A 20-lb bag for $23.44

An 8-lb bag for $9.88

A 40-lb bag for $49.00

Which size bag has the lowest cost per pound rounded to the nearest cent?

• The 8-lb bag

• The 20-lb bag

• The 40-lb bag

• I have a cat

Multiple Choice

A unit rate is a rate in which the unit in the denominator is:

• 0

• 3

• 1

• 2

Multiple Choice

A car is going 50 miles per hour. A rate that describes this would have units of

• Miles and cars

• Miles and hours

• Miles only

• Hours only

Multiple Choice

A rate is a ratio that compares

• A part to a part

• A part to a whole

• Quantities with different units

• Quantities with the same units

Multiple Choice

You're throwing a party, and you ordered 15 pizzas for your guests. Your total came to $97.50. What was your unit cost per pizza?

• $4.95 per pizza

• $5.75 per pizza

• $7.25 per pizza

• $6.50 per pizza

Multiple Choice

Which is the better buy? A 12-pack of Pepsi for $3.50 or a 6-pack for $1.80?

• The 12-pack

• The 6-pack

• They're the same

• Neither, I prefer Coke

Multiple Choice

Which one is a real life example of a RATIO?

• 12 noodles
• 4 meatballs : 1 cup of sauce
• 1 jar of sauce
• 15 desserts