Ratios, Unit Rate, and Proportions

Ratios, Unit Rate, and Proportions

Constructed Response AssessmentOctober 17th

A ratio is a comparison of two quantities using division.

Ratios can be written in three different ways: 7 to 5, 7:5, and Order matters when writing a ratio.

7 5

Day 1: Ratios

Find the ratio of boys to girls in Donnelly’s class.

Lucky Ladd Farms has: 16 cows, 8 sheep, and 6 pigs

cows to sheep pigs to total animals sheep to pigs

Always simplify your ratio to the lowest term.

Practice: Write each problem in 3 different ways.

The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.

For every vote candidate A received, candidate C received nearly three votes.

Make a table or model to represent one of the above situations.

Ratios:

Beak Wing1 22 43 64 8

Remember, a ratio makes a comparison.

The ratio of green aliens to total aliens is 3 to 7.

****Make sure you write the ratio just like they ask for it!****

The ratio of total aliens to purple

aliens is 7 to 4. Not 4 to 7

Day 2: RATIOS

Use the picture to write the ratios being asked

1. What is the ratio of blue balloons to red balloons?

2. What is the ratio of total balloons to orange balloons?

3. What is the ratio of yellow balloons to total balloons?

4. What is the ratio of green balloons to purple balloons?

Ratios that make the same comparison are equivalent ratios. To check whether two ratios are equivalent, you can write both in simplest form.

Day 3: Equivalent Ratios

20 cars : 30 trucks

10 : 15 2 : 3 80 : 120

Check It Out! Example 1

Write the ratio 24 shirts to 9 jeans in simplest form.

249

83

The ratio of shirts to jeans is , 8:3, or 8 to 3.

=shirtsjeans

24 ÷ 39 ÷ 3

Write the ratio as a fraction.

= = Simplify.

83

Lesson Quiz: Part IWrite each ratio in simplest form.1. 22 tigers to 44 lions

2. 5 feet to 14 inches

415

3.

721

4.

830

1245Possible answer: ,

13

1442Possible answer: ,

Find a ratios that is equivalent to each given ratio.

12

307

Determining Whether Two Ratios Are Equivalent

Simplify to tell whether the ratios are equivalent.

1215

B. and 2736

327

A. and 218

Lesson Quiz: Part II

7. Kate poured 8 oz of juice from a 64 oz bottle. Brian poured 16 oz of juice from a 128 oz bottle. Are the ratios of poured juice to starting amount of juice equivalent?864

16128

and ; yes, both equal 1 8

85

85= ; yes16

105.

3624

6.

Simplify to tell whether the ratios are equivalent.

and 32 20

and 28 18

32

149 ; no

Day 4: RATESA rate is a ratio that compares quantities

thatare measured in different units. This spaceship travels at a certain speed.

Speed is an example of a rate.

This spaceship can travel 100 miles in 5 seconds is a rate.

It can be written 100 miles 5 seconds

RATESA rate is a ratio that compares quantities

thatare measured in different units.

One key word that often identifies a rate is PER.• Example: Miles per gallon, Points per free throw,Dollars per pizza, Sticks of gum per pack

What other examples of rates can your group think of?

Remember: A rate is a ratio that compares two quantities measured in different units (miles, inches, feet, hours, minutes, seconds).

The unit rate is the rate for one unit of a given quantity. Unit rates have a denominator of 1.

Day 5: Unit Rate

UNIT RATESA unit rate compares a quantity to one unit

ofanother quantity. These are all examples ofunit rates.

2 eyes per alien1 foot per leg

6 tentacles per head1 tail per body

3 windows per spaceship3 riders per spaceship

Unit Rate

150 heartbeats2 minutes

Unit Rate (divide to get it):150 ÷ 2 = 7575 heartbeats to 1minute OR75 heartbeats per minute

Rate

Find the Unit RateAmy can read 88 pages in 4 hours (rate). What is the unit rate? (How many pages can she read per hour?)

88 pages4 hours

22 pages / hour

Unit rates are rates in which the second quantity is 1.

unit rate: 30 miles,1 hour or 30 mi/h

The ratio 903 can be simplified by dividing:

903 = 30

1

Try this by yourself!

Check It Out! Can you solve?Penelope can type 90 words in 2 minutes. How many words can she type in 1 minute?

90 words 2 minutes Write a rate.

=

Penelope can type 45 words in one minute.

90 words ÷ 2 2 minutes ÷ 2

Divide to find words per minute.

45 words 1 minute

Unit price is a unit rate used to compare price per item.

Use division to find the unit prices of the two products in question.

The unit rate that is smaller (costs less) is the better value.

Day 6: Comparing Unit Prices

ExampleJuice is sold in two different sizes. A 48-fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy?

$2.0748 fl.oz. 0.04312

5 $0.04 per fl.oz.

$1.6432 fl.oz. 0.05125 $0.05 per

fl.oz.The 48 fl.oz. bottle is the better value.

Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which pack has the lower unit price?

Additional Example: Finding Unit Prices to Compare Costs

Divide the price by the number of pens.

price for packagenumber of pens =$1.95

5= $0.39

price for packagenumber of pens = $6.20

15 $0.41

The 5-pack for $1.95 has the lower unit price.

Try this by yourself

John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which bottle has the lower unit price?

$2.1924= $0.09

= $3.7936 $0.11

The 24 oz jar for $2.19 has the lower unit price.

price for bottlenumber of ounces

price for bottlenumber of ounces

Divide the price by the number of ounces.

710 , 21

30

x 3

x 3

Yes, these two ratios DO form a proportion, because the same relationship exists in both the numerators and denominators.

89

, 23

÷ 4

÷ 3

No, these ratios do NOT form a proportion, because the ratios are not equal.

Day 7: A proportion is an equation stating that two ratios are equal.

A proportion is an equation stating that two ratios are equal.

Example:

Example:  

Proportion

A piglet can gain 3 pounds in 36 hours. If this rate continues, the pig will reach 18 pounds in _________ hours. 

Jessica drives 130 miles every two hours. If this rate continues, how long will it take her to drive 1,000 miles?

Proportion ExampleJoe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline?

25 miles1 gallonUnit Rate = 8 gallons

x 8

x 8

25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas.