Ratio, Rates, & Proportions

Ratios• A ratio is a comparison of two numbers.

oExample: Tamara has 2 dogs and 8 fish. The ratio of dogs to fish can be written in three different ways.

  

*** Be careful with the fraction ratios – they don’t always have identical meanings to other fractions***

• There are two different types of ratioso .Part-to-Part Ratios▪Example: Tamara’s dogs to cats is 2 to 8

or 1 to 4o .Part –to-Whole Ratios▪Example: Tamara’s dogs to total pets is 2

to 10 or 1 to 5

  

Try the following Apples to bananas• There are 12 apples

and 3 bananas

• So the ratio of apples to bananas is

4:1, 4 to 1, OR

Oranges to apples

• There are 15 oranges and 12 apples

• So the ratio of oranges to apples is

5:4, 5 to 4, OR 14

45

• The ratio is comparing two number. If you changed it to a mixed number it

would no longer be a comparison. This is why fraction ratios are tricky 

929

Explain why the ratio

9

is not written as a mixed number:

Comparing Ratios• Compare ratios by writing in simplest form

oAre these ratios equivalent?250 Kit Kats to 4 M&M’s and 500 Kit Kats to 8 M&M’s

o  12 out of 20 doctors agree and 12 out of 30 doctors agree

o The ratio of students in Ms. B’s classes that had HW was 8 to 2 and 80% of Mrs. Long’s class had HW

 

=5.624250

= 5.628500

=

53

2012

= ≠ 52

3012

=

108

= 10080

Rates• A rate is a ratio that compares two different quantities

or measurements.

• Rates can be simplified

• Rates us the words per and foroExample: Driving 55 miles per houroExample: 3 tickets for $1

  

Unit Rates• A unit rate is a rate per one unit. In unit

rate the denominator is always one.oExample: Miguel types 180 words in 4 min.

How many words can he type per minute?

= or words per minute

rate unit rate word form

45 45 . 1

• Unit rates make it easier to make comparisons.oExample: Taylor can type 215 words in 5 min

▪How many words can he type per minute?

▪Who is the faster typist? How much faster? Taylor is 2wpm faster than Miguel

  

wpm435215

=

1. Film costs $7.50 for 3 rolls

3. 90 students and 5 teachers

5. **Snowfall of 12 ¾ inches in 4 ½ hours.

7. Ian drove 30 miles in 0.5 hours

2. Drive 288 miles on 16 gallons of gas.

4. Earn $49 for 40 hours of work

6. Use 5 ½ quarts of water for every 2 lbs of chicken

8. Sarah drove 5 miles in 20 minutes

Try the Following

$2.50perroll

15mph

2¾quartsperlb

$1.23perhour

18mpg

18studentsperteacher

25/6perhour

60mph

Complex Unit Rates

• Suppose a boat travels 30 miles in 2 hourso How do you write this rate?

• Suppose a boat travels 12 miles in 2/3 hourso How do you write this as a rate?

o How do you write this as a division problem?

o Determine the unit rate: 18mph

mphhoursmiles 15

230

=

3212÷ 18

2312 =∗

hoursmiles3/212

• Suppose a boat travels 8 ¾ miles in 5/8 hours.o How do you write this as a rate?

o How do you write this as a division problem?

o Determine the unit rate: 14 mph

hoursmiles

8/54/83

85

438 ÷ 14

58

435

=∗

1. Mary is making pillows for her Life Skills class. She bought yards of fabric. Her total cost was $16. What was the cost per yard?

3. Doug entered a canoe race. He rowed miles in hour. What is

his average speed?

3. Mrs. Robare is making costumes for the school play. Each costume requires 0.75 yards of fabric. She bought 6 yards of fabric. How many costumes can Mrs. Robare make?

4. A lawn company advertises that they can spread 7,500 square feet of grass seed in hours. Find the number of square feet of grass seed that can be spread in an hour.

TRY the FOLLOWINGWrite each rate. Then determine the unit rate and write in both fraction and

word form

$5.82peryard

3000ftperhour

7mph

8costumes

432

2122

13 21

Comparing Unit Rates Dario has two options for buying boxes of pasta. At CornerMarket he can buy

seven boxes of pasta for $6. At SuperFoodz he can buy six boxes of pasta for $5.

• He divided 7 by 6 and got 1.166666667 at CornerMarket. He then divided 6 by 7 and got 0.85714286. He was confused. What do these numbers tell him about the price of boxes of pasta at CornerMarket?

• Decide which makes more sense to you

• Compare the two stores’ prices. Which store offers the better deal?

1.166667isthenumberofboxesyoucangetfor$1 0.85714286isthepriceperbox

Priceperbox

CM-$0.86perbox SF-$0.83perbox