Unit Rates and Ratios

Mr. Swaner

Rates/ratios

• Can be written three different ways

a to b

a:b

a

b

• Because ratios are fractions, they must always be reduced to simplest form

Example

• On average, a baseball team scores 3 runs to every 7 hits. Write a ratio for the situation

Example

• On average, a baseball team scores 3 runs to every 7 hits. Write a ratio for the situation

3 to 7

3:7

3

7

Using the ratio

• We can use the ratio to find the runs or the hits for a scenario. – The team scored 6 runs, how many hits did

they have?

3 6

7

Unit Rates

This is the value per unit.

You use these all the time:

At the grocery store

For cars

At your job

Speed

Unit Rates

• The denominator must be 1

Example

• What is the unit rate: $15 for a 5oz package of cashews. (how much per oz)

$15

5oz

You

• A car can go 270 miles on 9 gallons of gas. What is the unit rate?

The Hamburglar Strikes Again!

You

• Jim can type 500 words in 10 minutes. What is the unit rate?

You

• A plane can fly 480 miles per hour. What is the rate in minutes?

Trial Number Passed

Time Ratio Rate Unit Rate

1

2

3

4

Class # of boys # of girls Ratio of boys to girls

1

2

3

5

6

Are the ratios of boys to girls in the two classes equivalent?

What could these ratios tell us?

If there is a larger ratio of boys to girls in one class than in the grade as a whole, what does that mean must be true about the boy/girl ratio in other classes?

• Value-Mart is advertising a Back-to-School sale on pencils. A pack of 30 sells for $7.97 whereas a 12-pack of the same

• brand cost for $ 4.77. Which is the better buy? How do you know?

Pack of 30 Pack of 12

Ratio:

Rate:

Unit Rate:

Unit of Measure:

Pack of 30 Pack of 12

Ratio: $7.97 for every 30 pencils

$15.94 for every 60 pencils

$4.77 for every 12 pencils

$23.85 for every 60 pencils

Rate: 7.97/30, or approx. 0.27 dollars per pencil

4.77/12, or approx. 0.40 dollars per pencil

Unit Rate: 0.27 0.40

Unit of Measure: dollars per pencil dollars per pencil

• How is finding an associated rate or unit rate helpful when making comparisons between quantities?

Video

Exit Ticket

• 1. At the conclusion of the video, your classmate takes out his calculator and says, “Wow that was amazing! That means the dog went about 5 meters in 1 second!” Is your classmate correct and how do you know?

• 2. After seeing this video, another dog owner trained his dog, Lightning, to try to break Tillman’s skateboarding record.

• Lightning’s fastest recorded time was on a 75-meter stretch where it took him 15.5 seconds. Based on this data, did Lightning break Tillman’s record for fastest dog? Explain how you know.