Ratios, Rates, and Unit Rates across the Universe

RATIOS

A ratio makes a comparison of two quantities using division. There are 3 green aliens and 4 purple aliens. The ratio of green aliens to purple aliens is 3 to 4.

RATIOS

A ratio makes a comparison. The ratio of green aliens to total aliens is 3 to 7. The ratio of total aliens to purple aliens is 7 to 4.

RATIOS

A ratio makes a comparison using division. Ratios can be written in three different ways.

3 to 4 3:4 3 4

Find Each Ratio

1. Purple to total 2. Green to total 3. Purple to green 4. Green to purple

Using Tape Diagrams to Solve

Using Table to Solve

Think About It

•

This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.“ 3cups :4 cups

Think About It

• •

52 wings:26 beaks “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.”

Write the ratios in simplest form.

• • • • 1. 5 to 13 5/13 because it cannot be simplified. 2. 7 to 35 1/5 because you can divide both by 7. 3. 6 to 9 2/3 because you can divide both by 3.

The ratio of wins to losses for a team with 14 wins and eight losses. 14 = 14/2 = 7 wins 8 8/2 4 losses

Ratio- Real Life Application

• You are painting a room and want to mix red and blue to make purple. The ratio should be 15 oz. red to 20 oz. blue. 15:20 Put this in simplest terms: • 15 = 15/5 = 3 oz. red 20 20/5 4 oz. blue

Solve

RATES

A rate is a ratio that compares quantities that are measured in different units. This spaceship travels at a certain speed. Speed is an example of a rate.

Speed can be measured in many different ways. This spaceship can travel 100 miles in 5 seconds. 100 miles in 5 seconds is a rate.

RATES

A rate is a ratio that compares quantities that are measured in different units. Rates are often written in fraction form.

100 miles in 5 seconds It can be written as…..

is a rate.

100 Miles 5 Seconds

RATES

A rate is a ratio that compares quantities that are measured in different units. One key word that often identifies a rate is PER .

Miles per gallon, Points per free throw, Dollars per pizza, Sticks of gum per pack Per means DIVIDE What other examples of rates can your group think of?

UNIT RATES

Most of the time when we work with rates we use a unit rate. A unit rate compares a quantity to one unit of another quantity.

This alien can walk at a rate of 10 miles in 2 hours. We need to find out how fast he can walk in 1 hours. Divide 2/2 to get 1 hour. Then divide 10/2 to get 5.

His speed is a unit rate of 5 miles per 1 hour or simply 5 miles per hour.

10 2 Miles Hours

=

5 1 Miles Hour

UNIT RATES

A unit rate compares a quantity to

one

unit of another quantity. These are all examples of unit rates .

2 eyes per alien 1 foot per leg 6 tentacles per head 1 tail per body 3 windows per spaceship 3 riders per spaceship 2 people riders per dog rider

Think About It

•

"We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger." How do we know if this is right? $75 ÷ 15 = 5

Real Life Application

A car traveled 300 miles on 10 gallons of gas. What is the unit rate (miles per gallon)?

300 = 300/10 = 30 miles 10 10/10 1 gallon of gas (30 miles per gallon)

Solve It

• JoJo earned $50 in five hours cutting grass. What is the unit rate?

50 = 50/5 = 10 dollars 5 1 1 hour ($10 per hour)

Real Life Application

• On vacation, Mike hiked 30 miles in six hours. What is the unit rate?

30 = 30/6 = 5 miles 6 6/6 1 hour (five miles per hour)

Find the unit rate.

• 1) 84 students in 4 classrooms 84 students x 4 classrooms = 1 21 students/per classroom • 2) $30 for 8 lunches $30 = x 8 1 $3.75/per lunch

Find the unit rate

• 3) 15,000 cars sold by 2000 dealers 15,000 = x 7.5 cars/dealer 2,000 1 • 4) Your heart beats 70 beats/min. How many beats per hour is this?

4200 beats/hour