**Check it out #1**

The ratio of games won to games lost for a baseball team is 3:2. The team won 18 games. How many games did the team lose?

**Example 3**

Converting Rates...

Example 3 continued...

B.

Example 2

Finding Unit Rates...

Check it out #2

Cory earns $52.50 in 7 hours. Find the unit rate.

Why learn this?

Ratios and proportions are used to draw accurate maps.

Example 1

Using Ratios...

**Rates, Ratios, Proportions**

Rates,Ratios, and Proportions

Rates,Ratios, and Proportions

Ratio-

Rate-

Scale-

Unit rate-

Conversion Factor-

Proportion-

Cross products-

Scale drawing-

Scale model-

A ratio of two quantities with different units

A comparison of two quantities by division

A ratio between two sets of measurements

A arithmetical multiplier for converting a quantity expressed in one set of units into an equivalent expressed in another

**Vocabulary**

A rate with a second quantity of 1 unit

A statement that two ratios are equivalent

Two equal products obtained by multiplying the second term of each ratio by the first term of the other ratio in a proportion

Both a scale to represent an object as smaller or larger than the actual object

The ratio of faculty members to students at a college is 1:15. There are 675 students. How many faculty members are there?

faculty

------------

students

----->

1

15

----->

----

1.) Write a ratio comparing faculty to students

1/15

=

X/675

2.) Write a proportion. Let X= the # of faculty members

<-----

<-----

3.) Multiply both sides of the equation by 675 since x is divided by 675

<-----

675(x/675) = 675(1/15)

x = 45

Takeru Kobayashi of Japan ate 53.5 hot dogs in 12 minutes to win a contest. Round you answer to the nearest hundreth.

53.5/12

=

x/1

1.) Write a proportion to find an equivalent ratio with a second quantity of 1

4.46 = x

2.) Divide on the left side to find x

<-----

<-----

A.

As you go deeper underground, the earth's temperature increases. In some places, it may increase by 25 Degrees Celcius per kilometer. What in this rate in degrees per meter?

25C/1km * 1km/1000 m

C = Degrees Celcius

0.025C/1m

The rate is 0.025C per meter

To convert the second quantity in a rate, multiply by a conversion factor with that unit in the first quantity

<-----

There are 45 faculty members.

The dwarf sea horse Hippocampus zosterae swims at a rate of 52.68 feet per hour. What is this speed in inches per minute

Step 1

Convert the speed to inches per hour

52.68ft/1h * 12in/1ft

To convert the first quanitity in a rate, multiply by a conversion factor with that unit in the second quanitity

632.16in/1h

<------

The speed is 632.16 inches per hour

Step 2

Convert this speed to inches per minute

632.16in/1h * 1h/60in

The speed is 10.536 inches per minute

To convert the second quanity in a rate, multiply by a conversion factor with that unit in the first quanitity.

<------

10.536in/1min

Solving Proportions...

5/9 = 3/w

5/9 = 3/w

5(w) = 9(3)

5w = 27

5w/5 = 27/5

w = 27/5

A.

B.

Use cross products

<--

Divide both sides by 5

<--

8/x+10 = 1/12

8/x+10 = 1/12

8(12) = 1(x + 10)

96 = x + 10

-10 -10

86 = x

<---

<---

Check it out #4

-5/2 = y/8

4a.

4b.

g+3/5 = 7/4

Example 5

A. On the map, the distance from Chicago and Waukeganis 4 mi. What is the distance on the map?

map

------

actual

---->

---->

1in

------

18 mi

1/18 = 0.625/x

x*1 = 18(0.625)

x = 11.25

The actual distance is 11.25mi

Write the scale as a fraction

Let x be the actual distance

Use cross products to solve

<----

<----

<----

Example 5 continues...

The actual distance between North Chicago and Waukegan is 4 mi. What is the distance on the map?

map

actual

---------

----->

----->

1in

-----

18mi

1/18

=

x/4

4 = 18x

4/18 = 18x/18

0.2 = x

Write the scale as a fraction

<---

Let x be the distance on the map

<---

Use cross products to solve the proportion.

<---

Since x is multiplied by 18 , divide both sides by 18 to undo the multipication.

The distance on the map is about 0.2in

Example 4

The unit rate is approximateley 4.46 hot dogs per minute.