Today:Make-Up Tests?

K. Academy TopicsWarm-Up: (0 Questions)Ratios/Rates/Unit Rates

Measurement RatiosClass Work

Khan Academy Topics

1. Ratio Word Problems2. Rate Problems .53. Rates & Proportional RelationshipsTopics are due by December 20 for on-line and Alt.Khan.**Waaaaay too many people have a grade of zero for their homework grade (Khan), which is 20% of your overall grade.

Solving Ratio Problems

A fraction is a 'part over the whole' comparison of one number. Remember the root comes from the Latin "to break up". We are taking one number and breaking it up.

A ratio is the comparison of two different numbers. Therefore, we must solve ratio problems differently.

Class Notes Section of Notebook. please

Ratios, Proportions, & Rates

A Proportion is an equation that two ratios are equal. To determine if ratios are equal, cross-multiply and check for equality. 2/5 and 6/15 are proportional ratios.

We have used the Percent Proportion to solve percent problems, but there are other problems which do not involve percents.

A Ratio is a comparison of two numbers by division. Ratios can be expressed by: 4:3, or 4 to 3, or 4/3.

A Rate is the comparison (ratio) of two different units of measure. Ex: miles per hour, gallons an hour, dollars a pound

Solving Proportions

Example 1: Ben runs 4 miles in 45 minutes. If he only has 30 minutes, how far can he run? Set up a proportion and solve: 4 (miles) = x (miles) 45 (min.) 30 (min.)

Example 2: Jill can jump rope 420 times in 2.5 minutes. At this rate, how many can she do in 30 minutes? Set up a proportion and solve: 402(jumps) = x (jumps) 2.5 (min.) 30 (min.)

Proportions and Similar Figures.

You can use proportions to find dimensions of objects that are difficult to measure directly…

In the Figure below, ABC ~ (is similar) DFE. Find DE.

C

A

21 cm18 cm

15 cmB

x

D F10 cm

ESet up the proportion: 15 = 21 10 x

Example 1: Writing Ratios in Simplest Form

Write the ratio 15 bikes to 9 skateboards in simplest form.

159

53

The ratio of bikes to skateboards is , 5:3, or 5 to 3.

=

15 ÷ 39 ÷ 3

Write the ratio as a fraction.

= = Simplify.

53

bikesskateboards

Example 1: Using Ratios

The ratio of the number of bones in a human’s ears to the number of bones in the skull is 3:11. There are 22 bones in the skull. How many bones are in the ears?

Write a ratio comparing bones in ears to bones in skull.

Write a proportion. Let x be the number of bones in ears.

Since x is divided by 22, multiply both sides of the equation by 22.

There are 6 bones in the ears.

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

Example 2

The team lost 12 games.

Write a ratio comparing games lost to games won.

Write a proportion. Let x be the number of games lost.

Since x is divided by 18, multiply both sides of the equation by 18.

The ratio of games lost to games won for a baseball team is 2:3. The team has played 45 games. How many games did the team lose?

Example 2A

The team lost 18 games.

Write a ratio comparing games lost to total games

Write a proportion. Let x be the number of games lost.

Solving Ratio Problems

1. Chas and Dave share 60 Magic Wizard Cards in a 2:3 ratio. How many cards does each receive?2. $1225 is shared in a 3:4 ratio. How much does each person receive?

3. The ratio of Freshmen to Seniors at MHS has been right around 5:3 for a number of years. If there are 510 freshmen, how many can we expect to graduate? (Be careful when setting up proportion)

Solving Rate Problems

Ex. 1: Darlene runs at an average of 3.25 miles per hour. How long will it take her to run 13 miles?

A rate is the comparison of two quantities measured in different units. Rate:90

miles3 hours

Read as “90 miles per 3 hours.”

Ex. 2: Simplify the following ratio: Note:*** When changing from one measure to another, always change the larger to the smaller.

Ratios must use the same unit or measure for comparison, unlike a rate which compares different units

Ratio & Rate Comparison