HONORS GEOMETRY 7.1. Ratios and Proportions

Schedule: Tuesday: Ratio and Proportions Wednesday: Similar Polygons Thursday + Friday: Similar Triangles Monday: MLK Day (No school) Tuesday: Review for Quiz Wednesday: Quiz Thursday + Friday: Midyear Review Midyear: Tuesday morning exam!

Ratio A comparison of two quantities using division Can we written three different ways: 1. a to b 2. a : b 3. a/b * Ratios must be in the most reduced form- meaning don’t give me 2:4, give me 1:2

Extended Ratio Comparison of three or more quantities using division Two different ways to write it: 1. a:b:c 2. a to b to c

Example One: A baseball player’s average is the ratio of the number of base hits to the number of at-bats, not including walks. Minnesota Twins’ Joe Mauer has the highest batting average in Major League Baseball in If he had 521 official at bats and 181 hits, find his batting average.

Example Two: In Logan’s high school there are 190 teachers and 2650 students, what is the approximate student-teacher ratio at her school?

Example Three: A tree is 18 inches wide and stands 2 ft tall. What is the ratio of the width of the tree to its height? **Notice: This problem is trickier because of the different units! We have feet and inches!

You Try! The number of students that participate in sports programs at Central High School is 520. The total number of students in the school is Find the athlete to student ratio to the nearest decimal place.

Example Four: Slightly Different Members of the school band are buying pots of tulips and pots of daffodils to sell at their fundraiser. They plan to buy 120 pots of flowers. The ratio of number of tulip pots : number of daffodil pots will be 2:3. How many pots of each type of flower should they buy?

Example Five: The ratio of the measures of an angle in a triangle is 3:4:5. Find the measures of the angles.

Example Six: In a triangle, the ratio of the measures of the sides is 3:3:8 and the perimeter is 392 inches. Find the length of the longest side of the triangle.

You Try! The lengths of the sides of a triangle are in the extended ratio 4 : 7 : 9. The perimeter is 60 cm. What are the lengths of the sides?

Proportion: An equation stating that two ratios are equal Note: a and d are called the extremes of the proportion Note: c and b are called the means of the proportion

Cross Products The product of the extremes (ad) and the product of the means (bc) are called cross products

Cross Product Property In a proportion, the product of the extremes equals the product of the means. **What’s the one restriction? Then ad = bc

Equivalent Proportions: The following proportions are all equivalent

Example Seven: Solve the following proportions:

Example Eight: Fernando conducted a survey of 50 students driving to school and found that 28 owned cars. If 755 students total drive to school, predict the total number of students who own cars. **Think: Part vs. Whole

Example Nine: In an experiment, students netted butterflies, recorded the number with tags on their wings, and then released them. The students netted 48 butterflies and 3 of those had tagged wings. Predict the number of butterflies that would have tagged wings if 100 butterflies were netted by the students.

You Try! Monique randomly surveyed 30 students from her class and found that 18 had a dog or a cat as a pet. If there are 522 students in the whole school who have a dog or cat as a pet, how many total students attend Monique’s school?

Practice Problems Try some on your own/in your table groups As always don’t hesitate to ask me and/or your table mates questions if you are confused. They are your greatest resource!

Exit Ticket: Out of 18 students in this class, there are 6 boys. If Ms. Stonebraker has 20 total boys in all her classes, how many students does she likely teach?