Ratios and Proportions By Ms. Pearce

Instructions You can follow along with this tutorial at your own pace. Please read and follow all directions carefully. Please attempt all “You Try!” exercises in your spiral notebook. These will be checked for completeness at the end of the unit. All typed assignments should be completed in Microsoft Word and submitted to me through your Schoolloop email.

Lesson 1: Ratios and Rates

Ratio A comparison of two numbers Can be written three ways: As a fraction - 4/7 Using words – 4 to 7, 4 out of 7 Using a colon – 4:7

Rate A ratio of two different measurements with different units $10 5 lb

Unit Rate A rate that has a denominator of 1. 65 mi 1 hr 65 miles per hour (per means “for each”)

Writing Ratios in Three Ways Click on the link below to watch a video on how to write ratios three different ways: http://www.phschool.com/atschool/academy123/english/academy123_content/wl-book-demo/ph-053s.html

Now You Try! Write the following ratios in three ways. Simplify if possible. 1. 25 baskets in 30 attempts 2. 75 points scored in 5 games (Click when you are ready to see the answers)

Now You Try! Write the following ratios in three ways. Simplify if possible. 1. 25 baskets in 30 attempts 2. 75 points scored in 5 games 25/30 = 5 baskets/6 attempts 5 baskets to 6 attempts 5 baskets:6 attempts 75/5 = 15 points/1 game 15 points to 1 game 15 points:1 game

Now You Try! Find a common unit of measure. Then write as a ratio in three ways. Simplify. 3. 4. 5. Which of the first four examples is a “Unit Rate?”

Now You Try! Find a common unit of measure. Then write as a ratio in three ways. Simplify. 3. 4. 5. Which of the first four examples is a “Unit Rate?” #2 because it has different units and a denominator of 1.

Word Problem A package of cheddar cheese contains 15 servings and has a total of 147 grams of fat. Find the unit rate of grams of fat per serving.

Word Problem A package of cheddar cheese contains 15 servings and has a total of 147 grams of fat. Find the unit rate of grams of fat per serving. To find the unit rate, divide the numerator and the denominator by the denominator.

Closure A ratio compares two quantities by division. A rate is a ratio that compares two quantities that have different units. A unit rate is a rate that has a denominator of 1.

Informal Evaluation Complete the Quia Quiz Game at the following website so see how well you understand rates and unit rates: http://www.quia.com/cb/158527.html

Lesson 2: Proportions

Introduction Click on the link below: http://www.arcademicskillbuilders.com/games/dirt-bike-proportions/dirt-bike-proportions.html Use what you already know about ratios and proportions to compete in proportion dirt bike racing!

Proportions and Cross-Products Proportion - An equation that shows 2 ratios are equal. Cross-Products – Used to tell if two ratios make a proportion. Cross-products are also used to find a missing value in a proportion. 2 x 2 = 4 1 x 4 = 4

Solving a Proportion Step 1: Use Cross Products Step 2: Multiply Step 3: Divide Step 4: Solve

You Try!

You Try!

Solving Problems Comparing Two Quantities You can use proportions to solve problems comparing two quantities by following these steps: Write a ratio in words for what is being compared. Set up a proportion with the given information. Solve the proportion.

You Try! Swimming goggles cost $84.36 for 12. At this rate, how much will new goggles for 17 members of a swim team cost?

You Try! Swimming goggles cost $84.36 for 12. At this rate, how much will new goggles for 17 members of a swim team cost?

Closure A proportion is a statement that two ratios are equal. You can solve a proportion with a variable in it by setting the cross products equal to each other and solving the equation.

Informal Assessment Solve each proportion in your notebook. Then type your answers into a Microsoft Word document and submit to me through Schoolloop email.

THE END!