Ratios and Proportions An introduction

Ratios express relationships 1 dozen eggs $ cups of flour 1 cake This expresses the relationship that 1 dozen eggs cost $2.50 This expresses the relationship that 2 cups of flour are needed to make 1 cake Let’s practice writing some ratios….

Complete the ratio: fill in the “?” ? This expresses the ratio that each student requires 2 pencils for class. This expresses the ratio that each magazine costs $3.00. Check your answers on the next slide…

Answers... 2 pencils 1 student $ magazine This expresses the ratio that each student requires 2 pencils for class. This expresses the ratio that each magazine costs $3.00.

Setting up proportions Proportions are used when two ratios have the same relationship. Proportions can be set up and solved to solve various math problems. If 1 cake requires 2 cups of flour, how much flour will you need to make 6 cakes? 2 cups of flour = ? 1 cake 6 cakes If a dozen eggs costs $2.50, how many dozen eggs can you buy with $10? 1 dozen eggs = ? $2.50 $10.00 Proportions have the form: A = B C D

Using proportions to solve problems: Example #1: the cake problem If 1 cake requires 2 cups of flour, how much flour will you need to make 6 cakes? Let’s first imagine what this problem is asking…

Visualize the proportion  ? 2 cups flour = ? 1 cake 6 cakes Now, solve for “?”

Solve… 2 cups flour = ? 1 cake 6 cakes (2 cups flour)(6 cakes) = ? 1 cake 12 cups flour = ? 

Example #2: Eggs If a dozen eggs costs $2.50, how many dozen eggs can you buy with $10? 1 dozen eggs = ___?___ $2.50 $10.00 (1 dozen eggs)($10.00) = ($2.50)(?) (1 dozen eggs)($10.00) = ? $ dozen eggs = ? Now, try one on your own…

Practice problem A There are 4 students in a class. Each student requires 2 pencils for a class. How many pencils does the entire class need? Sure, it’s easy… Try to follow the steps anyway… Set up the proportion Cross multiply and solve!!

Visualize the proportion  ? 2 pencils = ? 1 student 4 students Cross-multiply and solve…

Solve…  2 pencils = ? 1 student 4 students (2 pencils)(4 students) = ? 1 student 8 pencils = ?

Practice problem B A library needs to order six copies of Math! Magazine. Each copy costs three dollars. How much will the library spend on this purchase?

Visualize the proportion  $3.00 = ? 1 magazine 6 magazines $1 ?

Solve… $3.00 = ? 1 magazine 6 magazines ($3.00)(6 magazines) = ? 1 magazine $18.00 = ?  $1