1. P ROPORTIONS AND R ATIOS EQ: How can finding equivalent ratios help us solve proportions?

2. W HAT IS A R ATIO ? A ratio is a comparison of two numbers by division In other words, a ratio looks like a fraction Example: How many blue colored pencils do I have compared to my total number of colored pencils? Right! I have 5 to 13 or 5/13 or 5:13.

3. W HAT IS A P ROPORTION ? A proportion is an equation that says that two ratios are equivalent (equal) For example, 4/8 = 2/4 =

4. H OW CAN WE USE CROSS PRODUCTS ? For two ratios to form a proportion, their cross products must be equal. CROSS PRODUCTS Cross products in proportions are equal 3 5 __ 9 15 ___ = 4 8 __ 2 4 = 9 6 3 2 = 14 7 __ 2 1 = 8 2 =4 5 9 =3 15 16 = 16 45 = 45 6 3 =9 2 18 = 18 7 2 =14 1 14 = 14

5. H OW CAN WE USE CROSS PRODUCTS TO SOLVE A PROPORTION ? Example #1: Find the missing value 6n6n 6 ___ 5 6 __ n 18 __ = Find the cross products. 6 n = 5 18 The cross products are equal. 6 n = 90 n is multiplied by 6. 90 6 ___ = Divide both sides by 6 to undo the multiplication. n = 15

6. H OW CAN WE USE CROSS PRODUCTS TO SOLVE A PROPORTION ? Example #2: Find the missing value. 5n5n 5 ___ 3 5 __ n 15 __ = Find the cross products. 5 n = 3 15 The cross products are equal. 5 n = 45 n is multiplied by 5. 45 5 ___ = Divide both sides by 5 to undo the multiplication. n = 9

7. O N Y OUR O WN : Find the missing value. 5 7 __ 25 m __ =

8. H OW TO SOLVE PROBLEMS USING PROPORTIONS ? Out of 32 students, 24 prefer dogs as pets. Based on these results, how many of the 500 students in the school prefer dogs as pets? 32 s 32 ___ 24 32 __ s 500 __ = 32 s = 24 500 32 s = 12,000 12,000 32 ______ = s = 375 Prefer dogs Total students in classTotal students in school Prefer dogs So, 375 out of 500 students prefer to have a dog as a pet.

9. O N Y OUR O WN : At West High Middle School, the teacher to student ratio if 3 to 78. If there are 468 students enrolled at the school, how many teachers are there at the school?

10. O N Y OUR O WN : Barbara’s goal is to practice piano 20 minutes for every 5 minutes of lesson she takes. If she takes a 20 minute piano lesson this week, how many minutes should she practice?

11. TOD: On a sheet of paper answer the following: In your own words, explain how you would use cross products to find the missing value in a proportion.