1. R ATIO AND P ROPORTION MSM 2: Unit 1

2. R ATIOS Ratios compare two quantities by division Ratios can be written as a fraction ¾ of the students got an A on the quiz Ratios can be written as a comparison with “to” The ratio of girls to boys is 3 to 4. Ratios can be written with a “:” The ratio of girls to boys is 3:4

3. E XAMPLE P RACTICE Write the ratio of red hearts to blue clouds in 3 ways:

4. E XAMPLE P RACTICE Write the ratio of red hearts to blue clouds in 3 ways: Answer: 4/2, 4:2, 4 to 2

5. E QUIVALENT R ATIOS Compare ✔✔ to  (in order) 2/52:52 to 50.4 Your turn: 1. Compare  to ΔΔΔ 2. Compare ♯♯♯ to ♪♪♪♪♪♪♪♪

6. E QUIVALENT R ATIOS Compare ✔✔ to  (in order) 2/52:52 to 50.4 Your turn: 1. Compare  to ΔΔΔ 5/35:35 to 31.67 2. Compare ♯♯♯ to ♪♪♪♪♪♪♪♪ 3/83:83 to 80.375

7. R ATIOS A S F RACTIONS IN S IMPLEST F ORM 1. 16/202. 34:403. 27” to 24” 4. 90/155. 12:86. 4 feet to 18 in 7. 33/778. 16: 49. 45 min to 3 hours

8. R ATIOS A S F RACTIONS IN S IMPLEST F ORM 1.16/20 4/5 2.34:40 34/40 = 17/20 3.27” to 24” 27/24 = 9/8 4.90/15 6/1 (keep the 1 in the denominator) 5.12:8 3/2 6.4 feet to 18 in 48”/18” = 8/3 7.33/77 3/7 8.16: 4 16/4 = 4/1 9.45 min to 3 hours 45 min/180 min = 9/36 = 1/4

9. T ELL WHETHER THE RATIOS ARE EQUIVALENT BY S IMPLIFYING : 10. 7 to 10 and 35/5011. 64/80 and 20:25 12. 6:3 and 8:413. 42:49 and 54 to 63 14. 15/5 and 90 to 3615. 18 to 42 and 20:44

10. T ELL WHETHER THE RATIOS ARE EQUIVALENT BY S IMPLIFYING : 10. 7 to 10 and 35/50 yes 7/10 35/50 = 7/10 11.64/80 and 20:25 yes 64/80 = 8/10 = 4/5 20/25 = 4/5 12. 6:3 and 8:4 yes 6/3 = 2/1 8/4 = 2/1 13. 42:49 and 54 to 63 42/49 = 6/7 64/63 = 6/7 14. 15/5 and 90 to 36 no 15/5 = 3/1 90/36 = 5/2 15. 18 to 42 and 20:44 no 18/42 = 3/7 20/44= 5/11

11. A PPLICATION There are 20 chaperones for 325 stduents going on the 6 th grade field trip. Does this ratio of parents to students meet the 1:15 requirement by the county?

12. A PPLICATION There are 20 chaperones for 325 stduents going on the 6 th grade field trip. Does this ratio of parents to students meet the 1:15 requirement by the county? Actual: 20 chaperones: 235 stdunets = 0.085 Requirement: 1 chaperone: 15 stduents = 0.066 0.085 ≥ 0.066, so the ratio meets the requirement!

13. A PPLICATION Write a ratio to compare the number of consonants to vowels in the word MATHEMATICS. Express the ratio as a decimal.

14. A PPLICATION Write a ratio to compare the number of consonants to vowels in the word MATHEMATICS. Express the ratio as a decimal. C : V = 7/4 = 1.75

15. T HE G OLDEN R ATIO The Golden Ratio is the comparison of two numbers in which the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The Golden Ratio is Φ or 1.618.

16. M ATH AND B EAUTY The Golden Ratio is a proportion that is seen all over the natural world. In humans the “perfect” proportion of the distance from foot to navel: navel to head is the Golden ratio. Try it! 1. With a partner, measure the distance from a) foot to navel ___________________ cm and b) navel to head ____________________cm 2. Find the ratio (in a decimal) of a:b