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RATIO AND PROPORTION MSM 2: Unit 1 RATIOS Ratios compare two quantities by division Ratios can be written as a fraction Ratios can be written as a comparison with “to” ¾ of the students got an A on the quiz 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 EXAMPLE PRACTICE Write the ratio of red hearts to blue clouds in 3 ways: EXAMPLE PRACTICE Write the ratio of red hearts to blue clouds in 3 ways: Answer: 4/2, 4:2, 4 to 2 EQUIVALENT RATIOS Compare ✔✔ to (in order) 2/5 2:5 2 to 5 Your turn: 1. Compare to ΔΔΔ 2. Compare ♯♯♯ to ♪♪♪♪♪♪♪♪ 0.4 EQUIVALENT RATIOS Compare ✔✔ to (in order) 2/5 2:5 2 to 5 Your turn: 1. Compare to ΔΔΔ 5/3 5:3 5 to 3 1.67 2. Compare ♯♯♯ to ♪♪♪♪♪♪♪♪ 3/8 3:8 3 to 8 0.375 0.4 RATIOS AS FRACTIONS IN SIMPLEST FORM 1. 16/20 2. 34:40 3. 27” to 24” 4. 90/15 5. 12:8 6. 4 feet to 18 in 7. 33/77 8. 16: 4 9. 45 min to 3 hours RATIOS AS FRACTIONS IN SIMPLEST FORM 1. 16/20 2. 34:40 3. 27” to 24” 4/5 34/40 = 17/20 27/24 = 9/8 4. 90/15 5. 12:8 6. 4 feet to 18 in 6/1 (keep the 1 in the denominator) 3/2 48”/18” = 8/3 7. 33/77 8. 16: 4 9. 45 min to 3 hours 3/7 16/4 = 4/1 45 min/180 min = 9/36 = 1/4 TELL WHETHER THE RATIOS ARE EQUIVALENT BY SIMPLIFYING: 10. 7 to 10 and 35/50 11. 64/80 and 20:25 12. 6:3 and 8:4 13. 42:49 54 to 63 14. 15/5 and 90 to 36 15. 18 to 42 and and 20:44 TELL WHETHER THE RATIOS ARE EQUIVALENT BY SIMPLIFYING: 10. 7 to 10 and 35/50 yes 11.64/80 and 20:25 yes 7/10 35/50 = 7/10 64/80 = 8/10 = 4/5 20/25 = 4/5 12. 6:3 and 8:4 yes 13. 42:49 6/3 = 2/1 8/4 = 2/1 42/49 = 6/7 64/63 = 6/7 14. 15/5 and 90 to 36 no 15. 18 to 42 and 15/5 = 3/1 90/36 = 5/2 18/42 = 3/7 20/44= 5/11 and 54 to 63 20:44 no APPLICATION There are 20 chaperones for 325 stduents going on the 6th grade field trip. Does this ratio of parents to students meet the 1:15 requirement by the county? APPLICATION There are 20 chaperones for 325 stduents going on the 6th 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! APPLICATION Write a ratio to compare the number of consonants to vowels in the word MATHEMATICS. Express the ratio as a decimal. APPLICATION 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 THE GOLDEN RATIO 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. MATH AND BEAUTY 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