RATIO AND PROPORTION
MSM 2: Unit 1
RATIOS
Ratios compare two quantities by division
 Ratios can be written as a fraction
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Ratios can be written as a comparison with “to”
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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 “:”
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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
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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
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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