Lesson 4-1: Rational Number Equivalents: Fifths, Thirds, Tenths, Elevenths and Ninths.
1/3 = .33333…
1/5=.2
2/3= .6666…
3/5=.6
1)
4
5
2)
2
5)
2
1
5
9
11
8)
5
11)
4
2
9
5
11
14)
5
17)
5
1
11
2
3
20)
1
23)
4
1
9
2
3
26)
1
29)
2
3
5
4
5
32)
2
35)
3
8
10
1/10=.1
2/9= .22222….
3/11 = .272727…
2/10 =.2
7/9 = .7777…
6/11= .545454…
1
10
3)
3
3
5
10
6)
1
1
3
4
3
9
1
3
9)
1
3
1
10
3
9
10
12)
4
7
9
5
9
11
15)
1
2
3
5
4
11
18)
3
5
10
5
5
11
21)
3
7
10
4
1
9
24)
2
4
5
2
4
5
27)
5
4
11
4
5
9
30)
4
6
9
3
5
10
33)
2
1
5
2
1
5
36)
1
1
3
0.80
0.09
4)
7)
0.20
0.45
0.10
10)
13)
0.50
0.70
0.33
16)
19)
0.33
0.33
0.82
22)
25)
0.45
0.67
0.90
28)
31)
0.22
0.56
0.11
34)
0.80
0.80
0.67
0.36
0.20
0.80
0.11
0.50
0.67
0.33
0.60
0.80
0.20
0.36
0.67
0.82
0.78
0.10
0.50
Lesson 4-2: Rational Number Equivalents: Fifths, Thirds, Tenths, Elevenths and Ninths
Percents
1/3 ≈33.3%
2/3≈66.6%
1)
2
1/5= 20%
1/10= 10%
3/5= 60%
2/10 = 20%
4
5
2)
5
2/9 ≈22.2%
3/11 ≈ 27.2%
7/9 ≈77.8%
6/11 ≈ 54.5%
6
11
3)
3
5
10
80.0%
77.8%
4)
5)
4
8
9
1
9
8)
4
7)
6)
5
6
11
8
11
9)
5
4
8
9
1
1
3
88.9%
33.3%
54.5%
10)
1
11
11)
5
14)
1
1
3
17)
4
7
9
20)
3
6
10
13)
4
7
9
12)
1
2
3
4
6
9
15)
2
2
5
5
7
11
18)
1
2
3
2
1
5
21)
2
3
5
50.0%
60.0%
72.7%
16)
19)
54.5%
88.9%
11.1%
22)
2
3
23)
1
9
10
26)
3
29)
1
1
3
32)
4
2
9
25)
1
1
3
24)
3
4
10
5
1
11
27)
5
6
11
3
6
10
30)
3
7
10
5
9
11
33)
2
3
5
20.0%
40.0%
77.8%
28)
31)
9.1%
60.0%
33.3%
34)
2
3
5
35)
1
2
3
36)
1
2
3
40.0%
60.0%
90.0%
54.5%
66.7%
22.2%
66.7%
81.8%
70.0%
33.3%
9.1%
60.0%
66.7%
63.6%
60.0%
66.7%
66.7%
66.7%
33.3%
Lesson 4-3: Rational Number Equivalents: Twentieths, Twenty-Fifths and 5oths
1/20 = .05
1/25 = .04
1/50 = .02
9/20 = .45
10/25 =.40
12/50 = .24
13/20 =.65
16/25 = .64
33/50 = .66
1)
12
20
2)
1
5)
4
16
50
29
50
8)
3
11)
2
17
25
14)
1
8
20
5
20
3)
1
6)
2
19
25
3
20
9)
1
12)
1
9
20
15)
2
2
25
1
13
20
4
41
50
2
17
25
3
34
50
1
17
20
0.76
0.85
4)
7)
0.65
0.68
0.6
10)
13)
0.52
0.58
0.15
16)
47
50
17)
4
20)
3
30
50
22)
1
8
20
17
25
22)
2
22)
3
48
50
19)
10
20
18)
1
21)
2
12
25
22)
3
12
50
17
25
22)
2
22)
2
13
25
2
9
25
2
5
25
3
8
50
1
18
20
3
25
50
0.68
0.82
0.08
22)
22)
0.24
0.94
0.36
22)
0.5
0.48
0.6
0.2
0.45
0.5
0.32
0.25
0.4
0.68
0.68
0.4
0.68
0.96
0.16
0.9
Lesson 4-4: Rational Number Equivalents: Reducing
1)
4
4400
5000
100
50
2)
6
20
30
10
3
3)
7
10
50
10
0.20
5
66.7%
4)
3
3700
5000
100
50
5)
4
240
500
10
50
6)
6
20
30
10
0.80
3
0.88
7)
47000
4 50000
1000
50
8)
2
1600
2500
100
25
9)
3
4400
5000
100
50
0.05
0.27
10)
5
30
110
10
11
11)
1
1000
20000
1000
20
12)
7
4000
5000
1000
5
0.70
0.94
13)
7
40
50
10
5
14)
6
2000
3000
1000
3
15)
2
2200
2500
100
25
0.80
0.92
16)
3000
5 11000
1000
11
17)
3
20000
50000
1000
50
18)
1
10
200
10
0.67
20
40.0%
19)
9000
5 11000
1000
11
20)
4
350
500
10
50
21)
1
14000
20000
1000
20
0.45
80.0%
22)
7
3000
5000
1000
5
23)
7
40
50
10
5
24)
4
460
500
10
0.82
50
0.60
25)
4
210
500
10
50
26)
4
2000
50000
1000
50
27)
6
2000
3000
1000
3
4.0%
0.42
28)
6
100
300
100
3
29)
3
260
500
10
50
30)
1
9000
20000
1000
20
52.0%
0.33
70.0%
64.0%
0.88
66.7%
0.27
48.0%
0.74
5.0%
0.88
0.67
Lesson 4-5: Rational Number Equivalents: Test Application
Percent Problems
1) If there are 9,000 people living in small town, and 5,000 of the people emigrated to the town, what percent of the people in
the town is this?
2) There are 500 trees at the park, and 120 of the trees are pine trees. What percent of the trees are pine trees?
3) Out of 1,100 ninth-graders only 300 will complete a four-year university program. How many students is this?
4) If there are 2,000 fish at the Long Beach Aquarium, and 1,300 of them are fish found off the coast of California, what
percent of the fish at the aquarium is this?
5) There are 3,000 Wallmart locations throughout the southwestern United States, and 2,000 of them are in California and
Nevada. What percent of the Wallmarts is this?
6) Out of 5,000 art contestants, only 400 will go on to the finals. What is the percent chance an art contestant will be chosen
for the finals?
7) 2500 people went into a local Petco, and only 900 of them purchased something. What percent of the people that go into a
Petco end up buying something?
8) Out of the 2,000 computers that were reported to Intel Corp. of having bad processors, only 600 actually needed their
processors replaced. What percent of the computers had bad processors?
9) 90 people came to the doctor’s office last Friday and 20 of them had the flu. What percent of the doctor’s patients had the
flu?
10) There were 500 people that attended the local high schools music festival. There were 200 parents, and the rest were
students. What percent of the people that attended were parents?
11) Out of 1,000 dogs at the kennel, only 200 found homes. What percent of the dogs at the kennel did not find homes?
12) Out of the 200 passengers on an airplane, 170 had a connecting flight. How passengers did not have a connecting flight?
13) Out of 5,000 car accidents that occurred in Los Angeles last year, 1200 involved elderly people. What percent of the
accidents involved people that weren’t elderly?
14) To win a game you must randomly select a golden ball out of a giant bucket. If there are 1,100 balls in the bucket and only
600 of them are gold, what is the percent chance you will not win?
8%
15%
18.2%
24%
27.3%
30%
36%
40%
45.5%
55.5%
65%
66.7%
76%
80%
Lesson 4-6a: Rounding to the nearest denominator to approximate equivalents
50ths
1)
7
3)
49
2)
30
30
62.5%
0.60
96.0%
0.14
0.95
0.05
0.59
0.37
0.83
0.17
0.78
0.25
0.29
59.6%
0.45
98.0%
0.58
0.10
0.59
0.82
0.57
0.12
0.19
0.96
48
4)
50
48
50
20ths
5)
10
6)
17
7)
20
1
20
8)
21
7
19
25ths
9)
4
11)
23
10)
18
6
24
12)
23
19
23
50ths
13)
14
14)
49
15)
22
28
47
16)
49
50
51
20ths
17)
13
18)
22
19)
2
14
17
20)
20
11
19
25ths
21)
13
22)
23
23)
5
27
3
26
24)
23
24
Lesson 4-6b: Rounding to the nearest denominator to approximate equivalents
1)
16.0%
2
16
24
66.7%
2
4
25
78.8%
1
7
22
41
52
31.8%
4
10
27
37.0%
2
91.8%
3
34
51
45
49
23.5%
3
16
23
59.1%
2
69.6%
1
13
22
66.7%
4
12
51
14
25
64.6%
2
26.5%
3
13
49
78.0%
3
19
52
36.5%
4
39
50
31
48
56.0%
4
2)
3)
4)
5)
11)
12)
13)
14)
15)
21)
22)
23)
24)
25)
6)
78.0%
1
13
21
5.0%
1
12
18
14.8%
2
4
27
1
20
61.9%
1
39
50
66.7%
3
60.9%
4
45
48
7
27
76.5%
2
14
23
84.0%
2
93.8%
3
39
51
25.9%
4
42
50
21
22
32.0%
1
92.3%
2
14
26
95.5%
2
8
25
75.0%
2
24
26
15
20
53.8%
1
7)
8)
9)
10)
16)
17)
18)
19)
20)
26)
27)
28)
29)
30)