Number Sense – AP Book 8, Part 2: Unit 1
AP Book NS8-75
page 1
AP Book NS8-76
page 2
1.
1.
2.
a)
5
b)
2
5
0.1, 0.2, 0.3, 0.4
e)
3
5
f)
1
10
a)
8
13 ≈ 0.6154
b)
0.033 333 33
c)
1÷8
c)
0.003 333 33
a)
24 ÷ 2 = (3 × 8) ÷ 2
d)
0.525 252 52
= 3 × (8 ÷ 2)
e)
0.817 817 81
AP Book NS8-77
page 4
3 ÷ 8 = (3 × 1) ÷ 8
f)
0.817 171 71
1.
= 3 × (1 ÷ 8)
b)
0.5, 0.6, 0.7, 0.8, 0.9
a)
0.2
g)
0.926 262 62
b)
0.75; 0.7
From above:
h)
0.253 737 37
c)
0.2; 0.25
3 ÷ 8 = 3 × (1 ÷ 8)
1
=3×8
i)
7.233 333 33
d)
0.4; 0.42
j)
8.253 953 95
a)
0.700, 0.667;
2
3
b)
0.143, 0.125, 0.111;
1
8
c)
3.500, 3.333, 2.667;
10
3
From above:
1 3
3÷8 =3× 8= 8
Circle:
rd
th
the 3 and 4 decimals
3.
a)
0.5
b)
2.34
c)
5.237
d)
57.12
e)
8.162
Teacher to check long
division.
a)
0.2
b)
3 ÷ 5; 0.6
c)
4 ÷ 10; 0.4
d)
2 ÷ 4; 0.5
e)
4 ÷ 8; 0.5
f)
2.5
g)
1.75
h)
0.9
i)
0.8
j)
0.6
a)
Teacher to check
long division.
b)
Start at 0.125 and
add 0.125 each time.
c)
0.5, 0.625, 0.75,
0.875, 1
f)
4.
5.
6.
7.
8.
Teacher to check
calculator checks.
b）
85, 0.85
c)
152, 0.152
d)
68
100 = 0.68
e)
35
100 = 0.35
f)
546
1000 = 0.546
g)
444
1000 = 0.444
5 625
BONUS 10 000 = 0.5625
AnswerKeysforAPBook8.2
2.
2.
0.125, 0.25, 0.375
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d)
1÷4
d)
5.
Teacher to check
long division.
0.333 333 33
c)
4.
a)
a)
b)
3.
10.
9.
3.
0.9105
a)
0.333; 0.333 333…
b)
0.666; 0.666 666…
a)
0.166 666; 0.16
b)
0.444 444; 0.4
c)
0.090 909; 0.09
d)
0.416 666; 0.416
5
4
6 ( 0.83 ), 5 ( 0.8 ),
0.3
5
13
0.4
0.29
4.
a)
i)
ii)
0.286
iii)
0.38
0.385
Teacher to check decimal
comparisons/circles.
a)
<
b)
>
c)
>
a)
0.4, 0.42, 0.42, 0.42
b)
0.1, 0.16, 0.16, 0.16
c)
0.387, 0.387, 0.387,
0.387
d)
0.546, 0.546, 0.546,
0.546
e)
f)
9
11 = 0.81
5
36 = 0.138
3
17 ≈ 0.1765
89
121 ≈ 0.7355
b)
INVESTIGATION
A.
b)
c)
5.
6.
1 38 725
10 , 100 , 1000
These decimals will
always terminate: using
place value, they translate to decimals with one,
two, or three decimal
places respectively.
83
0.83 = 100
80
4
> 100 = 5
i)
0.57 < 0.6
ii)
0.83 > 0.8
iii)
0.6 > 0.37
B.
If a decimal terminates,
it has a finite number of
decimal places, and this
number of decimal places
gives the number of 10s
in the “power of 10”
denominator. So one
decimal place refers to
tenths (denominator 10),
two decimal places refer
to hundredths (denominator 100), and so on.
C.
a)
625
0.625 (T); 1000
Answers will vary –
teacher to check.
a)
23
45
b)
0.285
Answers may vary slightly
– teacher to check.
Answers will vary –
teacher to check.
Sample answer:
57
0.57 = 100
60
3
< 100 = 5
2
200
3 = 300
111
> 300 = 0.37
5 3 8 89 9
36 , 17 , 13 , 121 , 11
AP Book NS8-78
page 5
56
13
73 ( ≈ 0.767 ), 17 ( ≈ 0.765 )
C, D, A, B
2
7
7.
b)
0.583 (R)
a)
c)
0.461538 (R)
0.383, 0.383, 0.383,
0.383
1
2
1
3
d)
0.46 (R)
b)
e)
0.786, 0.786, 0.786,
0.786
c)
3
10
0.1764705882352941
(R)
f)
65
0.0065 (T) ; 10 000
V‐1
D.
100 = 10 × 10
=2×5×2×5
d)
3.
1000 = 10 × 100
=2 × 5 × 2 × 5 × 2 × 5
E.
Answers will vary –
teacher to check.
NOTE: Correct answers
will always terminate.
Sample answer:
11
11
2 × 2 × 5 = 20 = 0.55
F.
1.
2.
1 1 1 2 5
6, 3, 2, 3, 6
Since their numerators
all have a factor of 3 too,
the 3 “cancels out” and
each one can be reduced
to a denominator that
terminates.
b)
0.3472
c)
0.95
d)
0.593
e)
0.30
a)
3, 9, 27, 81, …
f)
0.2
b)
Yes, they repeat:
their denominators
cannot be written as
products of 2s/5s.
a)
i)
0.3
ii)
0.7
a)
b)
a)
Teacher to check
long division.
2
11 = 0.18
3
11 = 0.27
4
11 = 0.36
b)
5
11 = 0.45
6
11 = 0.54
0.8
i)
8
11 = 0.72
7 2 3 5 11
12 , 3 , 4 , 6 , 12
ii)
2 5 7
9 + 9 = 9 = 0.7
9
11 = 0.81
Teacher to check.
4 4 8
iii) 9 + 9 = 9 = 0.8
10
11 = 0.90
c)
Answers will vary –
teacher to check.
11
11 = 0.99 = 0.9
a)
i)
1
ii)
1.1
b)
1 1 1 1 5 1
12 , 6 , 4 , 3 , 12 , 2 ,
3.
iv) 1.111
2
12 = 0.16
b)
3
12 = 0.25
c)
d)
6
12 = 0.5
4.
a)
9
12 = 0.75
11
12 = 0.916
0.583
ii)
0.083
iii)
0.94
d)
i)
ii)
e)
c)
0.97
d)
0.86
e)
0.07
f)
0.04
a)
39
99 = 0.39
b)
6
9 = 0.6
c)
36
99 = 0.36
d)
51
99 = 0.51
e)
5
9 = 0.5
f)
54
99 = 0.54
a)
46
99
b)
7
99
c)
5
15
99 = 33
d)
98
99
e)
6
2
9 = 3
f)
16
48
99 = 33
a)
b)
2.
0.034
ii)
0.008
iii)
0.734
v)
AP Book NS8-81
page 8
1.
a)
7
Teacher to check.
b)
23
b)
0.17; 0.1717;
c)
5
0.171717; 0.17
d)
441
17
1
99 = 17 × 99
= 17 × 0.01
= 0.17
a)
0.25
0.075
vi) 0.423
a)
c)
3.
i)
iv) 0.046
9
0.09 × 5 = 99 × 5
= 0.45
0.001
Teacher to check
long division.
0.45; 0.4545;
45
= 99
7
12 = 0.583
1
12 = 0.083
0.38
0.454545; 0.45
iv) 0.05
b)
6.
Any fraction with an
equal numerator and
denominator = 1.
9
11
So: 9 = 11 = 1
3 7
10
1
9 + 9 = 9 = 19
i)
5.
b)
 we know that 0.9
must equal 1.
They both have an
infinite number of
decimal places – so
there’s nowhere to
start adding.
= 1 + 0.1 = 1.1
8
12 = 0.6
10
12 = 0.83
Teacher to check.
Correct prediction: 1.1
5
12 = 0.416
7
12 = 0.583
c)
iii) 1.11
1
12 = 0.083
4.
1
11 = 0.09
1 2 3
9 + 9 = 9 = 0.3
4
12 = 0.3
1.
iii)
3 6
9
Only 12 , 12 & 12
terminate: just their
denominators are
products of 2s/5s.
V‐2
AP Book NS8-80
page 7
7
11 = 0.63
Correct prediction:
c)
1
iv) 18 = 0.05
Teacher to check that
lining up is correct.
3
Once simplified, only 6
has a “2 and/or 5 product”
denominator – therefore
only it will terminate.
2.
17
iii) 18 = 0.94
Teacher to check.
AP Book NS8-79
page 6
1.
(continued)
e)
652
f)
98
99
g)
5
9
AnswerKeysforAPBook8.2
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
Number Sense – AP Book 8, Part 2: Unit 1
Number Sense – AP Book 8, Part 2: Unit 1
2.
3.
4.
5.
h)
461
999
i)
38
99
27
4
= 10 + 990
j)
61
999
27
396
= 990 + 990
a)
254.444… = 254.4
b)
266.666… = 266.6
c)
2.49191... = 2.491
d)
32.32
e)
0.0032
b)
1 27 27
99 , 99 , 990 ;
423
= 990
c)
253 253
1
999 , 999 , 9990 ;
7.
253
56
= 10 + 9990
253
55 944
= 9990 + 9990
f)
5436.136
g)
0.0341
56 197
= 9990
h)
0.007432
i)
364.324
6 247
= 5 9990
b)
0.444…; 0.00444…
c)
0.666…; 0.000666…
d)
a)
0.13, 0.143, 0.1443
b)
Teacher to check.
e)
Correct prediction:
13
10
3
90 = 90 + 90
3
1
= 9 + 90
1.
)
7
2.
16
19 = 9
g)
2 99 = 99
h)
1
3
= 9 + 9 ÷ 10
14
90
f)
0.1444… = 0.14
(
41
5
5
9 , 49 = 9 ;
i)
35
233
4 357
24 337
= 0.1 + 0.03
= 0.14
d)
a)
40; 40%
b)
49; 49%
a)
50%
b)
72%
= 1.4 ÷ 10
c)
7%
= 0.14
d)
43%
a)
70
b)
13 : 100
c)
38 : 100
d)
8 : 100
a)
60; 60%
b)
10; 10%
a)
52%
b)
39%
c)
18%
d)
2%
13
13
90 = 9 ÷ 10
4
= 1 9 ÷ 10
6.
a)
1 8 8
9 , 9 , 90 ;
1.
2.
3.
8
1
= 2 + 90
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8
45
= 90 + 90
53
= 90
4.
5.
e)
AnswerKeysforAPBook8.2
6%
49
100
g)
7
100 , 0.07
d)
3
100
h)
100
100 , 1.00
e)
100
100
a)
0.25
b)
0.75
b)
7
c)
6.
Teacher to check
drawings.
c)
0.13
d)
0.40
52
100
67
100
18
100
e)
0.07
f)
0.09
52%
67%
18%
g)
0.70
h)
0.01
a)
20, 20%
b)
3, 30, 30%
Teacher to check
colouring.
c)
7 70
10 , 100 , 70%
10%; 40%; 50; 50%
d)
23, 23%
e)
57
100 , 57%
f)
8
100 , 8%
a)
40, 30, 70, 70%
b)
60, 10, 70, 70%
c)
60, 35, 25, 25%
d)
80, 40, 40, 40%
a)
47%
b)
90%
c)
40%
a)
21%
b)
1%
c)
41%
a)
1%; 10, 10%;
25, 25%
b)
35%; 52%
7.
a)
50%
70%
c)
40%
d)
10%
e)
90%
f)
27%
g)
60%
h)
53%
i)
7%
j)
99%
a)
≈ 38%
AP Book NS8-84
page 11
b)
≈ 93%
c)
≈ 38%
1.
a)
6 squares shaded
d)
≈ 10%
b)
4 squares shaded
2.
50%; 50%
3.
a)
7 dots shaded
b)
30%
4.
= 0.1  (0.3  10)
AP Book NS8-82
page 9
42
100 , 0.42
12
b)
3.
24 337
99 900
2 9 990 = 9 990
f)
a)
AP Book NS8-83
page 10
365
5
5
90 , 4 90 = 90
0.0137
c)
6.
(continued)
5.
c)
8.
74%
9.
4.
90 are not blue
5.
a)
80, 0.80
b)
75, 0.75
c)
21, 0.21
d)
9, 0.09
e)
15
100 , 0.15
10.
7
10 are classical;
30% are jazz
AP Book NS8-85
page 12
1.
b)
80
100 = 80%
c)
15
100 = 15%
d)
32
100 = 32%
V‐3
Number Sense – AP Book 8, Part 2: Unit 1
3.
40% ordered pizza
b)
c)
4.
5.
1
4 = 25%
e)
40%
f)
70%
g)
20%
h)
85%
i)
25%
a)
0.75, 75%
b)
0.8, 80%
c)
0.4, 40%
d)
0.6, 60%
7.
1.
0.13, 13%
a)
30
3
0.30 = 100 = 10
b)
84
21
0.84 = 100 = 25
55
11
0.55 = 100 = 20
4
1
0.04 = 100 = 25
e)
90
9
0.90 = 100 = 10
a)
75%
b)
25%
c)
50%
a)
42%
b)
0.3 ≈ 0.33 = 33%
c)
0.6 ≈ 0.67 = 67%
d)
0.2 ≈ 0.22 = 22%
e)
0.83 ≈ 0.83 = 83%
f)
≈ 0.14 = 14%
AP Book NS6-86
page 13
e)
d)
6.
1
2 = 50%
d)
c)
8.
1
20
5 = 100 = 20%
2.
a)
50%
b)
25%
c)
20%
d)
50%
e)
75%
f)
50%
g)
60%
a)
3 triangles shaded
b)
6 rectangles shaded
2.
3.
4, 20, 0.20, 20%
4.
From left to right:
0%, 40%, 50%, 70%, 100%
5.
a)
b)
c)
6.
3.
d)
100%
Estimates may vary a bit
– teacher to check.
e)
50%
a)
≈ 60%
f)
75%
b)
≈ 30%
g)
10%
1
Fraction shaded: 2
7.
Estimates may vary –
teacher to check.
Estimate
Actual
10
40 = 25%
0.275
b)
25
50 = 50%
≈ 0.47
c)
60
80 = 75%
≈ 0.71
15
25 = 60%
0.583
a)
d)
15%
4
2
10 = 5
0.40
40%
6
3
10 = 5
0.60
60%
6
15
0.40
40%
23
25
0.92
92%
75
3
100 = 4
0.75
55
11
100 = 20
0.55
0.405
d)
0.674
e)
0.009
f)
6.008
a)
1.5;
1.5, 4.5
b)
35, 3.5;
4, 3.5, 14
75%
c)
2.7, 0.27;
2, 0.27, 0.54
55%
d)
62, 6.2;
5, 6.2, 31
Teacher to check decimal
fractions.
e)
17, 1.7;
8, 1.7, 13.6
b)
<
f)
c)
<
0.7, 0.07;
3, 0.07, 0.21
d)
<
5%
10
21
0.5
e)
>
10%
20
42
1
f)
<
100%
200
420
10
g)
<
h)
=
i)
>
j)
>
k)
>
l)
>
a)
0.60, 0.42, 0.73
3
 42%, 5, 0.73
c)
1
Fraction completed: 4
4
≈ 0.095
40 = 10%
f)
20
30 ≈ 67%
≈ 0.68
Answers will vary –
teacher to check.
AP Book NS8-87
page 14
1.
0.25, 0.09, 0.15
1
 0.09, 15%, 4
6.
7.
8.
a)
3
b)
0.01 × 2 000 = 20
c)
0.01 × 15 = 0.15
d)
0.01 × 60 = 0.60
a)
4
b)
6
c)
24
a)
32
b)
1
c)
6.6
d)
0.08
e)
3.15
8%
10%
10
20
40
50
15
30
60
75
2.4
4.8
9.6
12
10
20
40
50
AP Book NS8-88
page 15
20%
50%
25% 100%
100
250
125
500
1.
150
375
187.5
750
24
60
30
120
100
250
125
500
4.
a)
b)
Drama
(65% vs 60%)
Pepperoni
(45% vs 35% / 20%)
a)
0.7
b)
1.0
D
P
c)
3.5
1
4
0.25
25%
d)
21.0
e)
0.64
0.35
5.
0.5, 0.73, 0.80
1
 2, 0.73, 80%
F
35
7
100 = 20
4.
4%
Percent completed: 25%
9.
3.
2%
Percent shaded: 50%
8.
0.39
b)
c)
Percent to complete: 75%
e)
0.15
b)
35%
2.
V‐4
3
20
f)
5.06
a)
0.1
9.
a)
18
b)
4
c)
160
AnswerKeysforAPBook8.2
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
2.
(continued)
Number Sense – AP Book 8, Part 2: Unit 1
d)
10.
$9 tip
11.
a)
b)
4.
65
30% of 50 = 15;
25% of $40 = $10;
They are the same since:
40 – (25% of $40)
= $40 – $10 = $30;
$30 is the sale price.
0.3 × 50 = (30 ÷ 100) × 50
Answers may vary
slightly – teacher
to check.
$32.99 ≈ $32 so
the sale price is
approximately
75% of $32 or $24
= 50 × (30 ÷ 100)
= (50 ÷ 100) × 30
= 0.5 × 30
AP Book NS8-90
page 18
2.
b)
AP Book NS8-89
page 17
Teacher to check
Step 1 multiplication.
a)
c)
85 × 17 = 1445;
3.
a)
7.26
b)
6.72
c)
19.8
d)
30.36
e)
62.25
f)
7.2
g)
16.12
h)
15.3
a)
i)
d)
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
Yes
c)
1
2 ; half of 40 (20);
3.
4.
b)
c)
24
7
25
?
7
?
25 = 100
d)
3
c)
21
3
6 is 4 of 8
d)
28
e)
9
5.
b)
? : 80 = 25 : 100,
25
?
80 = 100
2.
3.
f)
12
g)
65
h)
40
a)
20
b)
30
c)
35
d)
2
a)
12
b)
2
3 , 10
c)
2
5 , 18
d)
5
6 , 25
e)
f)
?
7
10 , 63
2
3 , 24
6
25
=
? 100
17
?
17
10 = 100
10
 1.7
d)
?
50
17
?
17
50 = 100
 8.5
80%
5.
25 × 4 = 100 so you just
multiply 3 by 4 to get x.
6.
a)
3
1
x
15 = 5 = 100
 20%
b)
6
1
x
24 = 4 = 100
 25%
15
b)
20 : 30 = ? : 3,
20
?
30 = 3
c)
Teacher to check arrows.
3
4 are shaded
25
 24
AP Book NS8-91
page 20
a)
?
30
g)
1.
6
g)
?
52
18 = 100
? : 16 = 3 : 4,
?
3
16 = 4
b)
f)
52
?
6
8 = 4
4
?
20 = 100
e)
18
18 : 20 = 9 : 10,
18
9
20 = 10
?
12
?
15 : 20 = 3 : 4,
3
15
20 = 4
20
3
12
=
? 100
f)
a)
4
6
5 : 10 = 1 : 2
2:8 = 1:4
a)
?
6
24 = 100
?
6
8 are shaded
F
20
90
?
%
7
20
=
? 100
4
4
12 are shaded
3
24
W
F
e)
c)
Sample explanation:
AnswerKeysforAPBook8.2
?
?
P
%
1
5 is 2 of 10
6 : 10 = 3 : 5
b)
Yes, it is reasonable.
14 ≈ 40 ÷ 3, just as
35% ≈ 100% ÷ 3
7
W
4
?
90 = 100
b)
40 × 35 = 1400
b)
c)
6:8 = 3:4
2.
25% of 40 = 10
10% of 40 = 4
 35% of 40 is
10 + 4 = 14
b)
P
4.
 20%
d)
4 : 12 = 1 : 3
1400 ÷ 100 = 14
35% of 40 is 14
ii)
6.
18 : ? = 3 : 100
3
18
= 100
?
1
2 are shaded
1
4 is 3 of 12
1445 ÷ 100 = 14.45;
17% of 85 is 14.45
2.
5
10 are shaded
d)
9 : 12 = ? : 100
9
?
12 = 100
1
3 are shaded
34 × 23 = 782;
782 ÷ 100 = 7.82;
23% of 34 is 7.82
b)
c)
50% of 30 = 15;
Sample answer:
1.
(continued)
c)
12
4
2
x
30 = 10 = 5 = 100
 40%
7.
b)
c)
P
?
45
W
48
60
d)
?
15
8.
a)
15
b)
36
c)
75%
9.
d)
9.6
a)
20
b)
18
c)
20
d)
25%
%
75
?
64
F
75
?
48 = 100
?
3
48 = 4
?
45
60 = 100
?
3
4 = 100
?
64
15 = 100
?
3.2
15 = 5
V‐5
10.
16% are blue;
f)
8x = 4 × 52
84% are not blue
g)
20 × 25 = 12x
11.
81 students
h)
12 × 10 = 3x
12.
20 students
a)
x = 4.5
b)
x=6
AP Book NS8-92
page 22
c)
x=8
d)
x = 0.63
1.
e)
x = 0.8
a)
90
x
100 = 6
2.
3.
4.
a)
a÷b=c
b)
a=b×c=c×b
c)
x = 11 × 3
d)
3x = 21
9
2
x = 100
1.
a)
With deal B, the price is
$1000.
100%, 25%, 125%
With deal C, the price is:
= (1000 × 1.15) × 0.85
= $977.50
b)
85 100 60 245
100 , 100 , 100 , 100 ;
0.85, 1, 0.6, 2.45;
 either A or C is the best
deal (they are equal).
AP Book NS8-93
page 25
100, 25, 25;
1, 0.25, 1.25;
85%, 100%, 60%,
245%
2.
Teacher to check.
3.
a)
365%
12 = 11x
x=7×9
x = 450
1.
g)
24 = 8x
1
1000
h)
6×7=x
5
x
8 = 100
2.
a)
0.3%, 0.003
b)
9
0.9%, 1000
c)
0.25, 25%
a)
27.3%
b)
84.8%
c)
36.9%
d)
40.5%
Estimates may vary a bit
– teacher to check.
e)
0.5%
a)
≈ 135%
f)
12.5%
b)
≈ 350%
b)
x = 40
c)
x = 2.5
d)
e)
b)
c)
x = 62.5%
a)
25%
x = 30
b)
4%
x=4
c)
25%
f)
x = 72
d)
4%
g)
x = 55
a)
≈ 21%
h)
x=9
b)
≈ 53%
b)
3×8=6×4
24 = 24 
c)
≈ 44%
d)
≈ 40%
1 × 10 = 2 × 5
10 = 10 
e)
≈ 5%
e)
2 × 12 = 3 × 8
24 = 24 
≠ ; no
b)
2 × 25 = 10 × 5;
yes
c)
9 × 100 ≠ 10 × 81;
no
d)
5 × 35 ≠ 28 × 7;
no
f)
9.
10.
3 × 20 = 4 × 15;
yes
5 × 42 = 6 × 35;
yes
a)
33.8 g
b)
44.77 m
c)
3.52 mL
d)
7.92 m
e)
888.8 min
2
13.
≈ 18 are vegans
14.
a)
40%
NOTE: Assuming
there were no ties.
15.
16.
b)
10 games
a)
120
b)
200
c)
400
a)
≈ 143
b)
≈ 231
c)
≈ 22
91 × 120 = 104 × 105;
yes
h)
14 × 48 ≠ 30 × 21;
no
17.
22 students
c)
11 × 2 = 5x
18.
a)
85%
d)
4 × 3 = 9x
b)
$1200
5x = 3 × 21
c)
$180
4.
5.
5.
140%
c)
225%
a)
100%
b)
85%
c)
625%
a)
6.
a)
110, 110%
624.2%
b)
350, 350%
Teacher to check.
c)
261, 261%
a)
1 10
h)
12.
4.
b)
b)
g） 7.7%
≈ 18%
g)
e)
3.
11.
Answers will vary –
teacher to check.
a)
e)
V‐6
x = 5.4
AP Book NS8-94
page 26
f)
d)
6.
8.
With deal A, the price is:
= (1000 × 0.85) × 1.15
= $977.50
e)
c)
5.
7.
19.
(continued)
7.
a)
7
35
200 = 40
b)
7
1000
b)
24
c)
8
64
1000 = 125
c)
3 25
d)
1
4
10 000 = 2500
d)
15 20
e)
33.3
33.3  3
=
100
100  3
e)
7 20
100 1
= 300 = 3
f)
g)
3
3
2
1
17
9.
Percent
Mixed #
12.5 × 2
12.5
100 = 100 × 2
920%
25
1
= 200 = 8
9 100
232%
2 100
190%
1 100
535%
5 100
340%
3 100
3.125 × 8
3.125
100 = 100 × 8
25
1
= 800 = 32
h)
8.
66.6
66.6  3
=
100
100  3
200 2
= 300 = 3
20
32
90
35
40
Decimal
9.2 = 9.20
2.32
1.90
5.35
3.4 = 3.40
AnswerKeysforAPBook8.2
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
Number Sense – AP Book 8, Part 2: Unit 1
Number Sense – AP Book 8, Part 2: Unit 1
9.
18.
continued
76
176%
1 100
108%
1 100
10.
11.
12.
13.
14.
8
1.76
1.08
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
a)
150%
b)
≈ 193%
c)
850%
≈ 438%
d)
≈ 186%
b)
≈ 593%
e)
≈ 293%
f)
≈ 5 391%
c)
≈ 501%
≈ 300%
a)
50
1
3.50 = 3 100 = 3 2
AP Book NS8-95
page 28
b)
40
2
5.40 = 5 100 = 5 5
1.
c)
75
3
2.75 = 2 100 = 2 4
d)
60
3
3.60 = 3 100 = 3 5
e)
15
3
5.15 = 5 100 = 5 20
Sample answers:
a)
250%
a)
b)
375%
b)
$5.20
c)
830%
c)
$8.74
d)
120%
d)
$10.73
e)
2 015%
3.
f)
1 736%
4.
a)
342%
b)
0.3 ≈ 3.33 = 333%
c)
4.6 ≈ 4.67 = 467%
d)
1.2 ≈ 1.22 = 122%
e)
≈ 2.14 = 214%
a)
1.5, 1.73, 1.8
b)
1.6, 1.57, 1.62
6
 1.62, 1 10 , 157%
c)
6.25, 6.09, 6.15
1
 6 4 , 615%, 6.09
a)
60
b)
125
c)
6.6
d)
6.6
16.
50, 500
17.
a)
400
c)
8
d)
6
AnswerKeysforAPBook8.2
1.
b
g
c
a)
7
6
13
b)
5
9
14
a)
37%
c)
18
22
40
b)
59%
d)
12
15
27
c)
71%
a)
6
6, 15
9
9, 15
15
b)
9
9, 17
8
8, 17
3.
R
Fb
Fg
b)
1:5
1
6
5
6
c)
11 : 9
11
20
9
20
55
45
d)
3:7
3
10
7
10
30
70
e) 12 : 13
12
25
13
25
48
52
f)
32
50
18
50
64
36
23
g) 23 : 27
50
27
50
46
54
9
20
55
45
19
81
2.
Answers will vary based
on where you live.
5.
6.
7.
g
b
a)
12
8
b)
18
24
c)
9
6
d)
9
15
e)
15
10
f)
21
7
a)
A: 24 vs 16 girls
b)
B: 12 vs 8 girls
4
Ron: 7 = $20
3
Ella: 7 = $15
8.
F
%
17
Soccer
1
5
20 0.20 4
%g
Swimming
2
5
40 0.40 8
Baseball
1
4
25 0.25 5
Gymnastics
3
20
15 0.15 3
Ontario’s sales tax is 13%.
$1.95
43% voted for Yen.
F
%
$
Drywall
11
20
55%
$220
Paint
3
20
15%
$60
3
10
30%
Wallpaper
5.
$120
He still has 80% to raise.
6.
Discount
($)
Sale Price
Shoes
$12.48
$37.44
CD
$4.47
$10.43
7.
Clare saved $533.33.
8.
F
Chair
1
4
Table
91
200
Sofa
59
200
500
b)
Erik now has
580 Canadian stamps.
580
29
They make up 1700 = 85
AP Book NS8-96
page 29
d)
2.
9.
or ≈ 34% of his collection.
a)
1
 180%, 1.73, 1 2
15.
Teacher to check
closeness of estimates.
(continued)
32 : 18
h)
11 : 9
11
20
i)
19 : 81
19 81
100 100
4.
16.6 83.3
Fb
Fg
b)
40
1
5
4
5
8
32
c)
24
3
4
1
4
18
6
38
5
19
14
19
10
25%
d)
Nb
AP Book NS8-97
page 31
2.
Ng
28
N
To find the number who
chose swimming, you can
simply double the number
who chose soccer.
1.
Ns
%
45.5%
%b
D
3.
a)
10
b)
21
c)
55
a)
8
b)
20
c)
25
d)
45
a)
3
5
b)
$40
4.
800 students
5.
a)
1
12
b)
7
12
c)
72
29.5%
6.
1250 stamps
7.
500 lights in total
V‐7
Number Sense – AP Book 8, Part 2: Unit 1
AP Book NS8-98
page 32
8.
$147.84; 23.2%
f)
2h
9.
It’s true that:
g)
$0.21
10% of original population
h)
16 m
b)
$6
c)
$35
5.
≈ 318.2 s
d)
8m
6.
160 ÷ 12 = 13.3
e)
$5
a)
80 × 0.2 = $16;
80 – 16 = $64
+ 15% of original population
b)
80 × 0.8 = $64
25% of original population
2.
$15
but…
3.
No, you need $28.50.
10% of original population
4.
b)
66.6
c)
30
5.
$20.18
6.
25%
7.
a)
200
b)
220
8.
$6.37
9.
9.5%
10.
b)
6%
c)
24%
11.
nd
+ 15% of increased 2 yr pop’n
> 25% of original population
1.
a)
b)
2.
a)
He sold 8%.
Mayah: $3.70
Tegan: $5.55
Matias: $5.55
2.
a)
Dillon: 2.3
c)
Choices will vary –
accept all justified
answers.
Melissa: 2.5
3.
4.
5.
7.
V‐8
$8
unit price:
$1.67 vs $2
 1 offer is better.
st
c)
1:7:4
unit price:
$18.26 vs $15.40
i)
3:5
2
ii)
5:4
iii)
4:3
iv)
5:3
v)
4:5
vi)
3:4
c)
9
nd
4.
Peaches: $16.20
1.
a)
b)
15 km rowed / 1 h
c)
b)
No, its density is
3
1.003 g/cm .
1 cup of flour :
20 cups of flour
d)
7 km / 30 L of gas
c)
400 mL of milk
e)
17 mL of ginger ale :
3 mL of orange juice
a)
12
b)
50
9 , 250
c)
39
2 , 19.5
d)
60
21 , 7
e)
72
32 , 9
f)
54
6 ,2
a)
72 km
3
34 545.45 s ≈ 9.6 h
a)
21 mL
b)
7 mL
c)
210 mL
a)
2.5 h
e)
green
b)
7h
a)
6 : 21
c)
14.5 h
b)
21 : 15
c)
6 : 15
a)
11
20
d)
15 : 21
e)
15 : 6
1.
b)
429
f)
21 : 6
2.
3.
a)
5 cm
b)
0.25 m
b)
72 days
≈ 1166.67 m
1
2 cup
a)
4:8
c)
3.2 km
c)
62.5%
b)
16, 9
d)
4.5 L
d)
b)
$738.75
c)
3, 15
e)
6.9 g
a)
4
35
d)
7, 8
f)
4 min
e)
11, 30
g)
70 h
f)
72, 6
h)
5 days
c)
780
a)
$2 625
Overestimating;
At a 15% rate (which is
already quite high), the
tax on $20 is $3. So, in
Ontario (13%), the tax
should be less than $3.
In fact, it’s almost $4, so
the total isn’t reasonable.
$4 840
4.
2.
AP Book NS8-101
page 35
1.
6 km walked / 1 h
1.224 g/cm
7.5 min
8.
AP Book NS8-103
page 37
a)
5.
7.
Grapes: $8.40
Watermelon: $9.00
offer is better.
6.
red = 15
green = 25
7.
TOTAL: $33.60
4:2:8
AP Book NS8-102
page 36
b)
6.
f)
 1 offer is better.
blue = 20
3.
 he will need 14 cans
of paint.
st
4 : 2 : 1,
David: 572.5 km
Jack: 1900 km
a)
b)
280 km
Felicity: 638 km
unit price:
$16 vs $17
20
Melissa: 92.9%
4.
2
2 : 2 : 4,
b)
d)
Dillon: 88.3%
b)
3.
AP Book NS8-100
page 34
AP Book NS8-99
page 33
1.
2.
3.
Measurements may vary;
teacher to check.
b)
6 km
c)
5m
E→C
d)
14 km
E→J
e)
1 kg
E → FM
Distance
(map)
Distance
(real life)
1.7 cm
204 km
2.0
240 km
2.3 cm
276 km
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
1.
(continued)
AnswerKeysforAPBook8.2