Number Sense – AP Book 8, Part 1: Unit 7
AP Book NS8-64
d)
page 179
1.
2.
3.
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
4.
5.
b)
‒
c)
+
d)
‒
e)
+
f)
+
g)
‒
b)
‒2+8
c)
‒4+3
d)
+6‒5
f)
+3+5‒6+2
g)
‒ 5 ‒ 8 + 10 + 5
h)
+4‒3‒2+5
b)
‒
c)
+
d)
‒
e)
+
f)
‒
g)
+
h)
‒
i)
‒
b)
‒1
c)
0
d)
0
e)
+2
f)
‒4
g)
+5
h)
‒5
i)
‒7
j)
‒3
k)
+3
l)
+7
m)
‒5
e)
f)
6.
b)
+4+3‒6
=+7‒6
= +1
+6+3+2‒4‒5
‒8‒1
= + 11 ‒ 18
= ‒7
h)
‒9
a)
<
b)
<
c)
>
d)
>
e)
>
7.
‒7, ‒3, ‒2, +5, +10
8.
23C, 13C, ‒17C,
‒18C, ‒48C
b)
‒2
9.
a), b)
c)
+4
d)
‒4
e)
+7
f)
+2
g)
+3
h)
‒8
i)
‒8
j)
+8
k)
+4
l)
‒6
m)
‒4
n)
‒3
o)
‒2
q)
+6+4
= +10
r)
+8‒4‒2‒4
= ‒2
‒b
+2
q)
0
AP Book NS8-65
r)
0
page 181
b)
+4‒3‒2
=+4‒5
= ‒1
2.
+4, 7, 9 , +2, +8
3.
a)
‒3
b)
‒6
c)
5
d)
‒6
a
b
‒5+4+2
=+6‒5
= +1
i)
+3‒5‒2+6
=+9‒7
= +2
j)
‒2‒3+4+1
=+5‒5
=0
k)
+4+0‒5‒3
=+4‒8
= ‒4
l)
+3+2‒2‒3
=+5‒5
=0
a)
‒2
b)
+5
c)
‒3
d)
+142
BONUS
‒5
c)
+5
AP Book NS8-66
d)
‒3
page 182
e)
+4
1.
2.
3.
4.
0 > ‒a > ‒b
b)
gain of 3
c)
loss of 2
d)
gain of 7
b)
(‒2) + 6 + (‒3)
c)
3 + 2 + (‒7)
d)
5 + (‒3) + (‒4)
e)
(‒3) + 1 + 5
f)
(‒3) + 4 + (‒2)
b)
+3+4
c)
‒3+4
d)
‒3‒4
e)
+a‒b
f)
+a+b
g)
‒a+b
h)
‒a‒b
b)
‒3+4
= +1
c)
Answers will vary –
teacher to check.
0
5.
h)
b)
The two +4s shouldn’t
have been cancelled out
– correct answer is +14.
p)
‒a
c)
+2‒7+2
= ‒3
+5
AnswerKeysforAPBook8.1
‒5
Teacher to check.
o)
+7‒5‒3
=+7‒8
= ‒1
+3
g)
6.
‒4
c)
f)
‒4‒3‒2‒5‒4
+5+6+8+1
= ‒ 18 + 20
= +2
n)
1.
4.
‒2
Answers will vary –
teacher to check.
s)
8.
+5+6‒4
= + 11 ‒ 4
= +7
e)
5.
c)
7.
+8+2‒5
= + 10 ‒ 5
= +5
‒5‒4
= ‒9
6.
7.
8.
0
f)
+2
b)
‒1‒1‒1
= ‒3
c)
+1+1+1‒1‒1‒1‒1
= ‒1
d)
+1+1+1+1‒1‒1
= +2
e)
+1+1+1+1+1
= +5
f)
‒1‒1‒1‒1‒1
= ‒5
g)
‒1‒1‒1‒1‒1
= ‒5
h)
‒1‒1‒1+1+1+1
=0
a)
‒1
b)
‒6
c)
+8
d)
‒6
e)
+3
0
d)
+2+6
= +8
f)
g)
‒10
e)
‒2‒9
= ‒11
h)
‒8
i)
‒12
f)
‒9+7
= ‒2
j)
‒2
K‐33
k)
9.
‒9
l)
+3
a)
T
b)
F
e)
f)
Counter-examples
will vary – teacher
to check.
g)
Sample:
‒ 2 + 7 = +5
h)
AP Book NS8-67
3, right;
3, left;
‒5
c)
Teacher to check.
a)
‒5, ‒5
b)
‒5, ‒5
c)
‒6, ‒6
d)
‒6, ‒6
4.
(‒a) ‒ b = (‒b) ‒ a
5.
b)
‒5, +5
c)
‒7, +7
They both equal ‒ (a + b)
d)
‒7, +7
Teacher to check
number lines.
b)
left
e)
‒6, +6
c)
left
f)
‒8, +8
a)
‒2
d)
right
b)
+5, (+1)
b)
‒5
a)
(‒4), (‒4)
c)
+7, (+5)
c)
+3
+7, (+3)
d)
‒2
e)
0
3.
4.
0
INVESTIGATION
Teacher to check
number lines.
5.
b)
(+4), (+4)
a)
‒3 + (+4) = +1
e)
+6, (+4)
b)
(+2) + (‒4) = ‒2
f)
+8, (+6)
c)
(+4) + (+5) = +9
7.
d)
(‒3) + (‒4) = ‒7
8.
(+3) + (+7) = +10
c)
(+3); +9
a)
(+3)
d)
(+1); ‒1
(‒7)
e)
(+4); +1
(+25)
f)
(+5); +3
c)
‒10
c)
d)
‒4
e)
‒3
b)
‒2, 0, +2
c)
7.
AP Book NS8-68
page 185
Teacher to check
number lines.
a)
b)
c)
d)
a)
b)
‒1, ‒4, ‒7
3, left;
3, right;
+8
6, 7, 8, 9, 10, 11,
12, 13, 14, 46
+2‒3
= ‒1
d)
‒4+6
= +2
e)
‒ 11 + 6
= ‒5
f)
+ 14 ‒ 8
= +6
g)
‒3+7
= +4
h)
‒ 25 + 5
= ‒20
i)
‒2‒3+4
= ‒1
j)
+3‒5+4
= +2
k)
‒ 9 ‒ 8 + 12
= ‒5
l)
‒4+5+6‒3
= +4
Teacher to check
number line:
A
C
E
G
4.
5.
‒2
b)
‒10
a)
+12
B
D
F
H
‒8
b)
+2
b)
‒18
6 ‒ (‒9) = 15
Spin +5 and ‒5,
in either order.
c)
+2
d)
‒1
d)
11, 12, 13, 14, 15,
16, 17, 18, 19, 51
e)
‒11
f)
+9
g)
‒5
AP Book NS8-71
h)
+9
page 190
i)
+5
1.
0
‒1
+4
j)
‒9
+5
+1
‒3
k)
‒9
‒2
+3
+2
page 187
l)
+9
1.
4, right;
4, left;
‒10
2.
a)
1, ‒1
b)
4, ‒4
AP Book NS8-70
c)
2, ‒2
page 189
d)
1, ‒1
1.
e)
b)
‒4‒2
3, ‒3
c)
‒5+6
f)
3, ‒3
d)
+3+5‒4+2‒6
g)
4, ‒4
a)
a)
They are opposite
each other, that is:
+3+2
= +5
b)
‒5‒3
= ‒8
2.
(+1)
(+3)
(‒5)
(‒8) or (+8)
a)
2, 3, 4, 5, 6, 7, 8, 9,
10, 42
The difference increases
by 1;
17 ‒ (‒15) is 15 more
than 17 ‒ 0.
(‒2)
(+2)
(+4)
(‒4.5)
a)
c)
a ‒ b = ‒ (b ‒ a)
K‐34 9.
3.
c)
AP Book NS8-69
2, right;
2, left;
+4
3, left;
3, right;
‒1
(+5); +10
f)
b)
a)
(+3); +7
(‒1) + (‒4) = ‒5
+6
2.
a)
e)
b)
No
a + (+b) = a + b
b)
‒8
6.
6.
d)
a)
B.
1.
3, left;
3, right;
+1
3.
‒3
right
f)
A.
1, left;
1, right;
+4
b)
a)
2.
page 184
1.
5, right;
5, left;
‒3
(continued)
2.
3.
4.
Toronto
25C
Montreal
31C
Vancouver
26C
a)
‒180, ‒50, +20,
+120, +470
b)
650C
c)
Saturn
a)
‒5C
b)
‒7C
AnswerKeysforAPBook8.1
COPYRIGHT©2010JUMPMATH:NOTTOBECOPIED
Number Sense – AP Book 8, Part 1: Unit 7
Number Sense – AP Book 8, Part 1: Unit 7
5.
6.
a)
+98 + (‒12)
= +86C
b)
+93 ‒ (‒3)
= +96C
Monday
10C
Tuesday
2C
Wednesday
4C
Thursday
12C
Answer will vary –
teacher to check.
a × (b – c)
= 7 × (2 – 4)
= 7 × (–2)
= –14
page 191
Yes, it holds.
(‒5) + (‒5) + (‒5)
= ‒15
b)
c)
d)
e)
f)
7 ‒ 35
= ‒28
(‒7) + (‒7)
= ‒14
c)
0 ‒ 15
= ‒15
(‒3) + (‒3) + (‒3)
+ (‒3)
= ‒12
d)
(0 ‒ 5) × 3
=0×3‒5×3
= 0 ‒ 15
= ‒15
f)
(‒8) + (‒8) + (‒8)
= ‒24
a)
14; ‒14
b)
12; ‒12
c)
30; ‒30
d)
‒72
e)
‒56
f)
‒20
b)
3×4‒3×2
6.
7.
A.
e)
8×3‒3×3
‒a
f)
4×3‒4×2
5×3‒2×3
INVESTIGATION 1
i)
=
(‒9)
ii)
=
(‒12)
iii)
=
iv)
=
‒b
(‒a) × b
a × (‒b)
‒4
‒5
(‒4) × 5
= ‒20
4 × (‒5)
= ‒20
‒5
‒3
(‒5) × 3
= ‒15
5 × (‒3)
= ‒15
e)
‒42
f)
+36
g)
‒24
h)
+81
10.
(‒2) × 0 ‒ (‒2) × 5
= 0 ‒ (‒10)
= 0 + 10
= +10
Yes, all three ways will
get the same answer.
11.
a)
i)
b)
(‒2) × 3 +
(‒2) × (‒3)
iii)
The numbers
are the same
in both cases
(2 & 3) but the
resulting signs
will be opposite
since, in one
case, they are
different and, in
the other, they
are the same.
iv)
‒6; +6
i)
(4 + (‒4)) = 0
since they’re
opposites and
(‒3) × 0 = 0
ii)
(‒3) × 4 +
(‒3) × (‒4)
iii)
See above.
iv)
‒12; +12
12.
(‒a) × (‒b) = a × b
13.
a)
+15
AP Book NS8-73
page 194
1.
(3 + (‒3)) = 0
since they’re
opposites and
(‒2) × 0 = 0
ii)
‒4
2.
3.
4.
c)
12 ÷ (‒3) = ‒4
12 ÷ (‒4) = ‒3
d)
(‒12) ÷ (‒3) = 4
(‒12) ÷ 4 = ‒3
e)
6÷3=2
6÷2=3
f)
(‒6) ÷ (‒3) = 2
(‒6) ÷ 2 = ‒3
g)
6 ÷ (‒3) = ‒2
6 ÷ (‒2) = ‒3
h)
(‒6) ÷ 3 = ‒2
(‒6) ÷ (‒2) = 3
a)
5, 5
b)
2, 2
c)
‒4, ‒4
d)
3, 3
e)
‒5, ‒5
f)
‒5, ‒5
g)
‒3, ‒3
h)
3, 3
a)
+
b)
parts e) and f);
‒5, ‒5;
‒
c)
parts c) and g);
‒4, ‒3;
‒
d)
parts b) and h);
2, 3;
+
a)
‒4
9
Teacher to check the last row.
b)
+36
b)
B.
c)
+24
c)
8
d)
+10
d)
‒8
e)
+32
e)
‒4
f)
+63
f)
5
g)
+48
g)
5
h)
+55
h)
12
a)
‒27
a)
‒5
8.
They’re equal.
a)
‒21
(‒15)
b)
‒20
(‒50)
c)
‒14
d)
‒40
e)
‒18
14.
AnswerKeysforAPBook8.1
‒24
(‒a) × b = ‒ (a × b)
INVESTIGATION 2
4×6+3×6
+56
d)
c)
Students will likely find
the method in f) easier
since one product is 0,
 the subtraction step is
much easier.
4×5+2×5
h)
c)
Solved (‒8) × 3 twice and
got ‒24 both ways.
5×3‒2×3
9×2‒4×2
(‒2) × 1 ‒ (‒2) × 6
= (‒2) ‒ (‒12)
= ‒ 2 + 12
= +10
(0 ‒ 8) × 3
=0×3‒8×3
= 0 ‒ 24
= ‒24
c)
g)
b)
(2 ‒10) × 3
= 2 × 3 ‒ 10 × 3
= 6 ‒ 30
= ‒24
d)
i)
A.
e)
(‒6) + (‒6) + (‒6)
+ (‒6) + (‒6)
= ‒30
3.
4.
5.
(‒2) + (‒2) + (‒2)
+ (‒2)
= ‒8
a × (‒b) = ‒ (a × b)
b)
Again students will
likely find the method
in c) easier since one
product is 0, and  the
subtraction step is much
easier.
b)
2.
‒72
a = 7, b = 2, c = 4
AP Book NS8-72
a)
9.
f)
Sample:
a×b–a×c=7×2–7×
4
= 14 – 28
= –14
1.
COPYRIGHT©2011JUMPMATH:NOTTOBECOPIED
B.
(continued)
5.
K‐35
Number Sense – AP Book 8, Part 1: Unit 7
b)
7
c)
‒6
8.
th
page 195
a)
b)
2.
3.
a)
‒1, +1, ‒1, +1, ‒1, ...
The 100 term will be +1
since the pattern shows
that odd terms are ‒1
and even terms are +1.
AP Book NS8-74
1.
(continued)
9.
+90, 90C;
‒90, ‒90C;
+5, 5;
‒4, 4
‒3
7
+1
‒2
0
+3
‒7
‒1
+2
0
‒3
+9
‒1
+5
+8
+6
+3
a)
‒a
b)
Answer will vary –
teacher to check.
‒90, ‒90C;
(‒30) × (‒3) = 90,
90C;
(‒210) ÷ (‒30) = 7,
 in 7 days;
360 ÷ (‒30) = ‒12,
 12 days ago
Sample:
Find the difference
between 3 and a,
and then add it to 3,
i.e. 3 + (3 ‒ a)
+4, ‒5
b)
+20, ‒5
c)
+5, ‒1
d)
‒3, ‒4
e)
‒2, ‒5
f)
‒16, +9
c)
10.
Day One
5C
Day Two
‒5C
+3
st
nd
1 row + 6 = 2 row
Answers will vary –
teacher to check.
Day Three 26C
4.
a)
False;
the sum is always
zero.
b)
False;
Answers will vary –
teacher to check.
Sample:
+5 is opposite to ‒5
because they have
different signs.
True
d)
True
a)
i)
0
ii)
‒2x
iii)
‒x
iv)
‒1
b)
6.
2
Answers will vary –
teacher to check.
COPYRIGHT©2010JUMPMATH:NOTTOBECOPIED
5.
c)
Yes, since we know:
(‒a) × (‒b) = a × b
= b × a = (‒b) × (‒a)
7.
a)
Teacher to check
number line.
distance = 9 shots
b)
K‐36 +5 ‒ (‒4) = +9
AnswerKeysforAPBook8.1