Exercise 1
1. Plot the following integers on the number line:
-121, -97, -82, -67, -43, -10, 0, 10, 36, 55, 64, 77, 110, 126, 147.
-121 -97
-82
-67
-43,
-10
0
10
36 55
64
77 110 126
147.
2. Use a number line if necessary to answer questions.
a) (−3) + (+2) + (+4) = . . ..
-3 +
2 +
4
= 3
b) (−7) + (+4) + (−1) = …
-7 +
4
–1 =
− ( 7 – 4) – 1 =
- 3–1=
- (3+1) = - 4
c) (−1) + (−2) + (−3) = …
-1
- 2
- 3
=
− ( 1 + 2 + 3) = - 6
3. a)
(+5) + (+4) = …
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b)
(+2) + (−3) = …
1
5+4=9
2–3=
-(3–2)= -1
c) (+3) + (−3) = …
d)
3–3=0
(+5) + (−7) = …
5–7=
-(7–5) =-2
e) (+2) + (−5) = …
f)
(−1) + (+2) = …
2–5=
-1+2=
-(5–2)=-3
+(2–1)=+1
g) (−3) + (+5) = …
h)
(−3) + (+2) + (+4) = …
-3+5=
-3+2+4=
+(5–3)=+2
-3+6=
+(6–3)=+3
i)
(−7) + (+4) + (−1) = ⋯
j)
– 7 + 4 – 1 = −𝟒
(−1) + (−2) + (−3) = ⋯
– 1 – 2 – 3 = −𝟔
k) (+3) − (+1) = 𝟐
l)
(+4) − (+3) = 𝟏
m) (+2) − (+4) = −𝟐 …
n)
(+5) − (+6) = −𝟏
o) (−3) − (−2) = −𝟏
p)
(−4) − (−1) − 𝟑
q) (−3) − (−2) = −𝟏
r)
(+4) − (−1) = 𝟓
s) (−5) − (−4) = −𝟏
t)
(−7) − (−2) = −𝟓
4. a) (+3) + (−4) + (−2) = …
b)
(−4) + (−3) + (+7) = …
3– 4–2 =–3
c) (−4) − (+2) + (+3) = …
–4–3+7=0
d)
–4 –2 +3=–3
5.
(−2) − (−3) − (+7) = …
–2+3–7=–6
e) (−5) − (−2) + (+3) = 𝟎
f)
(−3) + (−3) − (−6) = – 𝟎
g) (−1) − (−4) + (−3) = 𝟎
h)
(−4) − (−2) + (−3) = – 𝟓
i)
j)
(−3) − (−3) + (−3) = – 𝟑
(−2) + (−2) − (−2) =– 𝟐
a) The temperature is 15℃ and falls by 8℃. The final temperature is ….
15 – 8 = 7℃
b) The temperature is 12℃ and falls by 7℃. The final temperature is 5℃
c) The temperature is 9℃ and rises by 2℃. The final temperature is ….
9 + 2 = 11℃
d) The temperature is 8℃ and rises by 6℃. The final temperature is 14℃
e) The temperature is 3℃ and falls by 6℃. The final temperature is -3℃
f)
The temperature is 0℃ and falls by 8℃. The final temperature is −8℃
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g) The temperature is 23℃ and falls by 6℃. The final temperature is 17℃
h) The temperature is −6℃ and rises by 12℃.The final temperature is 6℃
i)
The temperature is −3℃ and falls by 6℃. The final temperature is -9℃
6) Complete the grids below. Some answers are already filled in.
Add +3
+4 +7
+1
−1
−3
−5
+3
+1
-1
-1
-3
-5
-7
-7
−9
-9
+2
+5
+5
+3
−2
+1
-1
+1
−3
−4
-1
-3
-5
−6
-3
-5
-7
-11
Subtract +5 +3 +1 −1 −3
+8
+3 +5 +7 +9 +11
+6
+1 +3 +5 +7 +9
+4
-1 +1 +3 +5 +7
−2
-7
−5 -3
-1
1
−6
-11
-9
-5
-3
-7
Exercise 2
200 – 300 + 200 = 100 points
300 m / 10 m/min = 30 min
( 509 BC = - 509 and 476 AD = + 476 )
476 – ( – 509) = 476 + 509 = 985 years
– 114 – ( – 39 ) = – 114 + 39 = – 75o C
10 – 15 = – 5o C
29,028 – ( – 1,312 ) = 29,028 + 1,312 = 30340 ft
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15 x 3 + 7 x ( – 1 ) = 45 – 7 = 38
5,500 – 2x 4,800 = 5,500 – 9600 = $ – 4,100
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Exercise 3
3 – 5 + 9 = 7 points
- 350 + 400 = 50 calories ( gain )
42 – 10 = 32 o C
98 – 20 = 78 points
18 – 3 x 2 = 18 – 6 = 12 points
below sea level below 0 feet, rises = upward , descend = downard
– 15 + 9 – 12 = – 18 feet , 18 feet below sea level
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– 114 – ( – 39 ) = – 114 + 39 = – 75o C
80 – 30 + 97 – 50 = ( 80 – 30 – 50 ) + 97 = 0 + 97 = 97 points
–
3 + 2 = – 1 oC
48 – 80 = $ – 32
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