Chapter 9 Add and Subtract Integers
9.1 Explore Integer Addition
Section 9.1
Page 313
a)
(+5) + (–5) = 0
b)
(–6) + (+4) = –2
c)
(–4) + (+8) = +4
Section 9.1
Page 313
a)
(+6) + (–9) = –3
b)
(–4) + (+4) = 0
c)
(+7) + (–3) = +4
Section 9.1
Page 314
a)
(+3) + (+4) = +7
b)
(–2) + (–4) = –6
c)
(+5) + (–2) = +3
d)
(–8) + (+8) = 0
Question 5
Question 6
Question 7
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Section 9.1
Page 314
a)
(–4) + (–1) = –5
b)
(+2) + (+6) = +8
c)
(–7) + (+4) = –3
d)
(+8) + (–3) = +5
Section 9.1
Page 314
Question 8
Question 9
a)
(+10) + (–4) = 6
Sharon has $6 left.
b)
(–7) + (+5) = –2
The snail was 2 cm below its original position.
c)
(+4) + (–1) = 3
The team won by 3 goals.
d)
(–4) + (–8) = –12
The diver’s final depth was 12 m under the water.
Section 9.1
Page 314
Question 10
(–6) + (–9) = –15
Miguel has $15 less at the end of the day than at the beginning.
Section 9.1
Page 314
Question 11
(+6) + (–10) = –4
The overnight low temperature was –4°C.
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Section 9.1
Page 314
Question 12
a)
(+6) + (+2) = +8
Nadia has 8 world-music CDs.
b)
(–5) + (+8) = +3
The change in temperature is +3°C.
c)
(+4) + (–4) = 0
Parminder is at the same place from where he started.
d)
(+6) + (–2) = +4
Joe has 4 char.
Section 9.1
Page 314
Question 13
a)
b)
The order in which you add two integers does not change the sum.
Section 9.1
Page 315
Question 14
a)
5 red chips = +5
7 red chips + 2 blue chips = (+7) + (–2)
= +5
10 red chips + 5 blue chips = (+10) + (–5)
= +5
b)
Answers will vary. For example,
Section 9.1
Page 315
Question 15
The integer 0 does not have an opposite. It is neither positive nor negative.
Section 9.1
Page 315
Question 16
The opposite of –3 is +3. The opposite of +3 is –3. The opposite of the opposite is the original integer, –3.
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Section 9.1
a)
+6
b)
–7
c)
+1
d)
–2
e)
–11
f)
0
Section 9.1
Page 315
Question 17
Page 315
Question 18
a)
In order for the difference between two opposites to be 8, half the difference on each side of zero
must be 4. The integer is +4.
b)
There is no integer that is 5 more than its opposite. Half the difference on each side of zero is 2.5,
and +2.5 and –2.5 are not integers. Integers must be positive or negative whole numbers.
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Section 9.1
Page 315
Question 19
a)
The number of dots in each symbol on the turtle’s back is equal to the number in the corresponding
location of the magic square. The magic sum is 15.
b)
The magic sum is –3 because the numbers in each row, column, and diagonal add to –3.
c)
The result is a magic square. The magic sum is +3.
d)
Answers may vary. A sample square is shown.
Section 9.1
Page 315
–5
2
–3
0
–2
–4
–1
–6
1
Question 20
a)
If one dart hits the target, the possible scores are +3, 0, and –1.
b)
If two darts hit the target, the possible scores are +6, +3, +2, 0, –1, and –2.
c)
If three darts hit the target, the possible scores are +9, +6, +5, +3, +2, +1, 0, –1, –2, and –3.
d)
Answers may vary.
e)
Answers may vary.
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9.2 Add Integers
Section 9.2
Page 320
a)
(+5) + (+4) = +9
b)
(–4) + (+4) = 0
c)
(+8) + (–9) = –1
Section 9.2
Page 320
a)
(–6) + (–2) = –8
b)
(+6) + (–4) = +2
c)
(–1) + (+7) = +6
Question 5
Question 6
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Section 9.2
Page 320
a)
(+5) + (+5) = +10
b)
(–3) + (–6) = –9
c)
(+4) + (–10) = –6
d)
(–7) + (+12) = +5
Section 9.2
Page 320
a)
(–4) + (+8) = +4
b)
(–4) + (–6) = –10
c)
(+5) + (–9) = –4
d)
(+10) + (–8) = +2
Section 9.2
Page 320
Question 7
Question 8
Question 9
(+20) + (–12) = +8
Kowmuk had $8 left.
Section 9.2
Page 320
Question 10
(–8) + (–6) = –14
The overnight low temperature was –14°C.
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Section 9.2
Page 320
Question 11
a)
(–20) + (+27) = +7
The final temperature was +7°C.
b)
(+12) + (–32) = –20
The final temperature was –20°C.
Section 9.2
Page 320
Question 12
a)
(–50) + (+34) = –16
Periscope depth for this submarine was 16 m below the surface of the water.
b)
(–16) + (–74) = –90
The cruising depth was 90 m below the surface of the water.
Section 9.2
Page 321
Question 13
The sum is 0. They are opposites. The numerals are equal in value, but opposite in sign.
Section 9.2
Page 321
Question 14
a)
Answers may vary. For example, –2 and +1; –3 and +2; –4 and +3; –5 and +4.
b)
Yes. There is an infinite number of integers for which the sum of the two integers is –1.
Section 9.2
Page 321
Question 15
a)
(+9) + (–5) = +4
(+8) + (–4) = +4
(+7) + (–3) = +4
(+6) + (–2) = +4
b)
The first integer decreases by 1 and the second integer increases by 1 from the top of the pattern to
the bottom of the pattern.
c)
(+5) + (–1) = +4
(+4) + 0 = +4
(+3) + (+1) = +4
Section 9.2
Page 321
Question 16
The possible totals that you can score by rolling both number cubes are
–5, –4, – 3, –2, –1, 0, +1, +2, +3, +4, +5.
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Section 9.2
Page 321
Question 17
a)
The last two sums are +5, and +4. As the value of the integer that is added to +6 decreases by one,
the value of the integer answer decreases by one.
b)
(+2) + (+2) = +4
(+2) + (+1) = +3
(+2) + 0 = +2
(+2) + (–1) = +1
(+2) + (–2) = 0
(+2) + (–3) = –1
(+2) + (–4) = –2
c)
(–3) + (+2) = –1
(–3) + (+1) = –2
(–3) + 0 = –3
(–3) + (–1) = –4
(–3) + (–2) = –5
(–3) + (–3) = –6
(–3) + (–4) = –7
(–3) + (–5) = –8
Section 9.2
Page 321
Question 18
a)
Never true. The sum of two negative integers is always a negative integer. For example,
(–5) + (–2) = –7.
b)
Sometimes true. The sum (+3) + (–2) = +1, but the sum (+3) + (–3) = 0.
c)
Always true. The sum of (+5) + 0 = +5. When 0 is added to any integer, the value of the integer does
not change.
d)
Sometimes true. The sum (+3) + (–5) = –2, but the sum (+3) + (–3) = 0.
Section 9.2
Page 321
Question 19
a)
Answers may vary. For example, you could use easily use 6 blue chips and 4 red chips to model the
addition.
(–6) + (+4) = –2
b)
Answers may vary. For example, you could use a number line since you would need too many
integer chips to easily model the addition.
(+90) + (–140) = –50
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Section 9.2
Page 321
Question 20
a)
(+4) + (+3) + (+7) = +14
b)
(–5) + (–7) + (–4) = –16
c)
(+6) + (–9) + (+5) = +2
d)
(–6) + (+3) + (–8) + (+2) = –9
Section 9.2
Page 321
a)
(+4) + (+5) = +9
b)
(–6) + (+4) = –2
c)
(–2) + (–5) = –7
d)
+6 = (+9) + (–3)
e)
(+8) + (–6) = +2
f)
–1 = (–5) + (+4)
Section 9.2
Page 322
Question 21
Question 22
a)
Answers may vary. For example, five other integers that can be expressed as a sum of three other
integers are
–6 = (–1) + (–2) + (–3)
–12 = (–3) + (–4) + (–5)
–15 = (–4) + (–5) + (–6)
+3 = 0 + (+1) + (+2)
+6 = (+1) + (+2) + (+3)
b)
Answers may vary. Any number that is the sum of three consecutive integers is a multiple of 3 or –3.
Section 9.2
Page 322
Question 23
x  (20)  (5)  (3)  (4)  ( 2)
x   26    2 
x   26    26    2    26 
x  28
Hing had $28 in her purse when she first went out that morning.
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9.3 Explore Integer Subtraction
Section 9.3
Page 327
a)
(+5) – (+3) = +2
b)
(–7) – (–4) = –3
Section 9.3
Page 327
a)
(–7) – (–1) = –6
b)
(+6) – (+6) = 0
Question 5
Question 6
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Section 9.3
Page 328
a)
(–5) – (+1) = –6
b)
(+5) – (+9) = –4
Question 7
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Section 9.3
Page 328
a)
(+3) – (–4) = +7
b)
(–4) – (–9) = +5
Question 8
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Section 9.3
Page 328
a)
(+6) – (+4) = +2
b)
(+5) – (–2) = +7
c)
(–6) – (+6) = –12
Question 9
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d)
(–4) – (–7) = +3
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Section 9.3
Page 328
a)
(–5) – (–1) = –4
b)
(+4) – (–2) = +6
c)
(–7) – (+4) = –11
Question 10
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d)
(+3) – (+8) = –5
Section 9.3
Page 328
a)
(+3) – (+1) = +2
(+1) – (+3) = –2
b)
(+2) – (–2) = +4
(–2) – (+2) = –4
c)
(+4) – 0 = +4
0 – (+4) = –4
d)
(–7) – (–9) = +2
(–9) – (–7) = –2
Section 9.3
Page 328
a)
(+5) – (+1) = +4
(+1) – (+5) = –4
b)
0 – (–5) = +5
(–5) – 0 = –5
c)
(+1) – (–3) = +4
(–3) – (+1) = –4
d)
(–6) – (–8) = +2
(–8) – (–6) = –2
Question 11
Question 12
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Section 9.3
Page 328
Question 13
a)
(+8) – (–4) = +12
(–4) – (+8) = –12
The difference of +12 h means that Perth, Australia is 12 h ahead of Bermuda. The difference of
–12 h means that Bermuda is 12 h behind Perth, Australia.
b)
(–5) – (–7) = +2
(–7) – (–5) = –2
The difference of +2 h means that Lima, Peru is 2 h ahead of Calgary, Alberta. The difference of
–2 h means that Calgary, Alberta is 2 h behind Lima, Peru.
c)
(+1) – (–10) = +11
(–10) – (+1) = –11
The difference of +11 h means that Lagos, Nigeria is 11 h ahead of Honolulu, Hawaii. The difference
of –11 h means that Honolulu, Hawaii is 11 h behind Lagos, Nigeria.
d)
(–4) – (–8) = +4
(–8) – (–4) = –4
The difference of +4 h means that Halifax, Nova Scotia is 4 h ahead of Dawson, Yukon Territory.
The difference of –4 h means that Dawson, Yukon Territory is 4 h behind Halifax, Nova Scotia.
Section 9.3
Page 329
Question 14
(–2) – (–8) = +6
(–8) – (–2) = –6
The difference of +6°C means that the afternoon temperature is 6°C above the morning temperature. The
difference of –6°C means that the morning temperature is 6°C below the afternoon temperature.
Section 9.3
Page 329
Question 15
a)
(+20) – (+16) = +4
He scored 4 more points on Tuesday than on Wednesday.
b)
(+3) – (–2) = +5
The temperature decrease was 5°C.
c)
(+10) – (+4) = 6
Sarah still owes Paola $6.
Section 9.3
Page 329
Question 16
(–3) – (+12) = –15
He rode 15 floors down.
Section 9.3
Page 329
Question 17
Answers may vary. For example, the difference is the opposite of the original non-zero integer.
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Section 9.3
Page 329
Question 18
a)
b)
Answers may vary. For example, the answers are opposites. The numerals are the same, but they are
opposite in sign.
c)
You cannot subtract the integers in either order. The order for this subtraction is given by the
question. If the integers were subtracted in the other order, the answer would have the opposite sign.
Section 9.3
Page 329
a)
(+9) – (+2) – (+4) = +3
b)
(–6) – (–4) – (–3) = +1
Question 19
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c)
(+3) – (–1) – (+4) = 0
d)
(–4) – (–2) – (+3) = –5
Section 9.3
Page 329
a)
(+5) – (+1) = +4
b)
(+2) – (+5) = –3
c)
(–3) – (+5) = –8
d)
(–4) – (–4) = 0
Question 20
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Section 9.3
a)
Page 329
1
1
3  0  3
2
2
Newfoundland is 3
b)
Question 21
1
h behind London, England.
2
1
1
3   8  4
2
2
Newfoundland is 4
1
h ahead of Victoria.
2
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9.4 Subtract Integers
Section 9.4
Page 333
a)
(+3) – (+4) = (+3) + (–4)
b)
(–1) – (–10) = (–1) + (+10)
c)
(–4) – (+5) = (–4) + (–5)
Section 9.4
Page 333
a)
(–7) – (–6) = (–7) + (+6)
b)
(+6) – (–3) = (+6) + (+3)
c)
(–9) – (+9) = (–9) + (–9)
Section 9.4
a)
Page 334
Question 5
Question 6
Question 7
The diagram represents (+2) + (+4) = +6.
(+2) – (–4) = (+2) + (+4)
= +6
b)
The diagram represents (–3) + (+7) = +4.
(–3) – (–7) = (–3) + (+7)
= +4
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Section 9.4
a)
Page 334
Question 8
The diagram represents (–4) + (–6) = –10.
(–4) – (+6) = (–4) + (–6)
= –10
b)
The diagram represents (–8) + (+8) = 0.
(–8) – (–8) = (–8) + (+8)
=0
Section 9.4
Page 334
a)
(+3) – (+9) = –6
b)
(–5) – (–10) = +5
c)
(–6) – (+7) = –13
d)
(+4) – (–4) = +8
Section 9.4
Page 334
a)
(+9) – (–1) = +10
b)
(–2) – (+5) = –7
c)
(+6) – (+10) = –4
d)
(–1) – (–3) = +2
Question 9
Question 10
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Section 9.4
Page 334
a)
(+4) – (+2) = +2
(+2) – (+4) = –2
b)
(+1) – (–1) = +2
(–1) – (+1) = –2
c)
(+5) – 0 = +5
0 – (+5) = –5
Section 9.4
Page 334
a)
0 – (–2) = +2
(–2) – 0 = –2
b)
(+2) – (–4) = +6
(–4) – (+2) = –6
c)
(–8) – (–9) = +1
(–9) – (–8) = –1
Section 9.4
Page 334
Question 11
Question 12
Question 13
(+1468) – (+65) = +1403
(+65) – (+1468) = –1403
Estimate: 1400 m
The difference of +1403 m means that Cypress Hills is 1403 m higher in elevation than Lake Athabasca.
The difference of –1403 m means that Lake Athabasca is 1403 m lower in elevation than Cypress Hills.
Section 9.4
Page 334
Question 14
(–63) – (+45) = –108
(+45) – (–63) = +108
The difference of +108ºC means that the record high temperature in Midale, Saskatchewan was 108ºC
higher than the record low temperature in Snag, Yukon Territory.
The difference of –108ºC means that the record low temperature in Snag, Yukon Territory was 108ºC
lower than the record high temperature in Midale, Saskatchewan.
Section 9.4
Page 334
Question 15
(+44) – (+12) = +32
(+12) – (+44) = –32
The difference of +32 s means that the rocket launch at T minus 12 was 32 s ahead of the rocket launch at
T minus 44.
The difference of –32 s means that the rocket launch at T minus 44 was 32 s behind the rocket launch at T
minus 12.
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Section 9.4
Page 334
Question 16
Estimate:
(+150) – (–450) = +600
Calculate:
(+156) – (–458) = +614
The depth of the lake is 614 m.
Section 9.4
Page 334
Question 17
(+357) – (–39) = +396
The boiling point of mercury is 396°C above its melting point.
Section 9.4
Page 335
Question 18
The last two differences are +4; and +5. As the integer that is subtracted decreases by 1, the integer that is
the answer increases by 1.
Section 9.4
Page 335
Question 19
a)
(+1) – (–1) = +2
(+2) – (–2) = +4
(+3) – (–3) = +6
(+4) – (–4) = +8
b)
Subtracting the opposite is the same as adding the first integer to itself.
c)
Adding +387 to itself gives +774.
Section 9.4
Page 335
a)
(+8) – (+1) = 7 units
b)
(+4) – (–5) = 9 units
c)
(–1) – (–10) = 9 units
d)
(+3) – (–2) = 5 units
Question 20
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Section 9.4
Page 335
Question 21
WXYZ is a square so all the sides are equal.
Side WX:
(–1) – (–5) = +4
P=4×4
=16
P = 16 units
A=4×4
= 16
A = 16 square units
Section 9.4
Page 335
Question 22
a)
(+3) – (–2) = +5
(+2) – (–1) = +3
(+1) – 0 = +1
0 – (+1) = –1
b)
Answers may vary. The first integer is decreasing by 1. The integer that is subtracted is increasing by
1. The integer answer is decreasing by 2.
c)
The next three lines in the pattern are:
(–1) – (+2) = –3
(–2) – (+3) = –5
(–3) – (+4) = –7
Section 9.4
Page 335
a)
(+8) – (+5) = +3
b)
(–1) – (+4) = –5
c)
(–2) – (–9) = +7
d)
–6 = (–7) – (–1)
e)
(+2) – (+2) = 0
f)
–2 = (+5) – (+7)
Section 9.4
Page 335
Question 23
Question 24
The possible values of the other integers are +13 and –3.
(–3) – (+5) = –8
(+5) – (+13) = –8
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9.5 Apply Integer Operations
Section 9.5
Page 339
Question 3
(+13) – (–17) = +30
The change in temperature was +30°C.
Section 9.5
Page 339
Question 4
(–14) + (+9) = –5
The temperature was –5°C in the late afternoon.
Section 9.5
Page 339
Question 5
Estimate:
(+6000) + (+4000) = +10 000
Calculate:
(+6033) + (+4170) = +10 203
The height of the mountain is 10 203 m.
Section 9.5
Page 339
Question 6
(+1774) – (+1794) = –20
The elevation of the tunnel is 20 m below the Fraser River.
Section 9.5
Page 339
Question 7
(+5) – (+25) = –20
The wind speed decreased by 20 km/h.
Section 9.5
Page 339
Question 8
a)
(+8) + (–12) = –4
The company’s total loss over the two years was $4 million.
b)
(+8) – (–12) = +20
The company’s result in the first year was $20 million better than in the second year.
Section 9.5
Page 340
Question 9
a)
The pattern is to add 3 to each preceding number. The next three integers will be +13, +16, +19.
b)
The pattern is to subtract 4 from each preceding number. The next three integers will be –7, –11,
–15.
c)
The pattern is to add 2 to each preceding number. The next three integers will be –3, –1, +1.
d)
The pattern is to subtract 5 from each preceding number. The next three integers will be 0, –5, –10.
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Section 9.5
Page 340
Question 10
The two integers are –11, –4.
(–11) + (–4) = –15
–4 – (–11) = +7
(–11) – (–4) = –7
Section 9.5
Page 340
Question 11
Answers may vary. For example,
(+3) + 0 = +3 or (+3) – 0 = +3
(+4) + 0 = +4 or (+4) – 0 = +4
(+5) + 0 = +5 or (+3) – 0 = +5
(+6) + 0 = +6 or (+6) – 0 = +6
Each pair of integers contains a value of zero.
Section 9.5
Page 340
Question 12
a)
0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + 0 + (–1) + (–1) + (–1) + (–1) + (+1) + (+1) = –2
She was 2 strokes below par for that round.
b)
(–2) – (–8) = +6
Michelle took 6 more strokes than Annika did in the first round.
c)
Annika:
(+72) + (–8) = +64
Michelle:
(+72) + (–2) = +70
Annika took 64 strokes to complete the first round. Michelle took 70 strokes to complete the first
round.
Section 9.5
Page 340
Question 13
a)
+15 = (+7) + (+8)
–9 = (–4) + (–5)
–1 = 0 + (–1)
–25 = (–12) + (–13)
b)
All even integers cannot be expressed as the sum of two consecutive integers.
c)
The integers +1 and –1 can be expressed as the difference between two consecutive integers.
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Section 9.5
Page 340
a)
3 – 5 = –2
b)
4 + (–3) = +1
c)
–6 + 2 = –4
d)
4 – (–6) = +10
e)
–8 – (–8) = 0
f)
–4 – 7 = –11
Section 9.5
Page 340
Question 14
Question 15
Answers may vary.
Section 9.5
Page 340
Question 16
a)
(+160) – (+135) = +25
Half of these 25 MPs would have to change their votes. Since half of 25 is 12.5, 13 MPs would have
to change their votes.
b)
(+135) + (+13) = +148 in favour
(+160) – (+13) = +147 against
There are 148 votes in favour and 147 votes against.
Section 9.5
Page 341
Question 17
a)
(+1) – (–8) = +9
3 p.m. Vancouver = midnight in Paris
Midnight + 11 h = 11 a.m.
This will make it 11 a.m. on Tuesday in Paris.
b)
Vancouver is 9 h behind Paris.
11 a.m. landing in Paris from Vancouver + 3 h later in Paris = 2 p.m. departure from Paris
2 p.m. departure from Paris – 9 h time difference to Vancouver + 12 h flight = 5 p.m. landing in
Vancouver on Tuesday.
c)
There is a 2 h differential between Vancouver and Honolulu. If the plane left Vancouver at 11 a.m.
Vancouver time, that would be 9 a.m. Honolulu time. From 9 a.m. Honolulu time to 3 p.m. also
Honolulu time, makes it a 6-h flight.
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Section 9.5
Page 341
Question 18
a)
(+45) – (–18) – (+1) = +62
It is 62 years from 18 B.C.E. to 45 C.E.
b)
(+5) – (+19) – (+1) = +15
19 years before 5 C.E. was the year 15 B.C.E.
c)
(–21) + (+38) – (+1) = +16
The year 16 C.E. was 38 years after 21 B.C.E.
376 MHR●MathLinks 7 Solutions
Chapter 9 Review
Chapter 9 Review
Page 342
Question 1
Examples of opposite integers are +2 and –2.
Chapter 9 Review
Page 342
Question 2
In a zero pair of integer chips, one chip represents +1, and the other chip represents –1.
Chapter 9 Review
a)
(+7) + (–4) = +3
b)
(–6) + (+5) = –1
c)
(+5) + (–8) = –3
Chapter 9 Review
a)
(–5) + (–3) = –8
b)
(+4) + (–4) = 0
c)
(+6) + (–3) = +3
d)
(–9) + (+4) = –5
Page 342
Question 3
Page 342
Question 4
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Chapter 9 Review
Page 342
Question 5
The sum of two integers is positive if the larger numeral is positive. For example, (+5) + (–3) = +2.
The sum of two integers is negative if the larger numeral is negative. For example, (–4) + (+3) = –1.
The sum of two integers is zero if the integers are opposites. For example, (+3) + (–3) = 0
Chapter 9 Review
Page 342
Question 6
(+4) + (–6) = –2
The pelican dove 2 m below the surface of the water.
Chapter 9 Review
a)
(–4) + (–5) = –9
b)
(+6) + (–3) = +3
Chapter 9 Review
a)
(–3) + (+3) = 0
b)
(+7) + (–2) = +5
c)
(–4) + (+12) = +8
d)
(+6) + (–8) = –2
Page 342
Question 7
Page 342
Question 8
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Chapter 9 Review
Page 342
Question 9
Answers may vary. Four possible answers are
(–5) + (–4)
(–6) + (–3)
(–7) + (–2)
(–8) + (–1)
Chapter 9 Review
Page 342
Question 10
(–86) + (+84) = –2
New Orleans is 2 m below sea level.
Chapter 9 Review
a)
(–7) – (+2) = –9
b)
(–4) – (–10) = +6
Page 343
Question 11
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Chapter 9 Review
a)
(–7) – (–5) = –2
b)
(+4) – (–3) = +7
c)
(+3) – (+8) = –5
Page 343
380 MHR●MathLinks 7 Solutions
Question 12
d)
(–1) – (+6) = –7
Chapter 9 Review
Page 343
Question 13
(+8) – (–7) = +15
Hong Kong is 15 h ahead of Lethbridge.
Chapter 9 Review
a)
Page 343
Question 14
The diagram represents (+4) + (–7) = –3.
(+4) – (+7) = (+4) + (–7)
= –3
b)
The diagram represents (–6) + (+4) = –2.
(–6) – (–4) = (–6) + (+4)
= –2
Chapter 9 Review
a)
(+5) – (+8) = –3
b)
(–4) – (–6) = +2
c)
(–2) – (+7) = –9
d)
(+4) – (–9) = +13
Page 343
Question 15
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Chapter 9 Review
Page 343
Question 16
Estimate:
(+ 8800) – (–400) = +9200
Calculate:
(+ 8848) – (–411) = +9259
The difference of +9259 m means that Mt. Everest is 9259 m higher in elevation than the Dead Sea.
The difference of –9259 m means that the Dead Sea is 9259 m lower in elevation than Mt. Everest.
Chapter 9 Review
Page 343
Question 17
a)
The pattern is to add +6 to each preceding number. The next three integers are +27, +33, +39.
b)
The pattern is to subtract 10 from each preceding number. The next three integers are 0, –10, –20.
Chapter 9 Review
a)
Page 343
Question 18
(–4) – (+3) = –7
Mike Weir needed 7 fewer strokes in the fourth round than in the
b)
(–4) – (–2) = –2
Mike Weir needed 2 fewer strokes in the second round than he did in the first round.
c)
(–2) + (–4) + (+3) + (–4) = –7
Mike was 7 strokes under par for the whole tournament.
d)
4 × 72 = 288
288 + (–2) + (–4) + (+3) + (–4) = 281
It took Mike 281 strokes altogether to complete the four rounds.
382 MHR●MathLinks 7 Solutions
third round.
Chapter 9 Practice Test
Chapter 9 Practice Test
Page 344
Question 1
The diagram represents (–8) + (+5). Answer D
Chapter 9 Practice Test
Page 344
Question 2
The diagram represents (–4) + (+7). Answer A
Chapter 9 Practice Test
Page 344
Question 3
The diagram represents (–2) – (–6). Answer B
Chapter 9 Practice Test
Page 344
Question 4
(+6) + (–2) = (–2) + (+6) Answer B
Chapter 9 Practice Test
Page 344
Question 5
(+4) + (+3) = (+4) – (–3) Answer C
Chapter 9 Practice Test
Page 34
Question 6
(–3) – (+3) does not equal 0. Answer D
Chapter 9 Practice Test
Page 344
Question 7
(+6) + (–10) = –4
The overnight low temperature was –4°C.
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Chapter 9 Practice Test
Page 344
Question 8
(+8) – (–9) = +17
The length of the line segment is 17 units.
Chapter 9 Practice Test
a)
(–4) + (–5) = –9
b)
(+3) + (–8) = –5
c)
(–9) – (–7) = –2
d)
(+6) – (–6) = +12
e)
(+2) – (+7) = –5
f)
(–3) – (–8) = +5
Chapter 9 Practice Test
Page 344
Question 9
Page 345
Question 10
a)
(–6) + (+4) = –2
The monkey is 2 m lower than where he started from.
b)
The sum is –2 m.
Chapter 9 Practice Test
Page 345
Question 11
The length of side DC:
(+2) – (–2) = +4
The length of side DE:
(–3) – (–6) = +3
Since the shape is a rectangle, with length 4 and width 3, the perimeter will be
P = 2l + 2w
= 2(4) + 2(3)
=8+6
= 14
P = 14 units
The perimeter of the rectangle is 14 units.
To calculate the area of a rectangle with length 4 and width 3, the area will be
A=l×w
=4×3
= 12
A = 12 square units
The area of the rectangle is 12 square units.
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Chapter 9 Practice Test
Page 345
Question 12
Estimate:
200 – (–100) = +300
Calculate:
(+176) – (–105) = +281
The depth of Lake Michigan is 281 m.
Chapter 9 Practice Test
Page 345
Question 13
Two integers that have a sum of +16 and differences of –8 and +8 are +4 and +12.
Chapter 9 Practice Test
Page 345
Question 14
a)
You don’t always know the sign of the difference between two positive integers, since it depends on
the value of the integer being subtracted.
For example,
(+5) – (+3) = +2
(+5) – (+7) = –2
b)
Subtracting a negative integer from a positive integer will always be positive, since subtracting a
negative is the same as adding a positive.
For example,
(+5) – (–3) = (+5) + (+3) = +8
c)
Subtracting a positive integer from a negative integer will always be negative, since subtracting a
positive is the same a adding a negative.
For example,
(–5) – (+2) = (–5) + (–2) = –7
d)
You don’t always know the sign of the difference between two negative integers, because subtracting
a negative is like adding a positive, so it depends on the value of the integer.
For example,
(–3) – (–4) = (–3) + (+4) = +1
(–3) – (–1) = (–3) + (+1) = –2
Chapter 9 Practice Test
Page 345
Question 15
a)
Add 273 to the temperature in degrees Celsius to get
kelvins. Alternatively, subtract 273 from the
kelvins to get the temperature in degrees Celsius.
b)
(+250) – (+273) = –23
The conversion of 250 K is –23°C.
c)
(–100) + (+273) = +173
The conversion of –100°C is 173 K.
the temperature in
temperature in
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