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CHAPTER2.3T
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1994-02-15
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à 2.3ïThe subtraction operation.
äïPlease perform the following subtractions.
âS
êêêï4 - 6ï=è 4 + (-6)ï=è-2
êêë 8 - (-6)ï=è 8 + (6)è=è 14
êêë -7 - (5)ï=è-7 + (-5)ï=è-12
êêè -10 - (-3)ï=è-10 + (3)ï=è -7
éS
ïTo subtract two numbers first change the operation to addition and
ïthen change the sign of the subtrahend.ïNext treat the problem as an
ïaddition problem using the two rules for addition.
ïGiven the problem, -6 - 10, change the operation to addition and
ïchange the sign of the subtrahend to get -6 + (-10).ïParençs
ïhave been placed around the "-10" for clarity.ïThe problem is then
ïtreated as an addition problem.ïSince -6 and -10 have like signs, the
ï6 and 10 are added and the sum takes the sign they have in common.
êêê -6 - 10 = -6 + (-10) = -16
1
êêêêë8 - 5
êê A) 3êB) 13êC) -3êD) -13
ü
êêêè 8 - 5 = 8 + (-5) = 3
Ç A
2
êêêêè 8 - (-5)
êê A) 3êB) -3êC) 13êD) -13
ü
êêêï8 - (-5) = 8 + (5) = 13
Ç C
3
êêêêè -8 - 5
êêïA) 13ë B) -13ë C) -3êD) 3
ü
êêêï-8 - 5 = -8 + (-5) = -13
Ç B
4
êêêêè -8 -(-5)
êê A) 3êB) 13êC) -13ë D) -3
ü
êêêï-8 -(-5) = -8 + (5) = -3
Ç D
5
êêêêë5 - 8
êêïA) -13ëB) 3ê C) -3êD) 13
ü
êêêè 5 - 8 = 5 + (-8) = -3
Ç C
6
êêêêè 5 - (-8)
êêïA) -3ë B) 13êC) 3ê D) -13
ü
êêêè5 - (-8) = 5 + (8) = 13
Ç B
7
êêêêè -5 - 8
êê A) -13êB) 3ê C) -3êD) 13
ü
êêêï-5 - 8 = -5 + (-8) = -13
Ç A
8
êêêêè-5 -(-8)
êê A) 3ê B) -13ë C) 13êD) -3
ü
êêêï-5 -(-8) = -5 + (8) = 3
Ç A
9
êë2è3êï17êï1êè 1êè17
êë─ - ─ë A) ──ëB) ──ëC) - ──ëD) - ──
êë3è4êï12ê 12êè12êè12
ü
êê 2è3ë 8è 9ë 8è ┌è9 ┐ê1
êê ─ - ─ï=ï── - ──ï=ï──ï+ │- ── │ =ï- ──
êê 3è4ë12è12ë12è └ï12 ┘ë 12
Ç C
10
êë5è1êï1ê 7êè 1êè 7
êè- ─ - ─ë A) ─ëB) ─ë C) - ─ë D) - ─
êë6è3êï2ê 6êè 2êè 6
ü
êê 5è1ë 5è2ê5è ┌ï2 ┐ë 7
êë - ─ - ─ï= - ─ - ─è= - ─ï+ │- ─ │ =ï- ─
êê 6è3ë 6è6ê6è └ï6 ┘ë 6
Ç D
11
êêêê -6.3 - (12.5)
êë A) 6.2ëB) -18.8ëC) -6.2ëD) 18.8
ü
êêè-6.3 - (12.5) = -6.3 + (-12.5) = -18.8
Ç B
12
êêêê -5 - (6 - 4)
êê A) -7êB) -15êC) 7ê D) 5
ü
è -5 - (6 - 4)ï=ï-5 - (6 + (-4))ï=ï-5 - (2)ï=ï-5 + (-2)ï=ï-7
Ç A
13
êë 7è┌ 3è 7 ┐êï3ê41ê11ê 7
êë── - │ ─ - ── │ë A) ─è B) ──è C) ──è D) ──
êë10è└ 8è10 ┘êï8ê40ê18ê18
üêê7ï┌ 3è 7 ┐è 28ï┌ 15è28 ┐
êêë── -│ ─ - ── │ =ï── -│ ── - ── │
êêë10ï└ 8è10 ┘è 40ï└ 40è40 ┘
êë28ï┌ 15ï┌ï28 ┐┐è 28ï┌ï13 ┐è 28è13è 41
êè= ── -│ ── +│- ── ││ =ï── -│- ── │ =ï── + ── =ï──
êë40ï└ 40ï└ï40 ┘┘è 40ï└ï40 ┘è 40è40è 40
Ç B
14
êêêï-2 + [(-6 - 8) - (-8 + 4)]
êê A) 8ê B) 12ê C) -8ê D) -12
üêêè-2 + [(-6 - 8) - (-8 + 4)]
êêêï= -2 + [(-6 + (-8)) - (-4)]
êêêï= -2 + [(-14) - (-4)]
êêêï= -2 + [-14 + (4)]
êêêï= -2 + [-10]
êêêï= -12
Ç D
15
êêê -8.5 - [(-4.9 + 1.3) - 2.6]
êêA) 7.8ë B) -2.3ë C) 4.7êD) -5.1
üêêè-8.5 - [(-4.9 + 1.3) - 2.6]
êêêï= -8.5 - [(-3.6) - 2.6]
êêêï= -8.5 - [(-3.6) + (-2.6)]
êêêï= -8.5 - [-6.2]
êêêï= -8.5 + (6.2)
êêêï= -2.3
Ç B
äïPlease express the following written phrases as numerical
êêexpressions and perform the operations.
âèThe sum of nine and minus seven is decreased by twelve.
êêêê [9 + (-7)] - 12
êêêë = [2] -12
êêêë =ï2 + (-12)
êêêë = -10
éS
ïPhrases such as "less than", "difference between", "subtracted from",
ïand "decreased by" indicate the subtraction operation.
ïPhrases such as "plus", "is added to", "more than", and "increased by"
ïindicate the addition operation.
16
êêêminus eight decreased by ten
êêA) 2ê B) -2ê C) -18êD) 18
ü
êêê -8 - 10 = -8 + (-10) = -18
Ç C
17
êêê the sum of 14 and -3 less 8
êê A) -3êB) 19ê C) -19êD) 3
ü
êè [14 + (-3)] - 8ï=ï[11] - 8ï=ï11 + (-8)ï=ï3
Ç D