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- 216
- à 8.5 The Order of Operations On Rational Numbers
- äïPlease simplify the following expressions using the
- correct Order of Operations.
-
- #âêêï-3 ∙ 5ì - 2 ∙ ( 5 - 9 ) - 2
- #êêêè-3 ∙ 5ì - 2 ∙ ( -4 ) - 2
- êêêè-3 ∙ 25 - 2 ∙ ( -4 ) - 2
- êêêê -75 - (-8) - 2
- êêêêï-75 + 8 - 2
- êêêêè -67 - 2
- êêêêë -69
- #éSèIn order to simplify the expression, -3 ∙ 5ì - 2 ∙ ( 5 - 9)-2,
- it is necessary to agree on the following order of operations:
-
- êêï1)ïPerform operations in parençs first.
- êêï2)ïSimplify exponents.
- êêï3)ïPerform multiplication and division first come
- êêë first serve from left to right.
- êêï4)ïPerform addition and subtraction first come first
- êêë serve from left to right.
- (Note that division can come before multiplication if it occurs further
- to the left).
- #êêê -3 ∙ 5ì - 2 ∙ ( 5 - 9 ) - 2
-
- First, perform the operation in the parençs.
- #êêê-3 ∙ 5ì - 2 ∙ ( 5 + (-9)) - 2
- #êêêï-3 ∙ 5ì - 2 ∙ ( -4 ) - 2
-
- Next, simplify the exponent.
- êêê -3 ∙ 25 - 2 ∙ ( -4 ) - 2
-
- Then perform the multiplication from left to right.
- êêêë -75 - (-8) - 2
-
- Finally, perform the subtraction from left to right.
- êêêê-75 + 8 - 2
- êêêêï-67 - 2
- êêêêï-67 + (-2)
- êêêêë-69
-
- ï1
- êêêïSimplify,è4 - 10 ÷ 2.
-
-
- êA)ï2êëB)ï-1êè C)ï4êëD)ïå
-
-
- ü
- êêè1) First divide.ê 4 - 10 ÷ 2
- êêè2) Then subtract.êè4 - 5
- êêêêêê 4 + (-5)
- êêêêêêè-1
-
- ÇïB
- ï2
- êêêïSimplify,è-18 ÷ 2 + 5.
-
-
- êA)ï6êëB)ï5êëC)ï-4êè D)ïå
-
-
- ü
- êêï1) First divide.ê -18 ÷ 2 + 5
- êêï2) Then add.êê -9 + 5
- êêêêêêè-4
-
-
- ÇïC
- ï3
- êêêïSimplify,è6 + (-9) + 4
-
-
- êA)ï1êëB)ï2êëC)ï-5êè D)ïå
-
-
- ü
- ë 1) First add.êè6 + (-9) + 4
- ë 2) Then add again.êï-3 + 4
- êêêêê 1
-
-
- ÇïA
- ï4
- #êêêëSimplify,è8 - 3Ä.
-
-
- êA)ï-5êè B)ï6êëC)ï-19êèD)ïå
-
-
- ü
- #ë 1) Exponent first.êï8 - 3Ä
- ë 2) Then subtract.êè8 - 27
- êêêêè 8 + (-27)
- êêêêê-19
-
- ÇïC
- ï5
- êêë Simplify,è3 ∙ ( 6 - 10 ) - 3.
-
-
- êA)ï12êè B)ï-15êèC)ï-6êè D)ïå
-
- ü
- ë 1) Parençs first.ë3 ∙ ( 6 - 10 ) - 3
- êêêêè3 ∙ ( 6 + (-10)) - 3
- ë 2) Multiplication.êè 3 ∙ (-4) - 3
- ë 3) Then subtraction.êè - 12 - 3
- êêêêêï-12 + (-3)
- êêêêêë-15
- Ç B
- ï6
- êêêïSimplify,è5 - (-4) - 6.
-
-
- êA)ï3êëB)ï-9êè C)ï18êè D)ïå
-
-
- ü
- ë 1) First subtraction.ê5 - (-4) - 6
- êêêêê5 + 4 - 6
- ë 2) Then subtractionêë9 - 6
- êïagain.êêê9 + (-6)
- êêêêêè 3
- Ç A
- ï7
- êêêïSimplify,è12 ÷ 6 ∙ 2.
-
-
- êA)ï4êëB)ï6êëC)ï12êè D)ïå
-
-
- ü
- ë 1) First divide.êë12 ÷ 6 ∙ 2
- ë 2) Then multiply.êê2 ∙ 2
- êêêêêè 4
-
-
- Ç A
- ï8
- êêêèSimplify,è4 ∙ 8 ÷ 16.
-
-
- êA)ï8êëB)ï12êè C)ï2êëD)ïå
-
-
- ü
- ë 1) First multiply.êè4 ∙ 8 ÷ 16
- ë 2) Then divide.êê 32 ÷ 16
- êêêêêè 2
-
-
- Ç C
- ï9
- êêë Simplify,è12 ÷ 3 ∙ 8 + 6 - 5.
-
-
- êA)ï16êè B)ï33êè C)ï24êè D)ïå
-
-
- ü
- ë 1) First divide.êë12 ÷ 3 ∙ 8 + 6 - 5
- ë 2) Then multiply.êê4 ∙ 8 + 6 - 5
- ë 3) Then add.êêê32 + 6 - 5
- ë 4) Finally, subtract.êê38 - 5
- êêêêêë 38 + (-5)
- êêêêêêï33
- Ç B
- ï10
- #êêêïSimplify,è3 ∙ ( 6 - 2 )ì.
-
-
- êA)ï36êè B)ï24êè C)ï48êè D)ïå
-
-
- ü
- #ë 1) First subtract.êè3 ∙ ( 6 - 2 )ì
- #êêêêë3 ∙ ( 6 + (-2))ì
- #ë 2) Then the exponent.êï3 ∙ ( 4 )ì
- ë 3) Finally, multiply.êè3 ∙ 16
- êêêêêè 48
-
- Ç C
- ï11
- #êêïSimplify,è5 ∙ 2ì + 3 ∙ ( 4 + 1 ) - 17.
-
-
- êA)ï18êè B)ï22êè C)ï-6êè D)ïå
-
-
- ü
- #ë 1) First parençs.ë 5 ∙ 2ì + 3 ∙ ( 4 + 1 ) - 17
- #ë 2) Then exponent.êë 5 ∙ 2ì + 3 ∙ 5 - 17
- ë 3) Then multiplication.ê 5 ∙ 4 + 3 ∙ 5 - 17
- ë 4) Then addition.êêè20 + 15 - 17
- ë 5) Finally, subtraction.êë 35 - 17
- êêêêêê35 + (-17)
- êêêêêêè18
- Ç A
- ï12
- #êêSimplify,è18 - 4 ∙ 8 + 3ì - (-16) ÷ (-8).
-
-
- êA)ï14êè B)ï-7êè C)ï-16êèD)ïå
-
-
- ü
- #ë 1) First the exponent.ë18 - 4 ∙ 8 + 3ì - (-16) ÷ (-8)
- ë 2) Then multiplication.ë18 - 4 ∙ 8 + 9 - (-16) ÷ (-8)
- ë 3) Then division.êë 18 - 32 + 9 - (-16) ÷ (-8)
- ë 4) Then subtraction.êë 18 - 32 + 9 - 2
- êêêêêè18 + (-32) + 9 - 2
- ë 5) Then addition.êêë-14 + 9 - 2
- ë 6) Finally, subtraction.êê -5 - 2
- êêêêêêï-5 + (-2)
- êêêêêêë-7
- Ç B
-