199 
… 2.4‹The multiplication operation.
„‹Please perform the following multiplication operations.
ƒS
ˆˆˆˆ (4)(5) = 20
ˆˆˆˆ(-3)(4) = -12
ˆˆˆ‰ (-2)(-7) = 14
ˆˆˆˆ(6)(-5) = -30
‚S


‹To multiply two numbers with the same sign, just multiply them and
‹attach a plus sign to the product.
ˆˆˆˆ (3)(5) = 15
ˆˆˆˆ (-4)(-3) = 12

‹To multiply two numbers with unlike signs, multiply the two numbers
‹and attach a minus sign.
ˆˆˆˆ (4)(-2) = -8
ˆˆˆˆ (-3)(6) = -18
 1
ˆˆˆˆŠ (6)(8)



ˆˆŠA) -48‰B) 14‰C) 48‰D) -14



ˆˆˆˆ (6)(8) = 48
€ C
 2
ˆˆˆˆŠ (-7)(4)



ˆˆ‰A) 28‰ B) 11‰C) -3‰D) -28
ˆˆˆ (-7)(4) = -28
€ D
 3

ˆŠ Ϊ‹2 ΏΪŠ9 Ώˆ‹3ˆ11ˆ18ˆ‹11
ˆŠ ³- Δ ³³- ΔΔ ³‰ A) Ċ B) ΔĊ C) ΔĊ D) - ΔΔ
ˆŠ ΐ‹3 Ωΐ‹14 و‹7ˆ17ˆ47ˆ‹17



ˆŠ Ϊ‹2 ΏΪŠ9 Ώ‰Ϊ 2 ΏΪ‹9 Ώ‰Ϊ 1 ΏΪ 3 Ώ‰3
ˆŠ ³- Δ ³³- ΔΔ ³‹=‹³ Δ ³³ ΔΔ ³‹=‹³ Δ ³³ Δ ³‹=‹Δ
ˆŠ ΐ‹3 Ωΐ‹14 Ω‰ΐ 3 Ωΐ 14 Ω‰ΐ 1 Ωΐ 7 Ω‰7
€ A
 4
ˆˆˆˆ(6 - 8)ω(4 + 3)



ˆˆŠ A) 6ˆB) -14Š C) -24Š D) 17



ˆ(6 - 8)ω(4 + 3)‹=‹(6 + (-8))ω(4 + 3)‹=‹(-2)ω(7)‹=‹-14
€ B
 5
ˆˆˆ‰(-6 - 5)ω(-3) + 7



ˆˆŠ A) -6‰ B) 13‰C) -12Š D) 40
ˆˆˆ(-6 - 5)ω(-3) + 7

ˆˆˆ‰ = (-6 + (-5))ω(-3) + 7
ˆˆˆ‰ = (-11)ω(-3) + 7
ˆˆˆ‰ = 33 + 7
ˆˆˆ‰ = 40
€ D
 6
ˆˆˆˆ‹6(-4) - (-8)



ˆˆŠ A) 12‰ B) -16Š C) -8‰D) 16



ˆŠ6(-4) - (-8)‹=‹(-24) - (-8)‹=‹(-24) + (8)‹=‹-16
€ B
 7
ˆˆˆŠ (-8 - 3)(-4) - (-7)



ˆˆŠ A) -42‰B) 17‰C) -23Š D) 51
ˆˆˆ(-8 - 3)(-4) - (-7)

ˆˆˆŠ = (-8 + (-3))(-4) - (-7)
ˆˆˆŠ = (-11)(-4) - (-7)
ˆˆˆŠ = 44 - (-7)
ˆˆˆŠ = 44 + (7)
ˆˆˆŠ = 51
€ D
„‹Please evaluate the following expressions if x = 3,
ˆˆy = -5, and z = 7.
ƒˆˆˆ‹(z - y) + x
ˆˆˆˆ= (7 - (-5)) + 3
ˆˆˆˆ= (7 + (5)) + 3
ˆˆˆˆ= (12) + 3
ˆˆˆˆ= 15
‚S


Š To evaluate an expression like 2x - 3y if x = 3 and y = -5, just
Š substitute the numbers in for the letters and simplify.

ˆˆˆˆŠ2x - 3y
ˆˆˆˆ = 2(3) - 3(-5)
ˆˆˆˆ = 6 -(-15)
ˆˆˆˆ = 6 + 15
ˆˆˆˆ = 21
 8
ˆˆˆˆ 2x - (y + z)



ˆˆŠA) 8ˆB) -6ˆC) 4ˆD) 12
ˆˆˆŠ2x - (y + z)

ˆˆˆˆ= 2(3) - (-5 + 7)
ˆˆˆˆ= 6 - (2)
ˆˆˆˆ= 6 + (-2)
ˆˆˆˆ= 4
€ C
 9
ˆˆˆˆ(x - y)(2z - y)



ˆˆ A) 129‰B) 86ˆC) 152‰D) -86
ˆˆˆ (x - y)(2z - y)

ˆˆˆ‰= (3 - (-5))(2ω7 - (-5))
ˆˆˆ‰= (3 + 5)(14 + (5))
ˆˆˆ‰= (8)(19)
ˆˆˆ‰= 152
€ C
 10
ˆˆˆˆ‹2(x + z) -21



ˆˆ A) -1‰ B) 2ˆ C) 23‰ D) 42
ˆˆˆŠ2(x + z) - 21

ˆˆˆˆ= 2(3 + 7) = 21
ˆˆˆˆ= 2(10) -21
ˆˆˆˆ= 20 -21
ˆˆˆˆ= -1
€ A
„‹Please express the folowing written phrases as numerical
ˆˆexpressions and perform the operations.
ƒŠ The product of eight and the difference between negative
ˆˆˆ‰ seven and four.

ˆˆˆˆ‹8(-7 - 4)
ˆˆˆˆ= 8(-7 + (-4)
ˆˆˆˆ= 8(-11)
ˆˆˆˆ= -88
‚S




‹Phrases such as 'times', 'the product of', 'twice', and 'percent of'
‹indicate the multiplication operation.
 11
ˆŠ eight subtracted from the product of negative five and
ˆˆˆˆŠ fourteen


ˆˆA) -78ˆB) 46ˆC) 84ˆD) -68

ˆˆˆˆ(-5)(14) - 8

ˆˆˆˆ= (-70) - 8
ˆˆˆˆ= -70 + (-8)
ˆˆˆˆ= -78
€ A
 12Š twice the difference between negative six and
ˆˆˆ‰ negative fifteen

ˆˆˆˆˆˆ27ˆ‰12
ˆˆA) -27ˆB) 18ˆC) ΔĈD) - ΔΔ
ˆˆˆˆˆˆ 4ˆ‰15

ˆˆˆˆ‹2(-6 - (-15)

ˆˆˆˆ‹= 2(-6 + 15)
ˆˆˆˆ‹= 2(9)
ˆˆˆˆ‹= 18
€ B