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Find each of the following products: a) 3 × (-1) b) (-1) × 225 c) (-21) × (-30) d) (-316) × (-1) e) (-15) × 0 × (-18) f) (-12) × (-11) × (10) g) 9 × (-3) × (-6) h) (-18) × (-5) × (-4)
Mathematics
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Step-by-step solution
18 stepsHere are the solutions to the problems.
1. Find each of the following products:
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a)
The product of a positive and a negative integer is negative.
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b)
The product of a negative and a positive integer is negative.
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c)
The product of two negative integers is positive.
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d)
The product of two negative integers is positive.
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e)
Any number multiplied by zero is zero.
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f)
Multiply the first two numbers.
$$ (-12) \times (-11) = 132 $$Multiply the result by the third number.
$$ 132 \times 10 = 1320 $$ $$ \boxed{1320} $$- g)
Multiply the first two numbers.
$$ 9 \times (-3) = -27 $$Multiply the result by the third number.
$$ (-27) \times (-6) = 162 $$ $$ \boxed{162} $$- h)
Multiply the first two numbers.
$$ (-18) \times (-5) = 90 $$Multiply the result by the third number.
$$ 90 \times (-4) = -360 $$ $$ \boxed{-360} $$- i)
Multiply the first two numbers.
$$ (-1) \times (-2) = 2 $$Multiply the result by the third number.
$$ 2 \times (-3) = -6 $$Multiply the result by the fourth number.
$$ (-6) \times 4 = -24 $$ $$ \boxed{-24} $$- j)
Multiply the first two numbers.
$$ (-3) \times (-6) = 18 $$Multiply the result by the third number.
$$ 18 \times (-2) = -36 $$Multiply the result by the fourth number.
$$ (-36) \times (-1) = 36 $$ $$ \boxed{36} $$2. Verify the following:
- a)
Evaluate the Left Hand Side (LHS).
$$ 18 \times [7 + (-3)] = 18 \times [7 - 3] = 18 \times 4 = 72 $$Evaluate the Right Hand Side (RHS).
$$ [18 \times 7] + [18 \times (-3)] = 126 + (-54) = 126 - 54 = 72 $$Compare LHS and RHS.
$$ 72 = 72 $$ The equation is verified.- b)
Evaluate the Left Hand Side (LHS).
$$ (-21) \times [(-4) + (-6)] = (-21) \times [-10] = 210 $$Evaluate the Right Hand Side (RHS).
$$ [(-21) \times (-4)] + [(-21) \times (-6)] = 84 + 126 = 210 $$Compare LHS and RHS.
$$ 210 = 210 $$ The equation is verified.
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