Download Algebra 2-4 Notes

Multiplying Rational Numbers (2.4)
Multiplication Rule:
If there are an __________ number of negative signs in a multiplication problem, the product will be ________
If there are an __________ number of negative signs in a multiplication problem, the product will be ________
Find the product of each.
Ex. (-5)(7) = ______
Ex. (-9)(-4) = ______
Ex. (-8)(5)(-2) = ______
Ex. (-4)(-2)(-9) = ______
Remember how to multiply decimals.
Step 1—Use long multiplication to multiply, ignore decimal
Step 2—Count the number of numbers behind the decimal in both numbers.
Step 3—Starting at the back of your answer, mover the decimal to the left the number of spaces as the total
number of numbers behind the decimal
Step 4—Decide whether the answer is positive or negative
Find the product.
Ex. 3.2(-15) = ________
Ex -8(-2.6) = __________
Ex. -6 (4)(-3.5) = _________
How to multiply a whole number by a fraction
Step 1—Divide the whole number by the denominator
Step 2—Multiply the answer by the numerator
Step 3—Decide whether the answer is positive or negative
Find the product.
Ex. ½ (-24) = _______  _______ = _______ • ________ = _______
Ex. -¾ (-20) = _______  _______ = _______ • ________ = _______
Ex.
/3 (18) = _______  _______ = _______ • ________ = _______
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Properties of Addition and Multiplication
Property
In Words
Algebraic
Examples
Commutative Property
Of Addition
The order in which you add two
numbers does NOT change the sum
a + b= b + c
3+4=4+3
Commutative Property
of Multiplication
The order in which you multiply
two numbers does NOT change the
product
a ● b = b● a
5●8=8●5
Associative Property
of Addition
The way you group three numbers
in a sum does NOT change the sum
(a + b) + c = a + (b + c)
(3 + 2) + 7 = 3 + (2 + 7)
Associative Property
of Multiplication
The way you group three numbers
in a product does NOT change the
product
(a ● b)●c = a●(b ● c)
(3●5)●2 = 3●(5●2)
Identity Property
of Addition
The sum of any number and 0 is
itself. (0 is the additive identity
element)
a+0=0
or
0+a=0
9+0=9
or
0+9=9
Identity Property
of Multiplication
The product of any number and 1 is
itself (1 is the multiplicative identity
element)
a●1=a
or
1●a=a
13 ● 1 = 13
or
1 ● 13 = 13
Inverse Property
of Addition
The sum of a number and its
opposite is 0
a + (-a) = 0
7 + -7 = 0
Multiplication Property
of 0
The product of a number and 0 is 0
a●0=0
(-5)● (0) = 0
Multiplication Property
of -1
The product of a number and -1 is
the opposite of the number
a ● -1 = -a
8 ● (-1) = -8
or
-6● (-1) = 6
Identify the property illustrated
Ex. 7 + (-7) = 0 ___________________________
Ex. 9  (-1) = -9 ________________________
Ex. -12 + 0 = -12 __________________________
Ex. -20 + 20 = 0 ___________________________
Ex. (9 3)  4 = 9  (3  4) ___________________
Ex. (m + 7) + 14 = m + (7 + 14) ______________
Ex. x + 8 = 8 + x _____________________
Ex. 1  (-8) = -8 ___________________________
Find the product.
(Remember in multiplication number always goes first in front of the variable)
Ex. m (-5)(-4) =
Ex (4)(-5)(-2x) =
Ex. 2/3 (-12t) =
Ex. –m (-11) =
Ex. -4r (-3r) =
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