Download 1.3 Multiplying and Dividing Integers

2.5-2.6 Multiplying and
Dividing Integers
Multiplying Integers
 Multiplication of 2 integers can be described as
repeated addition or subtraction.
 The product of an integer and zero is 0.
 The product of 2 integers with like signs is positive.
 The product of 2 integers with unlike signs is
negative.
 To find the product of more than 2 numbers, first
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find the product of their absolute values. If there is
an even number of negative factors, then the
product is positive. If there is an odd number of
negative factors, then the product is negative.
Examples:
a. 4 (10)
d. 3 (-12)
b. -6 9
e. -12 0
c. (-5)(-7)
f. (-2)(8)(-3)(-1)
Example: Volume of a box
 Find the volume:
15 in
5 in
12 in
Dividing Integers
 Division can be expressed in terms of multiplication.
 The result of dividing one integer by another is called
the quotient of the integers.
a
b
a is called dividend and numerator
b is called divisor and denominator
 Zero divided by a nonzero integer is 0, whereas a
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nonzero integer divided by zero is undefined.
The quotient of 2 nonzero integers with like signs
is positive.
The quotient of 2 nonzero integers with unlike
signs is negative.
Examples:
-42
-105
a. -6
d.
7
b. 36
e. -97
-9
0
c.
0
-13
Example: Stock Purchase
 On Monday you bought $500 worth of stock in a
company. The following table shows the gains and
losses.
Monday
Wednesday Thursday
Gained $15 Lost $18
Lost $23
Friday
Gained $10
 a) What is the value of the stock at the close of Wednesday?
 b) What about at the end of the week?
 c) What would the total loss have been if Thursday’s loss had
occurred each day of the week?
 d. What is the average daily gain (or loss)?
Factors and Prime Numbers
 If a and b are positive integers, then a is a factor (or
divisor) of b if and only if there is a positive integer c such
that a c = b
 The concept of factors allows you to classify positive
integers into 3 groups: prime numbers, composite numbers
and the number 1.
 A positive integer greater than 1 with no factors other than
itself and 1 is called a prime number, or simply prime.
 A positive integer greater than 1 with more than 2 factors
other is called a composite number, or simply composite.
Examples:
 Write the prime factorization for each number:
 a) 84
 b) 78
 c) 133
 d) 43
Divisibility Tests
 A number is divisible by 2 if it is even
 A number is divisible by 3 if the sum of its
digits is divisible by 3.
 A number is divisible by 9 if the sum of its
digits is divisible by 9.
 A number is divisible by 5 if its units digit is 0
or 5.
 A number is divisible by 10 if its units digit is 0.