2.4 multiplication integers ws day 1
22
Before the bell rings... Have your covered textbook with you. 1. 3/8 ÷ 2/3 = 2. 182 – 97 + 1306 – 110 =
Transcript of 2.4 multiplication integers ws day 1
Before the bell rings... Have your covered textbook with you.
1. 3/8 ÷ 2/3 =
2. 182 – 97 + 1306 – 110 =
Before the bell rings... Have your covered textbook with you.
1. 3/8 ÷ 2/3 =
2. 182 – 97 + 1306 – 110 =
9/16
1281
Multiplication of Integer Numbers
Section 2.4
P. 73 - 76
Multiplication When you first learned multiplication, your book
had pictures of equal number of objects in several rows.
You learned that 3 4 meant “three fours.” 3 4 = 4 + 4+ 4 Thus a Pos x Pos = Pos #
Negative Numbers
3 (-4) means “three negative fours” 3 (-4) = (-4)+(-4)+(-4) = -12 Using the addition rules you get -12
Thus a Pos x Neg = Neg #
Three Ways
There are three ways to write multiplication.
3 x 4 or 3(4) or
With variables
4y ab
3 4
Commutative
Remember: multiplication is COMMUTATIVE. (order does not matter)
3 4 = 4 3 and 3 (-4)= - 4 3
The same is true with pos. and neg. #’s
Multiplication Properties
Property of ZeroThe product of a number and zero = 0 -4 x 0 = 0 a (0) = 0
Identity Property of MultiplicationThe product of a number and the
multiplicative identity (1) is the number.(5) (1) = 5 (-27) (1) = -27
Multiplication Rules:
a POSITIVE times a POSITIVE is POSITIVE
a NEGATIVE times a NEGATIVE is POSITIVE
a POSITIVE times a NEGATIVE is NEGATIVE
a NEGATIVE times a POSITIVE is NEGATIVE
Practice: Perform the indicated operation.
4 6=4(-6)=-6 x 4=-6 x -4=
243 1=243 (-1)=-1 x 243=-1 x -243=
Practice: Perform the indicated operation.
4 6=4(-6)=-6 x 4=-6 x -4=
24
-24
-24
24
243243 1=243 (-1)=-1 x 243=-1 x -243=
-243
-243
243
GUIDED PRACTICE for Examples 1, 2 and 3
2. –1(4)
4. –6(–11)
5. –1(–12)(–9)= –108
Different signs, so product is negative.
Same sign, so product is positive.
Product of an integer and 0 is 0.
Multiply from left to right.
Multiply.
Find the product.
= –4 identity
3. 7(0) = 0 property of zero
= 66
= 12(–9)
If there are an even number of negative signs, the answer is __________.
If there are an odd number of negative signs, the answer is __________.
If there are an even number of negative signs, the answer is __________.
If there are an odd number of negative signs, the answer is __________.
positive
negative
EXAMPLE 2
a. –1(6)
b. –8(–2)
c. –15(0)
d. 4(–10)(–12)= 480
Different signs, so product is negative.
Same sign, so product is positive.
Product of an integer and 0 is 0.
Multiply from left to right.
Multiply.
Multiplying Two or More Integers
= –6 identity
= 16
= 0 property of zero
= –40(–12)
Evaluate the expressionEvaluate the expression
( 3)( 6) 2
4 12 2
( 3)( 6) 2
4 12 2
=
=
Evaluate the expressionEvaluate the expression
( 3)( 6) 2
4 12 2
( 3)( 6) 2
4 12 2
= 36
= 96
EXAMPLE 1 Multiplying Integers
Diving
A diver is swimming downward to explore a coral reef. The diver’s depth is changing by –2 feet per second. The diver started at sea level. What is the diver’s position relative to sea level after 10 seconds? after 30 seconds?
a. To find the diver’s position relative to sea level after 10 seconds, use the distance formula d = rt.
d = rt Write the distance formula.
d = –2 (10) Substitute –2 for r and 10 for t.
d = –20 Different signs, so product is negative.
SOLUTION
EXAMPLE 1 Multiplying Integers
d = rt Write the distance formula.
Substitute –2 for r and 30 for t.
Different signs, so product is negative.
The diver’s position relative to sea level is –20 feet.
ANSWER
b. Find the diver’s position relative to sea level after30 seconds.
d (30)–2 =
d = – 60
EXAMPLE 1 Multiplying Integers
d = rt Write the distance formula.
Substitute –2 for r and 30 for t.
Different signs, so product is negative.
The diver’s position relative to sea level is –20 feet.
ANSWER
ANSWER
The diver’s position relative to sea level is –60 feet.
b. Find the diver’s position relative to sea level after30 seconds.
d (30)–2 =
d = – 60
Another way to think about multiplication
The product of two integers with the same sign is POSITIVE.
The product of two integers with different signs is NEGATIVE.
Assignment: P 75 #1 - 23, 36 – 40
NO CALCULATORS!!!
Problems 3-22 there are 6 problems that will have a property listed with the answer to the multiplication problem.
Identity or property of zero
