Download multiplying integers

11-6 Multiplying Integers
Warm Up
Find each product.
1.
3.
5.
7.
8•4
3•9
80 • 6
40 • 90
32
27
480
3,600
2.
4.
6.
8.
7 • 12
6•5
50 • 6
20 • 700
84
30
300
14,000
11-6 Multiplying Integers
Problem of the Day
Catherine has $14.00 and earns $12.00
for each lawn she mows. If she mows 4
lawns and buys 5 DVDs that cost
$11.95 each, including tax, how much
money does she have left?
$2.25
11-6 Multiplying Integers
Sunshine State Standards
Preview of MA.7.A.3.1 Use and justify the
rules for…multiplying…integers.
Preview of MA.7.A.3.2
…Multiply…integers,…including solving
problems in everyday contexts.
11-6 Multiplying Integers
Numbers
3•2
–3 • 2
Words
3 groups of 2
the opposite of
3 groups of 2
Addition
2+2+2
–(2 + 2 + 2)
Product
6
–6
11-6 Multiplying Integers
Numbers
Words
Addition
Product
3 • (–2)
–3 • (–2)
3 groups of –2
the opposite of
3 groups of –2
(–2) + (–2) + (–2) –[(–2) + (–2) + (–2)]
–6
6
11-6 Multiplying Integers
Additional Example 1: Multiplying Integers
Find each product.
A. 5 • 2
5 • 2 = 10
Think: 5 groups of 2.
B. 4 • (–5)
4 • (–5) = –20
Think: 4 groups of –5.
Remember!
To find the opposite of a number, change the sign.
The opposite of 6 is –6. The opposite of –4 is 4.
11-6 Multiplying Integers
Additional Example 1: Multiplying Integers
Find each product.
C. –3
•
2
–3
•
2 = –6
D. –2
•
(–4)
–2
•
(–4) = 8 Think: the opposite of 2 groups of –4.
Think: the opposite of 3 groups of 2.
11-6 Multiplying Integers
Check It Out: Example 1
Find each product.
A. 3 • 4
3 • 4 = 12
Think: 3 groups of 4.
B. 2 • (–7)
2 • (–7) = –14
Think: 2 groups of –7.
11-6 Multiplying Integers
Check It Out: Example 1
Find each product.
C. –5
•
3
–5
•
3 = –15 Think: the opposite of 5 groups of 3.
D. –4
•
(–6)
–4
•
(–6) = 24 Think: the opposite of 4 groups of –6.
11-6 Multiplying Integers
MULTIPLYING INTEGERS
If the signs are the same, the product is positive.
4
•
3 = 12
–6
•
(–3) = 18
If the signs are different, the product is negative.
–2 • 5 = –10
7 • (–8) = –56
The product of any number and 0 is 0.
0
•
9=0
(–12)
•
0=0
11-6 Multiplying Integers
Additional Example 2: Evaluating Integer
Expressions
Evaluate –7x for each value of x.
A. x = –3
–7x
Write the expression.
–7 • (–3) Substitute –3 for x.
The signs are the same, so the answer
21
is positive.
B. x = 5
–7x Write the expression.
–7 • 5 Substitute 5 for x.
–35 The signs are different, Remember!
so the answer is
–7x means –7 • x.
negative.
11-6 Multiplying Integers
Check It Out: Example 2
Evaluate –4y for each value of y.
A. y = – 2
–4y
Write the expression.
–4 • (–2) Substitute –2 for y.
8
The signs are the same, so the answer
is positive.
B. y = 7
–4y
–4 • 7
–28
Write the expression.
Substitute 7 for y.
The signs are different, so the answer
is negative.