2-4 Multiplying and Dividing Integers
Preview
Warm Up
California Standards
Lesson Presentation
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2-4 Multiplying and Dividing Integers
Warm Up
Simplify each expression.
1. 17  5
85
2. 8  34
272
3. 4  86
344
4. 20  850
17,000
5. 275 ÷ 5
55
6. 112 ÷ 4
28
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2-4 Multiplying and Dividing Integers
California
Standards
NS2.3 Solve addition, subtraction,
multiplication, and division problems,
including those arising in concrete situations,
that use positive and negative integers and
combinations of these operations.
Also covered: AF1.4
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2-4 Multiplying and Dividing Integers
You can think of multiplication as repeated
addition.
3  2 = 2 + 2 + 2 = 6 and
3  (–2) = (–2) + (–2) + (–2) = –6
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2-4 Multiplying and Dividing Integers
Additional Example 1A: Multiplying Integers Using
Repeated Addition
Use a number line to find the product.
–7  2
–7  2 = 2  (–7)
Use the Commutative
Property.
Think: Start at 0.
Add –7 two times.
+ (–7)
-14 -13 -12 -11 -10 -9 -8 -7
–7  2 = –14
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+ (–7)
-6
-5
-4
-3 -2 -1
0
2-4 Multiplying and Dividing Integers
Additional Example 1B: Multiplying Integers Using
Repeated Addition
Use a number line to find the product.
–8  3
–8  3 = 3  (–8)
Use the Commutative
Property.
Think: Start at 0.
Add –8 three times.
+ (–8)
+ (–8)
+ (–8)
–24–23–22–21–20–19–18–17-16-15-14-13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
–8  3 = –24
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2-4 Multiplying and Dividing Integers
Check It Out! Example 1A
Use a number line to find the product.
2  (–3)
Think: Start at 0.
Add –3 two times.
+ (–3)
-14 -13 -12 -11 -10 -9 -8 -7
2  (–3) = –6
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-6
-5
-4
+ (–3)
-3 -2 -1
0
2-4 Multiplying and Dividing Integers
Check It Out! Example 1B
Use a number line to find the product.
–5  3
–5  3 = 3  (–5)
+ (–5)
Use the Commutative
Property.
Think: Start at 0.
Add –5 three times.
+ (–5)
-15 -14 -13 -12 -11 -10 -9 -8 -7
–5  3 = –15
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+ (–5)
-6
-5
-4 -3 -2 -1
2-4 Multiplying and Dividing Integers
Remember!
Inverse operations “undo” each other. Multiplying
by a number is the inverse operation of dividing
by that number.
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2-4 Multiplying and Dividing Integers
The patterns below suggest that when the signs
of integers are different, their product or
quotient is negative. The patterns also suggest
that the product or quotient of two negative
integers is positive.
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2-4 Multiplying and Dividing Integers
MULTIPLYING AND DIVIDING INTEGERS
If the signs are:
Your answer will be:
the same
positive
different
negative
Holt CA Course 1
2-4 Multiplying and Dividing Integers
Additional Example 2: Multiplying Integers
Find each product.
A. –6  (–5)
–6  (–5)
30
Both signs are negative, so
the product is positive.
B. –4  7
–4  7
–28
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The signs are different, so
the product is negative.
2-4 Multiplying and Dividing Integers
Check It Out! Example 2
Find each product.
A. –2  (–8)
–2  (–8)
16
Both signs are negative, so
the product is positive.
B. –3  5
–3  5
–15
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The signs are different, so
the product is negative.
2-4 Multiplying and Dividing Integers
Additional Example 3: Dividing Integers
Find each quotient.
A. 35 ÷ (–5)
35 ÷ (-5)
–7
The signs are different, so the
quotient is negative.
B. –48 ÷ 6
–48 ÷ (6)
–8
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The signs are different, so the
quotient is negative.
2-4 Multiplying and Dividing Integers
Check It Out! Example 3
Find each quotient.
A. –12 ÷ 3
–12 ÷ 3
–4
The signs are different, so the
quotient is negative.
B. –25 ÷ (–5)
–25 ÷ –5
5
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The signs are the same, so the
quotient is positive.
2-4 Multiplying and Dividing Integers
Additional Example 4: Weather Application
At 7:00, the temperature was 14ºF. As a cold front
approached, the temperature dropped 6ºF per
hour over the next 4 hours. What was the
temperature at 11:00?
Subtract the total number of degrees to find out
what the temperature was at 11:00.
14 – 6  4
Multiply 6 by 4 to find the total
number of degrees; then subtract it
from the original temperature of 14ºF.
14 – 24
Use the order of operations.
Multiply first. Then subtract.
–10
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The temperature at 11:00 was –10F.
2-4 Multiplying and Dividing Integers
Check It Out! Example 4
At 4:00, the train was 20 miles from the station. The
train traveled 18 miles away from the station per
hour over the next 6 hours. How far was the train
from the station at 10:00?
Add the total number of miles from the train station
to find out how far the train was at 10:00.
20 + 18  6
20 + 108
128
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Multiply 18 by 6 to find the total
number of miles; then add it to the
original distance of 20 miles.
Use the order of operations.
Multiply first. Then add.
The train was 128 miles from the station
at 10:00.
2-4 Multiplying and Dividing Integers
Lesson Quiz
Use a number line to find the product.
1. –8  2
–16
Find each product or quotient.
2. –3  5  (–2)
30
3. –75 ÷ 5
–15
4. –110 ÷ (–2)
55
5. The temperature in Bar Harbor, Maine, was –3°F.
It then dropped 3 degrees per hour over the next
3 hours. What was the temperature then?
–12°F
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