Holt CA Course 1

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

Holt CA Course 1

2-4 Multiplying and Dividing Integers

Use a number line to find the product.

Additional Example 1A: Multiplying Integers Using Repeated Addition

–7 2

+ (–7) + (–7)

–7 2 = 2 (–7)Think: Start at 0.Add –7 two times.

-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

–7 2 = –14

Use the Commutative Property.

Holt CA Course 1

2-4 Multiplying and Dividing Integers

Use a number line to find the product.

Additional Example 1B: Multiplying Integers Using Repeated Addition

–8 3–8 3 = 3 (–8)

–8 3 = –24

Think: Start at 0. Add –8 three times.

Use the Commutative Property.

+ (–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

Holt CA Course 1

2-4 Multiplying and Dividing Integers

Use a number line to find the product.

Check It Out! Example 1A

2 (–3)

+ (–3) + (–3)

-14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0

Think: Start at 0.Add –3 two times.

2 (–3) = –6

Holt CA Course 1

2-4 Multiplying and Dividing Integers

Use a number line to find the product.

Check It Out! Example 1B

–5 3–5 3 = 3 (–5)

–5 3 = –15

Think: Start at 0. Add –5 three times.

Use the Commutative Property.

+ (–5) + (–5) + (–5)

-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1

Holt CA Course 1

2-4 Multiplying and Dividing Integers

Inverse operations “undo” each other. Multiplying by a number is the inverse operation of dividing by that number.

Remember!

Holt CA Course 1

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.

Holt CA Course 1

2-4 Multiplying and Dividing Integers

MULTIPLYING AND DIVIDING INTEGERSMULTIPLYING AND DIVIDING INTEGERS

If the signs are: Your answer will be:the samedifferent

positivenegative

Holt CA Course 1

2-4 Multiplying and Dividing Integers

Find each product.

Additional Example 2: Multiplying Integers

A. –6 (–5)

–6 (–5) Both signs are negative, sothe product is positive.30

B. –4 7

–4 7 The signs are different, sothe product is negative.–28

Holt CA Course 1

2-4 Multiplying and Dividing Integers

Find each product.

Check It Out! Example 2

A. –2 (–8)

–2 (–8) Both signs are negative, sothe product is positive.16

B. –3 5

–3 5 The signs are different, sothe product is negative.–15

Holt CA Course 1

2-4 Multiplying and Dividing Integers

Find each quotient.

Additional Example 3: Dividing Integers

A. 35 ÷ (–5)

35 ÷ (5)

–7

B. –48 ÷ 6

–48 ÷ (6)

–8

The signs are different, so the quotient is negative.

The signs are different, so the quotient is negative.

Holt CA Course 1

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

The signs are the same, so the quotient is positive.

Holt CA Course 1

2-4 Multiplying and Dividing Integers

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?

Additional Example 4: Weather Application

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

Subtract the total number of degrees to find out what the temperature was at 11:00.

Use the order of operations. Multiply first. Then subtract.–10 The temperature at 11:00 was –10F.

Holt CA Course 1

2-4 Multiplying and Dividing Integers

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?

Check It Out! Example 4

20 + 18 6 Multiply 18 by 6 to find the total number of miles; then add it to the original distance of 20 miles.

20 108

Add the total number of miles from the train station to find out how far the train was at 10:00.

Use the order of operations. Multiply first. Then add.128 The train was 128 miles from the station at 10:00.

Holt CA Course 1

2-4 Multiplying and Dividing Integers Lesson QuizUse a number line to find the product.

1. –8 2

Find each product or quotient.2. –3 5 (–2) 3. –75 ÷ 5 4. –110 ÷ (–2)

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?