Dividing Integers

• LEARNING TARGET– I can divide positive and negative numbers.

• FOCUS QUESTION– How are the rules for multiplying integers and

dividing integers connected? Why?

Dividing Integers

I can divide positive and negative numbers.

Division Rules• a POSITIVE divided by POSITIVE is POSITIVE

(+) ÷ (+) = (+)

• a NEGATIVE divided by NEGATIVE is POSITIVE(-) ÷ (-) = (+)

• a POSITIVE divided by NEGATIVE is NEGATIVE(+) ÷ (-) = (-)

• a NEGATIVE divided by POSITIVE is NEGATIVE(-) ÷ (+) = (-)

EXAMPLE 1

=

c. 36–9 =

=d. 0–7

a. – 40–8

b. –142

Dividing Integers

=

EXAMPLE 1

Same sign, so quotient is positive.

= –7 Different signs, so quotient is negative.

c. 36–9 = –4 Different signs, so quotient is negative.

= 0d. 0–7

a. – 40–8

b. –142

Dividend is 0 so quotient is 0.

Dividing Integers

= 5

Practice: • Perform the indicated operation.

1. 21 ÷ -7 =

2. 35 ÷ 5 =

3. 64 ÷ -16 =

4. -88 ÷ 11 =

5. I -81 I ÷ I 9 I =

6. -10 ÷ 0 =

Practice: • Perform the indicated operation.

1. 21 ÷ -7 =

2. 35 ÷ 5 =

3. 64 ÷ -16 =

97

-4

-8-3

Undefined

4. -88 ÷ 11 =

5. I -81 I ÷ I 9 I =

6. -10 ÷ 0 =

Dividing with Zero

0 ÷ -7 = 0

-7 0

Dividing nothing into 7 groups means everyone gets nothing.

-10 ÷ 0 = undefined

0 -10

There is no way to put -10 into zero groups so it is undefined.

EXAMPLE 2 Finding a Mean

One of the coldest places on Earth is the Russian town of Verkhoyansk, located near the Arctic Circle. Find the mean of the average high temperatures during winter in Verkhoyansk. Use the data in the table.

Temperatures

EXAMPLE 2

SOLUTION

STEP 1 Find the sum of the temperatures.

–41 + (–40 ) + (–48 ) + (–18 )

STEP 2 Divide the sum by the number of temperatures.

–1474

ANSWER The mean of the temperatures is about -37oF.

Finding a Mean

= –147

= –36.75

GUIDED PRACTICE for Examples 2 and 3

Find the mean of the data.

1. –16, 17, 8, –23, –31

GUIDED PRACTICE for Examples 2 and 3

Find the mean of the data.

1. –16, 17, 8, –23, –31

SOLUTION

STEP 1 Find the sum of the values.

–16 + 17 + 8 + (–23) + (–31)

STEP 2 Divide the sum by the number of values.

–455

ANSWER The mean of the data is about –9.

= –45

= –9

GUIDED PRACTICE for Examples 2 and 3

Find the mean of the data.

2. 0, –4, –10, 4, 11, –9, –13

Find the mean of the data.

GUIDED PRACTICE for Examples 2 and 3

Find the mean of the data.

2. 0, –4, –10, 4, 11, –9, –13

SOLUTION

STEP 1 Find the sum of the values.

0 + (–4) + (–10) + 4 + 11 + (–9) + (–13)

STEP 2 Divide the sum by the number of values.

–217

ANSWER The mean of the data is about –3.

= –3

= –21

Find the mean of the data.

Order of Operations

A set of rules to simplify a numerical expression.

1.Evaluate expressions inside grouping symbols (brackets and parenthesis)

2.Multiply and divide from left to right

3.Add and subtract from left to right

EXAMPLE 3

Evaluating Expressions

Evaluate the expression when a = –24, b = 8, and c = –4.

a. ab

=–24 8

b. ab c

= –192 –4

= –24 8–4

EXAMPLE 3

Evaluating Expressions

Evaluate the expression when a = –24, b = 8, and c = –4.

a. ab

=–24 8

Substitute values.

Different signs, so quotient is negative.

b. ab c

Substitute values.

Multiply.= –192 –4

Same sign, so quotient is positive.= 48

= –24 8–4

= –3

Daily Homework Quiz For use after Lesson 2.5

Find the quotient.Evaluate the expression when k = – 36, m = 6, and n = 3.

1. mnk 2. m + n

k 3. m2 + 4n2

2k

Daily Homework Quiz For use after Lesson 2.5

Find the quotient.Evaluate the expression when k = – 36, m = 6, and n = 3.

1. mnk

ANSWERS 12

–

2. m + nk 3. m2 + 4n2

2k

ANSWERS – 4 ANSWERS – 1

Quick Write

How are the rules for multiplying integers and dividing integers connected? Why?