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

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.

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

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

b. ab c

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?

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 =