The document discusses dividing integers and their rules: - There are four rules for dividing integers based on the signs of the numbers: two positives or negatives give a positive, opposite signs give a negative. - Examples are provided to demonstrate applying the rules. - The mean, or average, of a data set is calculated by summing the values and dividing by the number of values. - Order of operations must be followed when evaluating expressions.

1. 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?

2. Dividing Integers
I can divide positive and negative
numbers.

3. 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
(-) ÷ (+) = (-)

4. EXAMPLE 1
=
a. – 40
–8
b. –14
2
c. 36
–9 =
d. 0 =
–7
Dividing Integers
=

5. EXAMPLE 1
Dividing Integers
Same sign, so quotient is positive.
= –7 Different signs, so quotient is negative.
a. – 40
–8
b. –14
2
c. 36
–9 = –4 Different signs, so quotient is negative.
d. 0 = 0
–7
Dividend is 0 so quotient is 0.
= 5

6. 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 =

7. Practice:
• Perform the indicated operation.
1. 21 ÷ -7 =
2. 35 ÷ 5 =
3. 64 ÷ -16 =
-8
-3
4. -88 ÷ 11 =
5. I -81 I ÷ I 9 I =
6. -10 ÷ 0 =
7 9
-4
Undefined

8. 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.

9. EXAMPLE 2 Finding a Mean
Temperatures
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.

10. EXAMPLE 2
Finding a Mean
SOLUTION
STEP 1 Find the sum of the temperatures.
–41 + (– 4 0 ) + (–48 ) + (–18 )
= –147
STEP 2 Divide the sum by the number of temperatures.
–147
4
= –36.75
ANSWER The mean of the temperatures is about -37oF.

11. GUIDED PRACTICE for Examples 2 and 3
Find the mean of the data.
1. –16, 17, 8, –23, –31

12. 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 )
= –45
STEP 2 Divide the sum by the number of values.
–45
5
= –9
ANSWER The mean of the data is about –9.

13. GUIDED PRACTICE for Examples 2 and 3
Find Find the the mean mean of of the the data.
data.
2. 0, –4, –10, 4, 11, –9, –13

14. GUIDED PRACTICE for Examples 2 and 3
Find Find the the mean mean of of the the data.
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)
= –21
STEP 2 Divide the sum by the number of values.
–21
7
= –3
ANSWER The mean of the data is about –3.

15. 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

16. EXAMPLE 3
Evaluating Expressions
Evaluate the expression when a = –24, b = 8, and
c = –4.
a. a
b
b. ab
c

17. EXAMPLE 3
Evaluating Expressions
Evaluate the expression when a = –24, b = 8, and
c = –4.
b = –24
a. a
8
b. ab
c
= –24 8
–4
= –192
–4

18. EXAMPLE 3
Evaluating Expressions
Evaluate the expression when a = –24, b = 8, and
c = –4.
b = –24
a. a
8
Substitute values.
Different signs, so quotient is negative.
b. ab
c
Substitute values.
= –3
= –24 8
–4
= –192 Multiply.
–4
= 48 Same sign, so quotient is positive.

19. Daily Homework Quiz For use after Lesson 2.5
Find the quotient.
Evaluate the expression when k = – 36, m = 6, and n = 3.
1. mn
k 3. m2 + 4n2
k 2. m + n
2k

20. Daily Homework Quiz For use after Lesson 2.5
Find the quotient.
Evaluate the expression when k = – 36, m = 6, and n = 3.
1. mn
k
ANSWERS 1
– 2
k 3. m2 + 4n2
2. m + n
2k
ANSWERS – 4 ANSWERS – 1

21. Quick Write
How are the rules for multiplying integers
and dividing integers connected? Why?