dividing integers
DESCRIPTION
.TRANSCRIPT
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 =