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Dividing Integers.

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Presentation on theme: "Dividing Integers."— Presentation transcript:

1 Dividing Integers

2 Dividing Integers Objectives: Divide integers. Identify properties of division. Combine multiplying and dividing of integers.

3 Calculator and Algebra
Dividing Integers Arithmetic vs. Algebra Arithmetic 7 Quotient 4 ) 28 Divisor Dividend Calculator and Algebra Dividend = 7 28 4 28 ÷ 4 = 7 Divisor Quotient

4 –15 –4 –14 –2 Dividing Integers Dividing Two Integers
If two numbers have different signs, the quotient is negative. Some examples are shown below. = –3 –15 5 = –5 20 –4 If two numbers have the same sign, the quotient is positive. Some examples are shown below. = 7 –14 –2 = 9 72 8

5 –30 –18 –9 Dividing Integers EXAMPLE 1 Dividing Two Integers Divide. 6
Numbers have different signs, so the quotient is negative. (a) = –5 –18 –9 Numbers have the same sign, so the quotient is positive. (b) = 2 (c) 36 ÷ –3 = –12 Numbers have different signs, so the quotient is negative.

6 Properties of Division
Dividing Integers Properties of Division Examples Pattern (Division Property) –14 = 1 28 = 1 When a nonzero number is divided by itself, the quotient is 1. –3 1 = –3 72 1 = 72 When a number is divided by 1, the quotient is the number.

7 Properties of Division
Dividing Integers Properties of Division Examples Pattern (Division Property) When 0 is divided by any other number (except 0), the quotient is 0. 38 = 0 –12 = 0 –7 is undefined Division by 0 is undefined. There is no answer. 23 is undefined

8 Taking a Closer Look at Division
Dividing Integers Taking a Closer Look at Division Why is division by zero “undefined”? Let’s take a look. 15 3 (a) = 5 Notice, 3 • 5 = 15. –9 (b) = 0 Notice, –9 • 0 = 0. 24 There is no number that you can multiply by 0 to get 24. So, division by 0 has no answer and is said to be undefined. (c) = ? = undefined

9 –32 –46 Dividing Integers EXAMPLE 2 Using Properties of Division
Divide. Then state the property illustrated by each example. –32 1 (a) = –32 Any number divided by 1 is the number. –46 (b) = 1 Any nonzero number divided by itself is 1.

10 –17 Dividing Integers EXAMPLE 2 Using Properties of Division
Divide. Then state the property illustrated by each example. –17 (c) = undefined Division by 0 is undefined. 39 (d) = 0 Zero divided by any nonzero number is 0.

11 (–) –17 Dividing Integers Example 2(c):
Calculator Tip You can use the negative sign key on your TI-30X IIS calculator for multiplication and division. –17 (–) 1 7 ÷ = Error (–)

12 Dividing Integers Calculator Tip You can use the change of sign key on your TI-30Xa calculator for multiplication and division. Example 2(c): + – –17 1 7 + – ÷ = Error + –

13 Dividing Integers Example 2(d): Calculator Tip Use your calculator (TI-30X IIS) to calculate Example 2(d). 39 ÷ 3 9 =

14 –40 ÷ 2 ( 5 ) –20 ( 5 ) –100 Dividing Integers
EXAMPLE Combining Multiplication and Division Simplify. (a) 4 ( –10 ) ÷ 2 ( 5 ) 4 ( –10 ) is –40. Continue from left to right. –40 ÷ 2 ( 5 ) Next, –40 ÷ 2 is –20. –20 ( 5 ) Finally, –20 ( 5) is –100. –100

15 –24 ÷ ( 3 • –2 ) • 2 –24 ÷ ( –6 ) • 2 Dividing Integers
EXAMPLE Combining Multiplication and Division Simplify. (b) –24 ÷ ( 3 • –2 ) • 2 Work inside parenthesis: ( 3 • –2 ) is –6. –24 ÷ ( –6 ) • 2 Working left to right, –24 ÷ ( –6 ) is 4. • 2 Finally, 4 • 2 is 8. 8

16 –60 ÷ 10 ÷ –2 • –5 –6 ÷ –2 • –5 –15 Dividing Integers
EXAMPLE Combining Multiplication and Division Simplify. (c) –60 ÷ 10 ÷ –2 • –5 Work left to right: ( –60 ÷ 10 ) is –6. –6 ÷ –2 • –5 Next, –6 ÷ –2 is 3. 3 • –5 Finally 3 • –5 is –15. –15


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