1. Ch 1 Sec 7: Slide #1 Columbus State Community College Chapter 1 Section 7 Dividing Integers

2. Ch 1 Sec 7: Slide #2 Dividing Integers 1.Divide integers. 2.Identify properties of division. 3.Combine multiplying and dividing of integers.

3. Ch 1 Sec 7: Slide #3 Arithmetic vs. Algebra Arithmetic 4 ) 28 Divisor Calculator and Algebra 28 ÷ 4 = 7 Dividend Quotient Divisor Dividend 7Quotient = 7 28 4

4. Ch 1 Sec 7: Slide #4 Dividing Two Integers If two numbers have different signs, the quotient is negative. Some examples are shown below. If two numbers have the same sign, the quotient is positive. Some examples are shown below. = – 3 – 15 5 = – 5 20 –4–4 = 7 – 14 –2–2 = 9 72 8

5. Ch 1 Sec 7: Slide #5 Dividing Two Integers EXAMPLE 1 Dividing Two Integers Divide. (a) Numbers have different signs, so the quotient is negative. – 30 6 = – 5 (b) Numbers have the same sign, so the quotient is positive. – 18 –9–9 = 2 (c) Numbers have different signs, so the quotient is negative. 36 ÷ – 3= – 12

6. Ch 1 Sec 7: Slide #6 Properties of Division ExamplesPattern (Division Property) – 14 = 1 28 = 1 When a nonzero number is divided by itself, the quotient is 1. –3–3 1 = – 3 72 1 = 72 When a number is divided by 1, the quotient is the number.

7. Ch 1 Sec 7: Slide #7 Properties of Division ExamplesPattern (Division Property) 0 38 = 0 0 – 12 = 0 When 0 is divided by any other number (except 0), the quotient is 0. –7–7 0 is undefined Division by 0 is undefined. There is no answer. 23 0 is undefined

8. Ch 1 Sec 7: Slide #8 = undefined Taking a Closer Look at Division Why is division by zero “undefined”? Let’s take a look. (a) Notice, 3 5 = 15. 15 3 = 5 (b) Notice, – 9 0 = 0. 0 –9–9 = 0 (c) 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. 24 0 = ?

9. Ch 1 Sec 7: Slide #9 Using Properties of Division EXAMPLE 2 Using Properties of Division Divide. Then state the property illustrated by each example. (a) Any number divided by 1 is the number. – 32 1 = – 32 (b) – 46 = 1 Any nonzero number divided by itself is 1.

10. Ch 1 Sec 7: Slide #10 Using Properties of Division EXAMPLE 2 Using Properties of Division Divide. Then state the property illustrated by each example. (c) Division by 0 is undefined. – 17 0 = undefined (d) 0 39 = 0 Zero divided by any nonzero number is 0.

11. Ch 1 Sec 7: Slide #11 (–) Example 2(c): Calculator Tip You can use the negative sign key on your TI-30X IIS calculator for multiplication and division. – 17 0 Calculator Tip – TI-30X IIS (–) ÷ 170= Error

12. Ch 1 Sec 7: Slide #12 Calculator Tip You can use the change of sign key on your TI-30Xa calculator for multiplication and division. Example 2(c): + – – 17 0 + – Calculator Tip – TI-30Xa + – ÷ 170= Error

13. Ch 1 Sec 7: Slide #13 Example 2(d): Calculator Tip Use your calculator (TI-30X IIS) to calculate Example 2(d). 0 39 Calculator Tip – TI-30X IIS ÷ 039= 0

14. Ch 1 Sec 7: Slide #14 Combining Multiplication and Division with Integers EXAMPLE 3 Combining Multiplication and Division Simplify. (a) 4 ( – 10 ) is – 40. Continue from left to right. 4 ( – 10 ) ÷ 2 ( 5 ) – 40 ÷ 2 ( 5 ) – 20 ( 5 ) – 100 Next, – 40 ÷ 2 is – 20. Finally, – 20 ( 5) is – 100.

15. Ch 1 Sec 7: Slide #15 Combining Multiplication and Division with Integers EXAMPLE 3 Combining Multiplication and Division Simplify. (b) Work inside parenthesis: ( 3 – 2 ) is – 6. – 24 ÷ ( 3 – 2 ) 2 – 24 ÷ ( – 6 ) 2 4 2 8 Working left to right, – 24 ÷ ( – 6 ) is 4. Finally, 4 2 is 8.

16. Ch 1 Sec 7: Slide #16 Combining Multiplication and Division with Integers EXAMPLE 3 Combining Multiplication and Division Simplify. (c) Work left to right: ( – 60 ÷ 10 ) is – 6. – 60 ÷ 10 ÷ – 2 – 5 – 6 ÷ – 2 – 5 3 – 5 – 15 Next, – 6 ÷ – 2 is 3. Finally 3 – 5 is – 15.

17. Ch 1 Sec 7: Slide #17 Dividing Integers Chapter 1 Section 7 – End Written by John T. Wallace