Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
MATH 60 Section 2.3 Multiplying and Dividing Signed Numbers I. Review: Multiplication means____________ ___________ 4 (3) means: 4 (-3) means: Multiplying a positive number by a negative number gives a ________________ number. Because of the commutative property of multiplication: 4 x (-3) = (-3) x 4 = So, multiplying a negative number by a positive number gives a _______________number. Now let’s look at patterns. Mathematics is the science of patterns. It is designed and defined so that patterns are followed (as much as possible): (-3) x 4 = (-3) x 3 = (-3) x 2 = (-3) x 1 = (-3) x 0 = (-3) x ( )= (-3) x ( )= (-3) x ( )= (-3) x ( ) = In order for the pattern to remain consistent, we find that multiplying a negative number times a negative number gives a ______________ number. M60 Sec. 2.3 p.2 II. Summary of Rules for Multiplication: 1. The product of two numbers with the same signs is _______________. Ex. 1: (5) (11) = Ex. 2: (-4) ( -7) = Ex. 3: 7 ( 3) = Ex. 4: -6 ( -4) = 2. The product of two numbers with the opposite signs is ____________. Ex. 5: (-2) (3) = Ex. 6: (+4) (-3) = Ex. 7: 6 (-2) = Ex. 8: -10 (5) = 3. The product of any number and zero is ____________. Ex. 9: 3 (0) = Ex. 10: 0 (4) = Part B: Relating Multiplication and Division: Division is the ________________ _________________ of multiplication. Division can be done by multiplying by the _____________________. So, the same rules of signs which apply to multiplication also apply to division: Ex. 1: 6 ÷ Ex. 2: -4 ÷-8= Ex. 3: 2 = M60 Sec. 2.3 p.3 Ex. 4: = Ex. 5: = Ex. 6: 36 ÷ - 9 = Ex. 7: -35 ÷ 4 = So Rules 1 and 2 can be further summarized: The product or quotient of Any two numbers with the same sign will give a _____________ number. And, the product or quotient of any two numbers with opposite signs will give a _________ number. 4. The quotient of zero and any non-zero number is _______________. That is, zero divided BY any number is ________________. Ex. 8: Ex. 9: 5. The quotient of any number and zero is ____________. That is, division BY ZERO is ___________________. Ex. 10: Ex. 11: 6. Multiplying and dividing by (-1) changes the _______________ Of the number. It is the same as taking the ______________ of the number. Ex. 12: - (-5) = -1 (-5) = (-5) ÷ (-1) = M60 Sec. 2.3 p.4 Revisit order of operations: Ex. 13: 12 ÷ (-6) (-3) Ex. 14: -48 ÷ (-8) (-2) ÷ 4 Practice for the proficiency test: Compute without a calculator: 1. –5 – (-7) 6. –19 + 12 2. –11 – 23 7. –12 + 13 3. –2 – 9 8. 18 – 20 4. –15 – (-18) 9. –3 + (-8) – 14 5. 10 – (-6) 10. –20 – 5 + 7 11. 23 1 12. 13. 27 3 14. 4 8 15. 16. 5 6 3 17. 18. 12 2 4 6 1 19. Evaluate the expression - x + y for x = - 7 and y = - 3 20. Evaluate the expression (- 2)(x) – (5)(y) for x = 3 and y = - 4