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Real Numbers Multiplication Guide

This informative guide covers the fundamentals of real numbers multiplication, including negative numbers, commutative property, and negative times negative rule. Learn through examples and visual aids to master this essential math concept.

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Real Numbers Multiplication Guide

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  1. Multiplication of Real Numbers Section 2-5-1

  2. Multiplication • When you first learned multiplication, your book had pictures of equal number of objects in several rows. • You learned that 3  4 meant “three fours.” • 3  4 = 4+4+4

  3. Negative Numbers • 3  (-4) means “three negative fours” • 3  (-4) = (-4)+(-4)+(-4) = -12 • using the addition rules.

  4. Think: Is Division Commutative?

  5. Three Ways • There are three ways to write multiplication. 3x4 or 3(4) or 34

  6. Commutative • Remember: multiplication is COMMUTATIVE. • 34 =43 and 3 (-4)=-43

  7. Practice: • Perform the indicated operation. • 46= • 4(-6) • -6x4 • 243100 • 243(-100) • -100243

  8. Negative Times Negative • So far you have learned • positive times positive, • positive times negative, • negative times positive. • There is only one pattern left. • Negative times a Negative is Positive

  9. Negative Times Negative • A little hard for students to envision • Think of pouring juice out of a clear jug. • This would be negative. • Now video tape the jug emptying. • Playing the tape backwards is also a negative • the jug appears to be filling (positive) when watched on the screen. • We will discuss in more detail why this is in section 2.7

  10. Rule: • a POSITIVE times a POSITIVE is POSITIVE • a NEGATIVE times a NEGATIVE is POSITIVE • a POSITIVE times a NEGATIVE is NEGATIVE • a NEGATIVE times a POSITIVE is NEGATIVE

  11. Division Rules • The multiplication and division rules are exactly the same.

  12. -2(-100) = 200 -5(-5) = 25 -23(-12) = 276 -3x 4 = -12 0.3 x (-2)=-0.6 -8(-4) = 2 -124 = -3 8(-4) = -2 Examples:

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