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# Property Of Numbers

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Chapter 2, Section1: Property of Numbers: Associative/Commutative/Identity

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### Property Of Numbers

1. 1. Chapter 2, Section 1: Properties of Numbers Ms. Dewey-Hoffman, 2009
2. 2. Commutative Properties (addition/multiplication) <ul><li>When JUST adding or multiplying (not at the same time), you can move the numbers around and the answer will be the same. </li></ul><ul><li>Addition </li></ul><ul><li>7 + 17 + 23 = 47 </li></ul><ul><li>23 + 7 + 17 = 47 </li></ul><ul><li>7 + 17 + 23 = 23 + 7 + 17 </li></ul><ul><li>A + B + C = B + A + C </li></ul><ul><li>Multiplication </li></ul><ul><li>5 • 3 • 11 = 165 </li></ul><ul><li>11 • 5 • 3 = 165 </li></ul><ul><li>11 • 5 • 3 = 5 • 3 • 11 </li></ul><ul><li>A • B • C = B • A • C </li></ul>
3. 3. Associative Properties (addition/multiplication) <ul><li>When JUST adding or multiplying (not at the same time), you can change the grouping symbol locations and get the same answer. </li></ul><ul><li>Addition </li></ul><ul><li>(3 + 4) + 7 = 14 </li></ul><ul><li>3 + (4 + 7) = 14 </li></ul><ul><li>(3 + 4) + 7 = 3 + (4 + 7) </li></ul><ul><li>A + (B + C) = (A + B) + C </li></ul><ul><li>Multiplication </li></ul><ul><li>(3 + 4) + 7 = 14 </li></ul><ul><li>3 + (4 + 7) = 14 </li></ul><ul><li>(3 + 4) + 7 = 3 + (4 + 7) </li></ul><ul><li>A + (B + C) = (A + B) + C </li></ul>
4. 4. Identity Properties of Addition and Multiplication <ul><li>The identity for ADDITION is ZERO. </li></ul><ul><li>When you ADD ZERO to a number, the sum is that number. </li></ul><ul><li>Addition likes ZERO. </li></ul><ul><li>5 + 0 = 5 </li></ul><ul><li>The identity for MULTIPLICATION is ONE. </li></ul><ul><li>When you MULTIPLY ONE by a number, the product is that number. </li></ul><ul><li>Multiplication likes ONE. </li></ul><ul><li>4 • 1 = 4 </li></ul>
5. 5. Identify the Property Shown <ul><li>3 + 6 = 6 + 3 </li></ul><ul><li>8 = 1 • 8 </li></ul><ul><li>(3z)m = 3(xm) </li></ul><ul><li>0 + b = b </li></ul>Commutative Property Multiplicative Identity Associative Property of Multiplication Additive Identity
6. 6. Mental Math and the Properties <ul><li>If it is easier to do Mental Math and all you’re doing is just Addition or just Multiplication, then move numbers to make it easier for you. </li></ul><ul><li>This works because of the Associative Property of Addition/Multiplication and the Commutative Property of Addition/Multiplication . </li></ul><ul><li>Example: </li></ul><ul><li>19 + (-30) + 21 = </li></ul><ul><li>19 + 21 + (-30)  easier to Add 19 and 21 first before adding (-30) </li></ul><ul><li>40 + (-30)  it is simplified, drop down the (-30) </li></ul><ul><li>40 + (-30) = 10 </li></ul><ul><li>10 </li></ul>
7. 7. More Examples <ul><li>Hint: Look for things that add to 10. 9+1, 8+2, 7+3, etc. </li></ul><ul><li>6 + 7 + 14 = </li></ul><ul><li>8 + 0 + 2 + (-7) = </li></ul><ul><li>5 + 12 + 18 + 5 = </li></ul><ul><li>7 + 2 + 8 + 23 = </li></ul>
8. 8. Moving Multiplication <ul><li>(4 • 9) • 5 = </li></ul><ul><li>(9 • 4) • 5  Commutative Property of Multiplication. </li></ul><ul><li>9 • (4 • 5)  Associative Property of Multiplication, because it is easier to multiply 4 and 5, instead of 4 and 9. </li></ul><ul><li>9 • 20  Simplify, Multiply inside the Parentheses. </li></ul><ul><li>180  Simplify, Multiply. </li></ul>
9. 9. More Examples <ul><li>25 • (3 • 4) = </li></ul><ul><li>3 • 1 • -5 • 8 = </li></ul><ul><li>2(-8)(-15) = </li></ul><ul><li>5 • 9 • 6 • (-2) • (-1) = </li></ul>
10. 10. #9 <ul><li>Page 71-72: 1-33 odd. #35 is Extra Credit. </li></ul><ul><li>Remember to show your steps, even for the Mental Math Problems. </li></ul><ul><li>Tell me which numbers you added or multiplied first. </li></ul>