Property of Numbers

Basic Number Properties

The Commutative Laws/Ley Conmunicativa

• The Commutative Law for Addition: For any numbers a and b,

  a+b = b+a 

  Example: 2+5 = 5+2​

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• The Commutative Law for Multiplication: For any numbers a and b, ab= ba.

  Example: 2(4) = 4(​2)

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Example 1

Use the commutative law of addition to write an expression equivalent to c+ 2d.

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c + 2d = 2d + c

Example 2

Use the commutative law of multiplication to write an expression equivalent to mn.

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mn = nm

Multiple Select

Check all that apply: Which of the following demonstrates the Commutative law of addition.

• 7(p +w) = 7(w + p)

• 4 + 5 = 5 + 4

• ab = ba

• a(b*c)= (a*b)*c

• q + r = r + q

The Associative Laws/Leyes Asociativas

• The Associative Law of Addition: for any numbers a, b, and c                                                                      a+(b+c) = (a+b)+c 

    

• The Associative Law of Multiplication: for any numbers a, b, and c                                                                 (a*b)*c=a*(b*c)    

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Example 1

Use the associative law of addition to write an expression equivalent to

​5+(2 + 1).

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5 + (2 + 1) = ( 5 + 2) + 1

Example 2

Use the associative law of multiplication to write an expression equivalent to 7(3*2).

7(3*2) =(7*3)*2

Fill in the Blank

Use the associative law of multiplication to write an expression equivalent to 5(xy)=________

Identities

• The identity of 0: for any number a                                                                                     a+0 = a

• The identity property of 1: for any number a                                                                      a * 1 = a

Multiple Choice

Name the property that is being shown.

-5 + (5 +8) = (-5 + 5) +8

• Associative Law of Addition

• Associative Law of Multiplication

• Commutative Law of Addition

• Commutative Law of Multiplication

• Identity Property of 0

Multiple Choice

Name the property that is being shown.

10(x + y) = 10(y + x)

• Associative Law of Addition

• Associative Law of Multiplication

• Commutative Law of Addition

• Commutative Law of Multiplication

• Identity Property of 0

Multiple Choice

Name the property that is being shown.

x*(y*z) = (x*y)*z

• Associative Law of Addition

• Associative Law of Multiplication

• Commutative Law of Addition

• Commutative Law of Multiplication

• Identity Property of 0