Presentation on theme: "Properties of Real Numbers"— Presentation transcript:
1 Properties of Real Numbers CommutativeAssociativeIdentity + ×Inverse + ×Zero PropertyReflexiveDistributive
2 Commutative Properties Changing the order of the numbers in addition or multiplication will not change the result.Commutative Property of Addition states: = or a + b = b + a.Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.
3 Verbal Hints for Commutative Property CommuteSwitch PlacesMove to a new location
4 Associative Properties Changing the grouping of the numbers in addition or multiplication will not change the result.Associative Property of Addition states: 3 + (4 + 5)= (3 + 4)+ 5 or a + (b + c)= (a + b)+ cAssociative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)
5 Verbal Hints for Associative Property RegroupThey simply group with a new friend( ) change places but numbers stay the same
6 Additive Identity Property There exists a unique number 0 such that zero preserves identities under addition.a + 0 = a and 0 + a = aIn other words adding zero to a number does not change its value.
7 Multiplicative Identity Property There exists a unique number 1 such that the number 1 preserves identities under multiplication.a ∙ 1 = a and 1 ∙ a = aIn other words multiplying a number by 1 does not change the value of the number.
8 Verbal Hints for Identity Property The value that returns the input unchangedRemember “I” in the word identity
9 Additive Inverse Property For each real number a there exists a unique real number –a such that their sum is zero.a + (-a) = 0In other words opposites add to zero.
10 Verbal Hints for Additive Inverse Opposite numbersSame number but different signZero Pairs
11 Multiplicative Inverse Property For each real number a there exists a unique real number such that their product is 1.
12 Verbal Hints for Multiplicative Inverse Flip the numberReciprocal
13 Zero Property of Multiplication Any number multiplied by 0 is equal to 0A ● 0 = 0-23 ● 0 = 0½ ● 0 = 00.25 ● 0 = 0“zero times any value is 0
14 A real number is always equal to itself Reflexive PropertyA number is always equal to itselfA = A-2 = -25 = 5A real number is always equal to itself
15 Distributive Property Multiplication distributes over addition.
16 Verbal Hints for Distributive Property Multiplication distributes across addition or subtraction.Multiply across the parentheses!!!!!