Presentation on theme: "Algebra Properties of Real Numbers"— Presentation transcript:
1 Algebra 2 1.2 Properties of Real Numbers The four basic math operations are addition, subtraction,multiplication, and division. Because subtraction is addition ofthe opposite and division is multiplication by the reciprocal, theproperties of real numbers focus on addition and multiplication.Properties Real NumbersIdentities and InversesFor all real numbers n,WORDSAdditive Identity PropertyThe sum of a number and 0, the additive identity, is the original number.NUMBERS3 + 0 = 0ALGEBRAn + 0 = 0 + n = nFor all real numbers n,WORDSMultiplicative Identity PropertyThe product of a number and 1, the multiplicative identity, is the original number.NUMBERSALGEBRAn 1 = 1 n = n
2 Algebra 2 1.2 Properties of Real Numbers For all real numbers n,WORDSAdditive Inverse PropertyThe sum of a number and its opposite, or additive inverse, is 0.NUMBERS5 + (–5) = 0ALGEBRAn + (–n) = 0For all real numbers n,WORDSMultiplicative Inverse PropertyThe product of a nonzero number and its reciprocal, or multiplicative inverse, is 1.NUMBERSALGEBRARecall from previous courses that the opposite of any number a is –a and the reciprocal of any nonzero number a is .
3 Algebra 2 1.2 Properties of Real Numbers Ex 1:Find the additive and multiplicative inverse of each number.12additive inverse: –12multiplicative inverse:additive inverse:multiplicative inverse:
4 Algebra 2 1.2 Properties of Real Numbers Properties Real NumbersAddition and MultiplicationFor all real numbers a and b,WORDSClosure PropertyThe sum or product of any two real numbers is a real numberNUMBERS2 + 3 = 52(3) = 6ALGEBRAa + b ab For all real numbers a and b,WORDSCommutative PropertyYou can add or multiply real numbers in any order without changing the result.NUMBERS=7(11) = 11(7)ALGEBRAa + b = b + aab = ba
5 Algebra 2 1.2 Properties of Real Numbers For all real numbers a and b,WORDSAssociative PropertyThe sum or product of three or more real numbers is the same regardless of the way the numbers are grouped.NUMBERS(5 + 3) + 7 = 5 + (3 + 7)(5 3)7 = 5(3 7)ALGEBRAa + (b + c) = a + (b + c)(ab)c = a(bc)For all real numbers a and b,WORDSDistributive PropertyWhen you multiply a sum by a number, the result is the same whether you add and then multiply or whether you multiply each term by the number and add the products.NUMBERS5(2 + 8) = 5(2) + 5(8)(2 + 8)5 = (2)5 + (8)5ALGEBRAa(b + c) = ab + ac(b + c)a = ba + ca
6 Algebra 2 1.2 Properties of Real Numbers Ex 2:Identify the property demonstrated by each question.A. 2 3.9 = 3.9 2Comm Property of MultiplicationB.Assoc Property of AdditionEx 3:Use mental math to find a 5% tax on a $42.40 purchase.Think: 10% of $42.4010%(42.40)= = 4.24Think: 5% = (10%)A 5% tax on a $42.40 is $2.12.
7 Algebra 2 1.2 Properties of Real Numbers Ex 4:Classifying each statement as sometimes, always, or never true. Give examples or properties to support your answers.a b = a, where b = 3True and false examples exist. The statement is true when a = 0 and false when a ≠ 0.sometimes truetrue example: 0 3 = 0false example: 1 3 ≠ 13(a + 1) = 3a + 3Always true by the Distributive Property.always true