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Study Guides > College Algebra CoRequisite Course

Summary: Review

Key Concepts

associative property of addition the sum of three numbers may be grouped differently without affecting the result; in symbols, a+(b+c)=(a+b)+ca+\left(b+c\right)=\left(a+b\right)+c associative property of multiplication the product of three numbers may be grouped differently without affecting the result; in symbols, a⋅(b⋅c)=(a⋅b)⋅ca\cdot \left(b\cdot c\right)=\left(a\cdot b\right)\cdot c commutative property of addition two numbers may be added in either order without affecting the result; in symbols, a+b=b+aa+b=b+a commutative property of multiplication two numbers may be multiplied in any order without affecting the result; in symbols, a⋅b=b⋅aa\cdot b=b\cdot a distributive property the product of a factor times a sum is the sum of the factor times each term in the sum; in symbols, a⋅(b+c)=a⋅b+a⋅ca\cdot \left(b+c\right)=a\cdot b+a\cdot c identity property of addition there is a unique number, called the additive identity, 0, which, when added to a number, results in the original number; in symbols, a+0=aa+0=a identity property of multiplication there is a unique number, called the multiplicative identity, 1, which, when multiplied by a number, results in the original number; in symbols, a⋅1=aa\cdot 1=a inverse property of addition for every real number aa, there is a unique number, called the additive inverse (or opposite), denoted −a-a, which, when added to the original number, results in the additive identity, 0; in symbols, a+(−a)=0a+\left(-a\right)=0 inverse property of multiplication for every non-zero real number aa, there is a unique number, called the multiplicative inverse (or reciprocal), denoted 1a\dfrac{1}{a}, which, when multiplied by the original number, results in the multiplicative identity, 1; in symbols, a⋅1a=1a\cdot \dfrac{1}{a}=1

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