{"id":327,"date":"2023-06-21T13:22:57","date_gmt":"2023-06-21T13:22:57","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-11\/"},"modified":"2023-06-21T13:22:57","modified_gmt":"2023-06-21T13:22:57","slug":"summary-review-11","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/gsu-collegealgebra\/chapter\/summary-review-11\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"\n\n

Key Concepts<\/h2>\nassociative property of addition <\/strong>the sum of three numbers may be grouped differently without affecting the result; in symbols, [latex]a+\\left(b+c\\right)=\\left(a+b\\right)+c[\/latex]\n\nassociative property of multiplication <\/strong>the product of three numbers may be grouped differently without affecting the result; in symbols, [latex]a\\cdot \\left(b\\cdot c\\right)=\\left(a\\cdot b\\right)\\cdot c[\/latex]\n\ncommutative property of addition <\/strong>two numbers may be added in either order without affecting the result; in symbols, [latex]a+b=b+a[\/latex]\n\ncommutative property of multiplication <\/strong>two numbers may be multiplied in any order without affecting the result; in symbols, [latex]a\\cdot b=b\\cdot a[\/latex]\n\ndistributive property <\/strong>the product of a factor times a sum is the sum of the factor times each term in the sum; in symbols, [latex]a\\cdot \\left(b+c\\right)=a\\cdot b+a\\cdot c[\/latex]\n\nidentity property of addition <\/strong>there is a unique number, called the additive identity, 0, which, when added to a number, results in the original number; in symbols, [latex]a+0=a[\/latex]\n\nidentity property of multiplication <\/strong>there is a unique number, called the multiplicative identity, 1, which, when multiplied by a number, results in the original number; in symbols, [latex]a\\cdot 1=a[\/latex]\n\ninverse property of addition <\/strong>for every real number [latex]a[\/latex], there is a unique number, called the additive inverse (or opposite), denoted [latex]-a[\/latex], which, when added to the original number, results in the additive identity, 0; in symbols, [latex]a+\\left(-a\\right)=0[\/latex]\n\ninverse property of multiplication <\/strong>for every non-zero real number [latex]a[\/latex], there is a unique number, called the multiplicative inverse (or reciprocal), denoted [latex]\\dfrac{1}{a}[\/latex], which, when multiplied by the original number, results in the multiplicative identity, 1; in symbols, [latex]a\\cdot \\dfrac{1}{a}=1[\/latex]\n\n","rendered":"

Key Concepts<\/h2>\n

associative property of addition <\/strong>the sum of three numbers may be grouped differently without affecting the result; in symbols, [latex]a+\\left(b+c\\right)=\\left(a+b\\right)+c[\/latex]<\/p>\n

associative property of multiplication <\/strong>the product of three numbers may be grouped differently without affecting the result; in symbols, [latex]a\\cdot \\left(b\\cdot c\\right)=\\left(a\\cdot b\\right)\\cdot c[\/latex]<\/p>\n

commutative property of addition <\/strong>two numbers may be added in either order without affecting the result; in symbols, [latex]a+b=b+a[\/latex]<\/p>\n

commutative property of multiplication <\/strong>two numbers may be multiplied in any order without affecting the result; in symbols, [latex]a\\cdot b=b\\cdot a[\/latex]<\/p>\n

distributive property <\/strong>the product of a factor times a sum is the sum of the factor times each term in the sum; in symbols, [latex]a\\cdot \\left(b+c\\right)=a\\cdot b+a\\cdot c[\/latex]<\/p>\n

identity property of addition <\/strong>there is a unique number, called the additive identity, 0, which, when added to a number, results in the original number; in symbols, [latex]a+0=a[\/latex]<\/p>\n

identity property of multiplication <\/strong>there is a unique number, called the multiplicative identity, 1, which, when multiplied by a number, results in the original number; in symbols, [latex]a\\cdot 1=a[\/latex]<\/p>\n

inverse property of addition <\/strong>for every real number [latex]a[\/latex], there is a unique number, called the additive inverse (or opposite), denoted [latex]-a[\/latex], which, when added to the original number, results in the additive identity, 0; in symbols, [latex]a+\\left(-a\\right)=0[\/latex]<\/p>\n

inverse property of multiplication <\/strong>for every non-zero real number [latex]a[\/latex], there is a unique number, called the multiplicative inverse (or reciprocal), denoted [latex]\\dfrac{1}{a}[\/latex], which, when multiplied by the original number, results in the multiplicative identity, 1; in symbols, [latex]a\\cdot \\dfrac{1}{a}=1[\/latex]<\/p>\n\n\t\t\t

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Candela Citations<\/h3>\n\t\t\t\t\t
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