{"id":6489,"date":"2014-01-22T13:46:27","date_gmt":"2014-01-22T13:46:27","guid":{"rendered":"https:\/\/schooltutoring.com\/help\/?p=6489"},"modified":"2014-12-02T08:26:54","modified_gmt":"2014-12-02T08:26:54","slug":"identity-and-equality-properties-in-algebra","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/help\/identity-and-equality-properties-in-algebra\/","title":{"rendered":"Identity and Equality Properties in Algebra"},"content":{"rendered":"

Overview:<\/strong><\/p>\n

Identity and equality properties in mathematics are some of the keys to solving algebraic equations.\u00a0 Those properties allow operations to be performed with numbers and variables.\u00a0 Some of them may have been learned in lower grades, without symbols to represent them.<\/p>\n

What Are Some Identity Properties?<\/strong><\/p>\n

Zero in addition has a special property.\u00a0 Any number a +0 = a, and so does 0 +a equal a.\u00a0\u00a0\u00a0 For example, the equation b + 15 = 15 is solved by 0, because 0 +15 =15.\u00a0 The number 1 is the identity for multiplication, because any number multiplied by 1 is that number. Also, any number multiplied by zero will equal zero.<\/p>\n

What Are Some Equality Properties?<\/strong><\/p>\n

The equality properties are always true for any numbers, a, b, or c.\u00a0 The reflexive property is that any number a is equal to itself.\u00a0 The symmetric property states that if a = b, then b = a.\u00a0 The transitive property states that if a = b and b=c, then a=c.\u00a0 The substitution property states that if a = b, then a may be replaced by b.\u00a0 Also, if a =b, then a +c = b + c, a-c = b-c, a\u2219c = b\u2219c, and as long as c does not equal 0, a\/c = b\/c.<\/p>\n

How Are They Used?<\/strong><\/p>\n

Identity and equality properties can be used to solve many problems. Suppose the problem is to solve 6(12-48\/4) +9\u22191.\u00a0 First, 12-48\/4 can be solved as 12-12 and then substituted so that the expression reads as 6 (12-12) + 9\u22191.\u00a0 Now 6(0) can be substituted, and solved as 0, and 9\u22191 can be solved as 9 because of the identity property for multiplication.\u00a0 Because 0 is the identity for addition, the entire expression can be solved as 9 +0 or 9.<\/p>\n

Why Are the Properties Important?<\/strong><\/p>\n

The identity and equality properties are important tools to use when solving equations.\u00a0 Suppose an equation is 3 +x = 12, so 3 – 3 +x\u00a0 = 12 -3.\u00a0 Solving both sides of the equation, 3-3 equals 0, so 0 +x = 12-3.\u00a0 # is subtracted from both sides, using the equality property for subtraction, as well as the additive property for 0, and then x = 12-3 =9 is substitution.<\/p>\n

Interested in algebra tutoring services<\/a>? Learn more about how we are assisting thousands of students each academic year.<\/p>\n

SchoolTutoring Academy<\/span> is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Mason City, IA visit: Tutoring in Mason City, IA<\/a><\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

Overview: Identity and equality properties in mathematics are some of the keys to solving algebraic equations.\u00a0 Those properties allow operations to be performed with numbers and variables.\u00a0 Some of them may have been learned in lower grades, without symbols to represent them. What Are Some Identity Properties? Zero in addition has a special property.\u00a0 Any […]<\/p>\n","protected":false},"author":22,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[587,908,1754,1797,1844],"class_list":["post-6489","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-equality-properties","tag-identity-properties","tag-substitution-properties","tag-symmetric-properties","tag-transitive-properties"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6489","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/users\/22"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/comments?post=6489"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/posts\/6489\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/media?parent=6489"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/categories?post=6489"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/help\/wp-json\/wp\/v2\/tags?post=6489"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}