{"id":167577,"date":"2024-11-15T20:17:16","date_gmt":"2024-11-15T20:17:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167577"},"modified":"2024-11-15T20:17:18","modified_gmt":"2024-11-15T20:17:18","slug":"name-the-property-of-real-numbers-illustrated-by-the-equation-5-x-1-5-1","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/name-the-property-of-real-numbers-illustrated-by-the-equation-5-x-1-5-1\/","title":{"rendered":"Name the property of real numbers illustrated by the equation 5 X 1\/5 = 1"},"content":{"rendered":"\n

Name the property of real numbers illustrated by the equation 5 X 1\/5 = 1
A Commutative Property
B Distributive Property
C Identity Property
D Inverse Property<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct answer is D) Inverse Property<\/strong>.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

The equation given is:<\/p>\n\n\n\n

[
5 \\times \\frac{1}{5} = 1
]<\/p>\n\n\n\n

This illustrates the Inverse Property<\/strong> of real numbers, specifically the Multiplicative Inverse Property<\/strong>. The Multiplicative Inverse<\/strong> of a number is another number that, when multiplied with the original number, results in the multiplicative identity<\/strong>, which is 1.<\/p>\n\n\n\n

In this case, the number 5 has a multiplicative inverse, which is ( \\frac{1}{5} ). When 5 is multiplied by ( \\frac{1}{5} ), the product is 1, which is the identity element for multiplication. This property shows that every real number (except 0) has an inverse that can “cancel out” the original number to yield 1.<\/p>\n\n\n\n

Inverse Property (Multiplicative Inverse Property):<\/h3>\n\n\n\n

This property states that for any nonzero real number ( a ), there exists a real number ( b ) such that:<\/p>\n\n\n\n

[
a \\times b = 1
]<\/p>\n\n\n\n

In the equation ( 5 \\times \\frac{1}{5} = 1 ), 5 is the number, and ( \\frac{1}{5} ) is its multiplicative inverse. The equation is a direct application of this property, where:<\/p>\n\n\n\n

[
a = 5 \\quad \\text{and} \\quad b = \\frac{1}{5}
]<\/p>\n\n\n\n

Thus, 5 and ( \\frac{1}{5} ) are inverses of each other, and their product equals 1, fulfilling the requirement of the Inverse Property.<\/p>\n\n\n\n

Other Properties:<\/h3>\n\n\n\n
    \n
  • A) Commutative Property<\/strong> involves changing the order of numbers in addition or multiplication, e.g., ( a + b = b + a ) or ( a \\times b = b \\times a ). This is not applicable here.<\/li>\n\n\n\n
  • B) Distributive Property<\/strong> refers to distributing multiplication over addition or subtraction, e.g., ( a \\times (b + c) = a \\times b + a \\times c ). This is not what is demonstrated here.<\/li>\n\n\n\n
  • C) Identity Property<\/strong> refers to the additive identity (0) or multiplicative identity (1), e.g., ( a + 0 = a ) or ( a \\times 1 = a ). While this is related, it doesn’t directly explain this equation as it involves the inverse rather than the identity itself.<\/li>\n<\/ul>\n\n\n\n

    Thus, the correct property illustrated by the equation ( 5 \\times \\frac{1}{5} = 1 ) is the Multiplicative Inverse Property<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Name the property of real numbers illustrated by the equation 5 X 1\/5 = 1A Commutative PropertyB Distributive PropertyC Identity PropertyD Inverse Property The Correct Answer and Explanation is: The correct answer is D) Inverse Property. Explanation: The equation given is: [5 \\times \\frac{1}{5} = 1] This illustrates the Inverse Property of real numbers, specifically […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-167577","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167577","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=167577"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167577\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167577"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167577"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167577"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}