{"id":12,"date":"2017-08-23T06:42:53","date_gmt":"2017-08-23T06:42:53","guid":{"rendered":"http:\/\/americanboard.org\/Subjects\/mathematics\/?page_id=12"},"modified":"2017-09-18T13:55:44","modified_gmt":"2017-09-18T13:55:44","slug":"operations-with-real-numbers","status":"publish","type":"page","link":"https:\/\/americanboard.org\/Subjects\/mathematics\/operations-with-real-numbers\/","title":{"rendered":"Operations with Real Numbers"},"content":{"rendered":"
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\u2b05 Previous Lesson<\/a>\u00a0Workshop Index<\/a>\u00a0Next Lesson \u27a1<\/a><\/div>\n

<\/p>\n

Operations with Real Numbers<\/h1>\n

Objective<\/h4>\n

In this lesson, you will study how to identify and use the arithmetical properties of real numbers, and how to\u00a0compare and order rational numbers in various forms. You will also study how to use the standard algorithms for\u00a0operations of whole numbers and decimals.<\/p>\n

Previously Covered:<\/h4>\n

Real numbers<\/em><\/strong> are the field of all rational and irrational numbers.<\/p>\n

\n

How do I compare numbers in different forms?<\/h3>\n

To compare numbers in different forms, change the numbers to\u00a0the same form and then compare them.<\/p>\n

For example, what inequality symbol correctly fills in the\u00a0blank\u00a0\u00a0__ 1.67?<\/p>\n

To solve, first change\u00a0\u00a0to 1.5. Then compare 1.5 and 1.67.\u00a0<\/p>\n

How do I order numbers in different forms?<\/strong><\/p>\n

To order numbers in different forms, write all numbers in the\u00a0same form, and then place them in the correct order.<\/p>\n

For example, place\u00a0,\u00a0213%,\u00a0,\u00a0\u00a0in order from least to greatest.<\/p>\n

First convert all the numbers to the same form.<\/p>\n

<\/p>\n

The order is\u00a0,\u00a0,\u00a02.13, 2.33. Change the numbers back to their original form to get\u00a0,\u00a0,\u00a0213%,\u00a0.<\/p>\n

\n

Question<\/h4>\n
\n

Which choice shows the correct result of putting\u00a0,\u00a0,\u00a0,\u00a0and 30% in order from least to greatest?<\/p>\n

    \n
  1. ,\u00a0,\u00a030%,\u00a0<\/li>\n
  2. ,\u00a0,\u00a0,\u00a030%<\/li>\n
  3. ,\u00a030%,\u00a0,\u00a0<\/li>\n
  4. 30%,\u00a0,\u00a0,\u00a0<\/li>\n<\/ol>\n<\/div>\n

    Reveal Answer <\/a><\/p>\n

    \n

    The correct answer is A. To solve, first change each number to\u00a0a decimal.<\/p>\n

    <\/p>\n

    Then place the numbers in order from least to greatest.<\/p>\n

    <\/p>\n

    Finally, change each number back to its original form.<\/p>\n

    <\/p>\n<\/div>\n<\/section>\n

    What are the standard algorithms for operations with whole numbers?<\/h3>\n

    What are the standard algorithms for operations with whole\u00a0numbers?<\/p>\n

    An algorithm<\/abbr> is a finite set of instructions for accomplishing some\u00a0task when given a problem in its initial states.<\/p>\n

    We will study four algorithms for operations with whole\u00a0numbers:<\/p>\n

    (1) addition,
    \n(2) subtraction,
    \n(3) multiplication, and
    \n(4) division.<\/p>\n

    Addition<\/strong><\/h4>\n

    Add numbers from right to left, carrying as needed.<\/p>\n

    For example,<\/p>\n

    <\/p>\n

    Subtraction<\/strong><\/h4>\n

    Subtract from right to left borrowing as needed.<\/p>\n

    For example,<\/p>\n

    <\/p>\n

    Multiplication<\/strong><\/h4>\n

    Multiply from right to left, carrying as needed. Insert a place\u00a0holder, which will be the number zero, for the second row of\u00a0multiplication. Add the numbers to arrive at the answer.<\/p>\n

    For example,<\/p>\n

    <\/p>\n

    Division<\/strong><\/h4>\n

    Determine the number of times the divisor goes into the\u00a0dividend. Subtract the result. Carry down the next digit.\u00a0Determine the number of times the divisor goes into the dividend.\u00a0Subtract the result.<\/p>\n

    For example,<\/p>\n

    <\/p>\n

    If a remainder exists, create a fraction using the remainder as\u00a0the numerator and the divisor as the denominator.<\/p>\n

    \n

    Question<\/h4>\n
    \n

    Which choice shows the correct algorithm?<\/p>\n

      \n
    1. <\/li>\n
    2. <\/li>\n
    3. <\/li>\n
    4. <\/li>\n<\/ol>\n<\/div>\n

      Reveal Answer <\/a><\/p>\n

      \n

      The correct answer is B. Choice A did not carry the 1 from\u00a0.\u00a0Choice C did not carry the 1 from\u00a0.\u00a0Choice D is not the complete algorithm.<\/p>\n<\/div>\n<\/section>\n<\/section>\n

      <\/p>\n

      \u2b05 Previous Lesson<\/a>\u00a0Workshop Index<\/a>\u00a0Next Lesson \u27a1<\/a><\/div>\n

      Back to Top<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

      \u2b05 Previous Lesson\u00a0Workshop Index\u00a0Next Lesson \u27a1 Operations with Real Numbers Objective In this lesson, you will study how to identify and use the arithmetical properties of real numbers, and how to\u00a0compare and order rational numbers in various forms. You will also study how to use the standard algorithms for\u00a0operations of whole numbers and decimals. Previously […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-12","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/12","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/comments?post=12"}],"version-history":[{"count":7,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/12\/revisions"}],"predecessor-version":[{"id":719,"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/pages\/12\/revisions\/719"}],"wp:attachment":[{"href":"https:\/\/americanboard.org\/Subjects\/mathematics\/wp-json\/wp\/v2\/media?parent=12"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}