{"id":5478,"date":"2023-06-29T18:47:17","date_gmt":"2023-06-29T18:47:17","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=5478"},"modified":"2024-10-18T20:50:41","modified_gmt":"2024-10-18T20:50:41","slug":"integers-learn-it-7","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/integers-learn-it-7\/","title":{"raw":"Integers: Learn It 7","rendered":"Integers: Learn It 7"},"content":{"raw":"

Dividing Integers<\/h2>\r\n

Division is the inverse operation of multiplication. So, [latex]15\\div 3=5[\/latex] because [latex]5\\cdot 3=15[\/latex] . In words, this expression says that [latex]\\mathbf{\\text{15}}[\/latex] can be divided into [latex]\\mathbf{\\text{3}}[\/latex] groups of [latex]\\mathbf{\\text{5}}[\/latex] each because adding five three times gives [latex]\\mathbf{\\text{15}}[\/latex].<\/p>\r\n

\r\n

If we look at some examples of multiplying integers, we might figure out the rules for dividing integers.<\/p>\r\n

\r\n

[latex]\\begin{array}{ccccc}5\\cdot 3=15\\text{ so }15\\div 3=5\\hfill & & & & -5\\left(3\\right)=-15\\text{ so }-15\\div 3=-5\\hfill \\\\ \\left(-5\\right)\\left(-3\\right)=15\\text{ so }15\\div \\left(-3\\right)=-5\\hfill & & & & 5\\left(-3\\right)=-15\\text{ so }-15\\div -3=5\\hfill \\end{array}[\/latex]<\/p>\r\n<\/center><\/section>\r\n

Division of signed numbers follows the same rules as multiplication. When the signs are the same, the quotient is positive, and when the signs are different, the quotient is negative.<\/p>\r\n

\r\n
\r\n

division of signed numbers<\/h3>\r\n

The sign of the quotient of two numbers depends on their signs.<\/p>\r\n

 <\/p>\r\nSame Signs<\/strong>\r\n

    \r\n\t
  • Two positives: Quotient is positive<\/li>\r\n\t
  • Two negatives: Quotient is positive<\/li>\r\n<\/ul>\r\nDifferent Signs<\/strong>\r\n
      \r\n\t
    • Positive & negative: Quotient is negative<\/li>\r\n\t
    • Negative & positive: Quotient is negative<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/section>\r\n
      Remember, you can always check the answer to a division problem by multiplying.<\/section>\r\n
      Divide each of the following:\r\n\r\n
        \r\n\t
      1. [latex]-27\\div 3[\/latex]<\/li>\r\n\t
      2. [latex]-100\\div \\left(-4\\right)[\/latex]<\/li>\r\n<\/ol>\r\n

        [reveal-answer q=\"324876\"]Show Solution[\/reveal-answer]
        \r\n[hidden-answer a=\"324876\"]<\/p>\r\n

          \r\n\t
        1. \r\n\r\n\r\n\r\n\r\n
          \u00a0<\/td>\r\n[latex]-27\\div 3[\/latex]<\/td>\r\n<\/tr>\r\n
          Divide, noting that the signs are different and so the quotient is negative.<\/td>\r\n[latex]-9[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n\t
        2. \r\n\r\n\r\n\r\n\r\n
           <\/td>\r\n[latex]-100\\div \\left(-4\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
          Divide, noting that the signs are the same and so the quotient is positive.<\/td>\r\n[latex]25[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n<\/ol>\r\n

          [\/hidden-answer]<\/p>\r\n<\/section>\r\n

          [ohm2_question hide_question_numbers=1]8911[\/ohm2_question]<\/section>\r\n

          Just as we saw with multiplication, when we divide a number by [latex]1[\/latex], the result is the same number. What happens when we divide a number by [latex]-1?[\/latex]<\/p>\r\n

          \r\n

          Let\u2019s divide a positive number and then a negative number by [latex]-1[\/latex] to see what we get.<\/p>\r\n

          \r\n

          [latex]\\begin{array}{cccc}8\\div \\left(-1\\right)\\hfill & & & -9\\div \\left(-1\\right)\\hfill \\\\ -8\\hfill & & & 9\\hfill \\\\ \\hfill \\text{-8 is the opposite of 8}\\hfill & & & \\hfill \\text{9 is the opposite of -9}\\hfill \\end{array}[\/latex]<\/p>\r\n<\/center><\/section>\r\n

          When we divide a number by [latex]-1[\/latex] we get its opposite.<\/p>\r\n

          \r\n
          \r\n

          dividing by [latex]-1[\/latex]<\/h3>\r\n

          Dividing a number by [latex]-1[\/latex] gives its opposite.<\/p>\r\n

           <\/p>\r\n

          \r\n

          [latex]a\\div \\left(-1\\right)=-a[\/latex]<\/p>\r\n<\/center><\/div>\r\n<\/section>\r\n

          [ohm2_question hide_question_numbers=1]8913[\/ohm2_question]<\/section>","rendered":"

          Dividing Integers<\/h2>\n

          Division is the inverse operation of multiplication. So, [latex]15\\div 3=5[\/latex] because [latex]5\\cdot 3=15[\/latex] . In words, this expression says that [latex]\\mathbf{\\text{15}}[\/latex] can be divided into [latex]\\mathbf{\\text{3}}[\/latex] groups of [latex]\\mathbf{\\text{5}}[\/latex] each because adding five three times gives [latex]\\mathbf{\\text{15}}[\/latex].<\/p>\n

          \n

          If we look at some examples of multiplying integers, we might figure out the rules for dividing integers.<\/p>\n

          \n[latex]\\begin{array}{ccccc}5\\cdot 3=15\\text{ so }15\\div 3=5\\hfill & & & & -5\\left(3\\right)=-15\\text{ so }-15\\div 3=-5\\hfill \\\\ \\left(-5\\right)\\left(-3\\right)=15\\text{ so }15\\div \\left(-3\\right)=-5\\hfill & & & & 5\\left(-3\\right)=-15\\text{ so }-15\\div -3=5\\hfill \\end{array}[\/latex]\n<\/div>\n<\/section>\n

          Division of signed numbers follows the same rules as multiplication. When the signs are the same, the quotient is positive, and when the signs are different, the quotient is negative.<\/p>\n

          \n
          \n

          division of signed numbers<\/h3>\n

          The sign of the quotient of two numbers depends on their signs.<\/p>\n

           <\/p>\n

          Same Signs<\/strong><\/p>\n

            \n
          • Two positives: Quotient is positive<\/li>\n
          • Two negatives: Quotient is positive<\/li>\n<\/ul>\n

            Different Signs<\/strong><\/p>\n

              \n
            • Positive & negative: Quotient is negative<\/li>\n
            • Negative & positive: Quotient is negative<\/li>\n<\/ul>\n<\/div>\n<\/section>\n
              Remember, you can always check the answer to a division problem by multiplying.<\/section>\n
              Divide each of the following:<\/p>\n
                \n
              1. [latex]-27\\div 3[\/latex]<\/li>\n
              2. [latex]-100\\div \\left(-4\\right)[\/latex]<\/li>\n<\/ol>\n