{"id":5492,"date":"2023-06-29T19:14:03","date_gmt":"2023-06-29T19:14:03","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=5492"},"modified":"2024-10-18T20:50:41","modified_gmt":"2024-10-18T20:50:41","slug":"integers-learn-it-8","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/integers-learn-it-8\/","title":{"raw":"Integers: Learn It 8","rendered":"Integers: Learn It 8"},"content":{"raw":"

Simplifying and Evaluating Expressions With Integers That Use all Four Operations<\/h2>\r\n

Now we\u2019ll simplify expressions that use all four operations\u2013addition, subtraction, multiplication, and division\u2013with integers. Remember to follow the order of operations.<\/p>\r\n

Order of operations is a set of rules in mathematics that dictates the sequence in which operations should be performed to correctly solve an expression. It is commonly remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
\r\n
\r\nFor instance, in the expression [latex]8 + (4 * 2)^2 \u00f7 4 - 2[\/latex] using the order of operations we must:\r\n\r\n
    \r\n\t
  1. Parentheses\/Brackets: Perform the operation inside the parentheses first.\r\n\r\n
      \r\n\t
    • This gives us: [latex]8 + (8)^2 \u00f7 4 - 2[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t
    • Exponents\/Orders: Next, solve for the exponent.\r\n\r\n
        \r\n\t
      • This gives us: [latex]8 + 64 \u00f7 4 - 2[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t
      • Multiplication and Division: Perform multiplication and division operations from left to right.\r\n\r\n
          \r\n\t
        • This gives us: [latex]8 + 16 - 2[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t
        • Addition and Subtraction: Finally, carry out addition and subtraction from left to right.\r\n\r\n
            \r\n\t
          • This gives us: [latex]24 - 2 = 22[\/latex]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ol>\r\n

            So, the result of the expression [latex]8 + (4 * 2)^2 \u00f7 4 - 2[\/latex] following the order of operations is [latex]22[\/latex].<\/p>\r\n<\/section>\r\n

            Simplify the following:
            [latex]7\\left(-2\\right)+4\\left(-7\\right)-6[\/latex]<\/center>
            \r\n[reveal-answer q=\"324876\"]Show Solution[\/reveal-answer]
            \r\n[hidden-answer a=\"324876\"]
            \r\nWe use the order of operations. Multiply first and then add and subtract from left to right.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
             <\/td>\r\n[latex]7\\left(-2\\right)+4\\left(-7\\right)-6[\/latex]<\/td>\r\n<\/tr>\r\n
            Multiply first.<\/td>\r\n[latex]-14+\\left(-28\\right)-6[\/latex]<\/td>\r\n<\/tr>\r\n
            Add.<\/td>\r\n[latex]-42 - 6[\/latex]<\/td>\r\n<\/tr>\r\n
            Subtract.<\/td>\r\n[latex]-48[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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

            [ohm2_question hide_question_numbers=1]8916[\/ohm2_question]<\/section>\r\n
            Simplify the following:
            [latex]12 - 3\\left(9 - 12\\right)[\/latex]<\/center>
            \r\n[reveal-answer q=\"843317\"]Show Solution[\/reveal-answer]
            \r\n[hidden-answer a=\"843317\"]
            \r\nAccording to the order of operations, we simplify inside parentheses first. Then we will multiply and finally we will subtract.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
             <\/td>\r\n[latex]12 - 3\\left(9 - 12\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
            Subtract the parentheses first.<\/td>\r\n[latex]12 - 3\\left(-3\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
            Multiply.<\/td>\r\n[latex]12-\\left(-9\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
            Subtract.<\/td>\r\n[latex]\\text{21}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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

            [ohm2_question hide_question_numbers=1]8917[\/ohm2_question]<\/section>\r\n
            Simplify the following:
            [latex]-30\\div 2+\\left(-3\\right)\\left(-7\\right)[\/latex]<\/center>
            \r\n[reveal-answer q=\"523980\"]Show Solution[\/reveal-answer]
            \r\n[hidden-answer a=\"523980\"]
            \r\nFirst we will multiply and divide from left to right. Then we will add.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
             <\/td>\r\n[latex]-30\\div 2+\\left(-3\\right)\\left(-7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
            Divide.<\/td>\r\n[latex]-15+\\left(-3\\right)\\left(-7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n
            Multiply.<\/td>\r\n[latex]-15+21[\/latex]<\/td>\r\n<\/tr>\r\n
            Add.<\/td>\r\n[latex]\\text{6}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

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

            [ohm2_question hide_question_numbers=1]8918[\/ohm2_question]<\/section>","rendered":"

            Simplifying and Evaluating Expressions With Integers That Use all Four Operations<\/h2>\n

            Now we\u2019ll simplify expressions that use all four operations\u2013addition, subtraction, multiplication, and division\u2013with integers. Remember to follow the order of operations.<\/p>\n

            Order of operations is a set of rules in mathematics that dictates the sequence in which operations should be performed to correctly solve an expression. It is commonly remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). <\/p>\n

            For instance, in the expression [latex]8 + (4 * 2)^2 \u00f7 4 - 2[\/latex] using the order of operations we must:<\/p>\n

              \n
            1. Parentheses\/Brackets: Perform the operation inside the parentheses first.\n
                \n
              • This gives us: [latex]8 + (8)^2 \u00f7 4 - 2[\/latex]<\/li>\n<\/ul>\n<\/li>\n
              • Exponents\/Orders: Next, solve for the exponent.\n
                  \n
                • This gives us: [latex]8 + 64 \u00f7 4 - 2[\/latex]<\/li>\n<\/ul>\n<\/li>\n
                • Multiplication and Division: Perform multiplication and division operations from left to right.\n
                    \n
                  • This gives us: [latex]8 + 16 - 2[\/latex]<\/li>\n<\/ul>\n<\/li>\n
                  • Addition and Subtraction: Finally, carry out addition and subtraction from left to right.\n
                      \n
                    • This gives us: [latex]24 - 2 = 22[\/latex]<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n

                      So, the result of the expression [latex]8 + (4 * 2)^2 \u00f7 4 - 2[\/latex] following the order of operations is [latex]22[\/latex].<\/p>\n<\/section>\n

                      Simplify the following:<\/p>\n
                      [latex]7\\left(-2\\right)+4\\left(-7\\right)-6[\/latex]<\/div>\n
                      <\/div>\n