{"id":7150,"date":"2017-05-09T17:18:14","date_gmt":"2017-05-09T17:18:14","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&p=7150"},"modified":"2021-05-21T21:00:04","modified_gmt":"2021-05-21T21:00:04","slug":"solve-equations-with-decimals","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/cpcc-algebra-trig-I-support\/chapter\/solve-equations-with-decimals\/","title":{"raw":"Introduction to Solving Equations Containing Decimals","rendered":"Introduction to Solving Equations Containing Decimals"},"content":{"raw":"

What you'll learn to do: Solve equations with decimals using properties of addition and subtraction<\/h2>\r\n[caption id=\"attachment_13318\" align=\"aligncenter\" width=\"1024\"]\"A<\/a> To calculate the difference between two swimmers' race times, you'll need to write an equation with decimals.[\/caption]\r\n\r\nKim and Alyssa are on the same high school swim team, and they're always competing for the fastest time in the 50-meter freestyle event. In the last race, the difference between Kim's time and Alyssa's time was 1.36 seconds. If Alyssa swam the race in 36.79 seconds, what was Kim's time? To solve this problem, you'll need to translate the information given to an equation and then solve it. Read on to find out more about solving equations with decimals.\r\n\r\nBefore you get started, take this readiness quiz.\r\n
\r\n

readiness quiz<\/h3>\r\n1)\r\n\r\n[ohm_question]146320[\/ohm_question]\r\n\r\nIf you missed this problem, review the example below.\r\n
Evaluate [latex]y-\\Large\\frac{5}{6}[\/latex] when [latex]y=-\\Large\\frac{2}{3}[\/latex]\r\n[reveal-answer q=\"848965\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"848965\"]Solution:\r\nWe substitute [latex]-\\Large\\frac{2}{3}[\/latex] for [latex]y[\/latex] in the expression.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]y-\\Large\\frac{5}{6}[\/latex]<\/td>\r\n<\/tr>\r\n
Substitute [latex]\\color{red}{--\\Large\\frac{2}{3}}[\/latex] for y.<\/td>\r\n[latex]\\color{red}{--\\Large\\frac{2}{3}} -\\Large\\frac{5}{6}[\/latex]<\/td>\r\n<\/tr>\r\n
Rewrite as equivalent fractions with the LCD, [latex]6[\/latex].<\/td>\r\n[latex]-\\Large\\frac{4}{6}-\\frac{5}{6}[\/latex]<\/td>\r\n<\/tr>\r\n
Subtract.<\/td>\r\n[latex]-\\Large\\frac{9}{6}[\/latex]<\/td>\r\n<\/tr>\r\n
Simplify.<\/td>\r\n[latex]-\\Large\\frac{3}{2}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n \r\n\r\n2)\r\n\r\n[ohm_question]145205[\/ohm_question]\r\n\r\nIf you missed this problem, review the following example.\r\n
\r\n\r\nEvaluate [latex]20-z\\text{ when}[\/latex]\r\n
    \r\n \t
  1. [latex]z=12[\/latex]<\/li>\r\n \t
  2. [latex]z=-12[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"34289\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"34289\"]\r\n\r\nSolution:\r\n1. To evaluate [latex]20-z\\text{ when }z=12[\/latex], substitute [latex]12[\/latex] for [latex]z[\/latex] in the expression.\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]20--z[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]\\text{Substitute }\\color{red}{12}\\text{ for }z[\/latex]<\/td>\r\n[latex]20--\\color{red}{12}[\/latex]<\/td>\r\n<\/tr>\r\n
    Subtract.<\/td>\r\n[latex]8[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n2. To evaluate [latex]20-z\\text{ when }z=-12,\\text{ substitute }-12\\text{ for }z\\text{in the expression.}[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n
    [latex]20--z[\/latex]<\/td>\r\n<\/tr>\r\n
    [latex]\\text{Substitute }\\color{red}{--12}\\text{ for }z[\/latex]<\/td>\r\n[latex]20--(\\color{red}{--12})[\/latex]<\/td>\r\n<\/tr>\r\n
    Subtract.<\/td>\r\n[latex]32[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n \r\n\r\n3)\r\n\r\n[ohm_question]146336[\/ohm_question]\r\n\r\nIf you missed this problem, review this video.\r\n\r\nhttps:\/\/youtu.be\/BN7iVWWl2y0\r\n\r\n<\/div>\r\n

    Contribute!<\/h2>
    Did you have an idea for improving this content? We\u2019d love your input.<\/div>Improve this page<\/a>Learn More<\/a>","rendered":"

    What you’ll learn to do: Solve equations with decimals using properties of addition and subtraction<\/h2>\n
    \"A<\/a><\/p>\n

    To calculate the difference between two swimmers’ race times, you’ll need to write an equation with decimals.<\/p>\n<\/div>\n

    Kim and Alyssa are on the same high school swim team, and they’re always competing for the fastest time in the 50-meter freestyle event. In the last race, the difference between Kim’s time and Alyssa’s time was 1.36 seconds. If Alyssa swam the race in 36.79 seconds, what was Kim’s time? To solve this problem, you’ll need to translate the information given to an equation and then solve it. Read on to find out more about solving equations with decimals.<\/p>\n

    Before you get started, take this readiness quiz.<\/p>\n

    \n

    readiness quiz<\/h3>\n

    1)<\/p>\n