{"id":8506,"date":"2023-10-03T15:07:31","date_gmt":"2023-10-03T15:07:31","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=8506"},"modified":"2024-10-18T20:56:39","modified_gmt":"2024-10-18T20:56:39","slug":"calculations-involving-rational-numbers-learn-it-2","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/calculations-involving-rational-numbers-learn-it-2\/","title":{"raw":"Calculations Involving Rational Numbers: Learn It 2","rendered":"Calculations Involving Rational Numbers: Learn It 2"},"content":{"raw":"

Subtracting Rational Numbers<\/h2>\r\n

When you subtract rational numbers, you must think about whether they have a common denominator, just like with adding rational numbers. When the two rational numbers have a common denominator, then subtracting the two numbers is straightforward.<\/p>\r\n

\r\n
\r\n

subtracting rational numbers with a common denominator<\/h3>\r\n

Subtract the numerators, and then place that value in the numerator and the common denominator in the denominator.<\/p>\r\n

 <\/p>\r\n

Symbolically, we write this as: If [latex]c[\/latex] is a non-zero integer, then

[latex]\\frac{a}{c}-\\frac{b}{c}=\\frac{a-b}{c}[\/latex]<\/center><\/p>\r\n<\/div>\r\n<\/section>\r\n
Calculate [latex]\\frac{45}{136}-\\frac{17}{136}[\/latex] .[reveal-answer q=\"160931\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160931\"]\r\n\r\n\r\n

Since the rational numbers have the same denominator, we perform the subtraction of the numerators, [latex]45-17[\/latex], and then place the result in the numerator and the common denominator, [latex]136[\/latex], in the denominator.<\/p>\r\n

[latex]\\frac{45}{136}-\\frac{17}{136}=\\frac{45-17}{136}=\\frac{28}{136}[\/latex]<\/p>\r\n

Once we have that result, reduce to lowest terms, which gives

[latex]\\frac{28}{136}=\\frac{4\u00d77}{4\u00d734}=\\frac{\\cancel{4}\u00d77}{\\cancel{4}\u00d734}=\\frac{7}{34}[\/latex]<\/center><\/p>\r\n\r\n\r\n[\/hidden-answer]<\/section>\r\n
\r\n

[ohm2_question hide_question_numbers=1]12693[\/ohm2_question]<\/p>\r\n<\/section>\r\n

Just like when adding rational numbers, when subtracting rational numbers that do not have common denominators, we have to transform the rational numbers so that they do have common denominators. This can be done the same way we did when adding rational numbers.<\/p>\r\n

\r\n

How To: Subtracting Rational Numbers With Unlike Denominators<\/strong><\/p>\r\n

    \r\n\t
  1. Find a common denominator.<\/li>\r\n\t
  2. Rewrite each fraction using the common denominator.<\/li>\r\n\t
  3. Now that the fractions have a common denominator, you can subtract the numerators.<\/li>\r\n\t
  4. Simplify by canceling out all common factors in the numerator and denominator.<\/li>\r\n<\/ol>\r\n<\/section>\r\n
    Calculate [latex]\\frac{14}{25}-\\frac{9}{70}[\/latex].[reveal-answer q=\"160932\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160932\"]\r\n\r\n\r\n

    The denominators of the fractions are [latex]25[\/latex] and [latex]70[\/latex]. We need to find the LCM of [latex]25[\/latex] and [latex]70[\/latex].<\/p>\r\n

    [latex]LCM(25,70)=350[\/latex]<\/p>\r\n

    Next, we rewrite each fraction with [latex]350[\/latex] as the common denominator.<\/p>\r\n

    [latex]\\frac{14}{25}=\\frac{14\u00d714}{350}[\/latex]<\/p>\r\n

    [latex]\\frac{9}{70}=\\frac{9\u00d75}{350}[\/latex]<\/p>\r\n

    Now, we can subtract the two fractions together.<\/p>\r\n

    [latex]\\frac{14\u00d714}{350}-\\frac{9\u00d75}{350}[\/latex]<\/p>\r\n

    [latex]\\frac{196}{350}-\\frac{45}{350}[\/latex]<\/p>\r\n

    [latex]\\frac{196-45}{350}[\/latex]<\/p>\r\n

    [latex]\\frac{151}{350}[\/latex]<\/p>\r\n

    [latex]\\frac{14}{25}-\\frac{9}{70}=\\frac{151}{350}[\/latex]<\/p>\r\n\r\n\r\n[\/hidden-answer]<\/section>\r\n

    \r\n

    [ohm2_question hide_question_numbers=1]12694[\/ohm2_question]<\/p>\r\n<\/section>","rendered":"

    Subtracting Rational Numbers<\/h2>\n

    When you subtract rational numbers, you must think about whether they have a common denominator, just like with adding rational numbers. When the two rational numbers have a common denominator, then subtracting the two numbers is straightforward.<\/p>\n

    \n
    \n

    subtracting rational numbers with a common denominator<\/h3>\n

    Subtract the numerators, and then place that value in the numerator and the common denominator in the denominator.<\/p>\n

     <\/p>\n

    Symbolically, we write this as: If [latex]c[\/latex] is a non-zero integer, then <\/p>\n

    [latex]\\frac{a}{c}-\\frac{b}{c}=\\frac{a-b}{c}[\/latex]<\/div>\n<\/div>\n<\/section>\n
    Calculate [latex]\\frac{45}{136}-\\frac{17}{136}[\/latex] .<\/p>\n