{"id":3894,"date":"2021-11-15T16:04:48","date_gmt":"2021-11-15T16:04:48","guid":{"rendered":"https:\/\/stgwebsite.mindspark.in\/wordpress\/?page_id=3894"},"modified":"2021-11-20T07:51:09","modified_gmt":"2021-11-20T07:51:09","slug":"types-of-fractions-definition-and-examples","status":"publish","type":"page","link":"https:\/\/stgwebsite.mindspark.in\/studymaterial\/math-concepts\/types-of-fractions-definition-and-examples\/","title":{"rendered":"Types of fractions \u2013 Definition and examples"},"content":{"rendered":"

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Types of fractions \u2013 Definition and examples<\/h1>\n

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In this article, we will understand different types of fractions with the help of some examples and learn how to identify them.<\/p>\n

 <\/p>\n

Types of fractions<\/h2>\n

Fractions are classified into three types based on the properties of numerator and denominator, these are:<\/p>\n

    \n
  1. Proper fraction<\/span><\/li>\n
  2. Improper fractions<\/span><\/li>\n
  3. Mixed fraction<\/span><\/li>\n<\/ol>\n

    <\/span><\/p>\n

    Group of fractions are classified into 2 types:\u00a0<\/span><\/p>\n

      \n
    1. Like fractions<\/span><\/li>\n
    2. Unlike fractions\u00a0<\/span><\/li>\n<\/ol>\n

      <\/span><\/p>\n

      Further, there are two more types of fractions:<\/span><\/p>\n

        \n
      1. Equivalent fractions<\/span><\/li>\n
      2. Unit fractions<\/span><\/li>\n<\/ol>\n

        Now let us understand each type of fraction with examples.<\/span><\/p>\n

        <\/b><\/h2>\n

        Proper fractions<\/b><\/h2>\n

        A fraction is a proper fraction if it has the following properties:<\/span><\/p>\n

          \n
        1. Numerator < Denominator.<\/span><\/li>\n
        2. Value of fraction is less than 1.<\/span><\/li>\n<\/ol>\n

          Examples:<\/strong><\/p>\n

          a \\frac{1}{7}<\/span><\/strong><\/p>\n

          b \\frac{2}{5}<\/span><\/strong><\/p>\n

          c \\frac{2}{35}<\/span><\/strong><\/p>\n

          d \\frac{3}{8}<\/span><\/strong><\/p>\n

           <\/p>\n

          Improper fractions<\/b><\/h2>\n

          A fraction is an improper fraction if it has the following properties:
          <\/span><\/p>\n

            \n
          1. Numerator > Denominator.<\/span><\/li>\n
          2. Value of fraction is more than 1.<\/span><\/li>\n<\/ol>\n

            Examples:<\/strong><\/p>\n

            a \\frac{8}{7}<\/span><\/strong><\/p>\n

            b \\frac{11}{5}<\/span><\/strong><\/p>\n

            c \\frac{36}{35}<\/span><\/strong><\/p>\n

            d \\frac{99}{8}<\/span><\/strong><\/p>\n

             <\/p>\n

            Mixed fraction<\/b><\/h2>\n

            A fraction is a mixed fraction if it has the following properties:<\/span><\/p>\n

              \n
            1. It consists of a whole number and a proper fraction.<\/span><\/li>\n
            2. Value of fraction is more than 1.\u00a0<\/span><\/li>\n<\/ol>\n

              A mixed fraction can also be written in the form of an improper fraction and vice-versa.<\/span><\/p>\n

              Examples:<\/strong><\/p>\n

              a. 2 \\frac{1}{7}<\/span><\/strong><\/p>\n

              2 is a whole number and \\frac{1}{7}<\/span>is a fraction.<\/p>\n

              b. 1\\frac{2}{5}<\/span><\/strong><\/p>\n

              1 is a whole number and \\frac{2}{5}<\/span> is a fraction.<\/p>\n

              c. 3 \\frac{2}{35}<\/span><\/strong><\/p>\n

              3\u00a0 is a whole number and \\frac{2}{35}<\/span> is a fraction.<\/p>\n

               <\/p>\n

              Like fractions<\/b><\/h2>\n

              A group of fractions are like fractions if they have the\u00a0 following properties:<\/span><\/p>\n

                \n
              1. Denominators of all the fractions in the group are equal.<\/span><\/li>\n
              2. The fractions may be proper or improper.<\/span><\/li>\n<\/ol>\n

                Examples:\u00a0<\/strong><\/p>\n

                a \\frac{1}{7}, \\frac{6}{7}, \\frac{5}{7}, \\frac{11}{7}, \\frac{10}{7}, \\frac{3}{7}<\/span><\/strong><\/p>\n

                The denominator 7 is common.<\/span><\/strong><\/p>\n

                b. \\frac{2}{5}, \\frac{3}{5}, \\frac{5}{5}, \\frac{12}{5}, \\frac{6}{5}, \\frac{1}{5}<\/span><\/strong><\/p>\n

                The denominator 5 is common.<\/span><\/p>\n

                 <\/p>\n

                Unlike fractions<\/b><\/h2>\n

                A group of fractions are unlike fractions if they have the following properties:<\/span><\/p>\n

                  \n
                1. Denominators of all the fractions in the group are not equal.<\/span><\/li>\n
                2. The fractions may be proper or improper.<\/span><\/li>\n<\/ol>\n

                  Examples:\u00a0<\/strong><\/p>\n

                  a. \\frac{1}{7}, \\frac{6}{8}, \\frac{5}{9}, \\frac{11}{7}, \\frac{10}{21}, \\frac{3}{7}<\/span><\/strong><\/p>\n

                  The denominator of all fractions is not equal.<\/span><\/strong><\/p>\n

                  b. \\frac{2}{5}, \\frac{3}{2}, \\frac{5}{8}, \\frac{12}{5}, \\frac{6}{15}, \\frac{1}{5}<\/span><\/strong><\/p>\n

                  The denominator of all fractions is not equal.<\/span><\/p>\n

                   <\/p>\n

                  Equivalent fractions<\/b><\/h2>\n

                  All the fractions giving the same value after simplification are known as equivalent fractions.<\/span><\/p>\n

                  Examples:\u00a0<\/strong><\/p>\n

                  a. \\frac{1}{2}, \\frac{3}{6}, \\frac{5}{10}, \\frac{12}{24}<\/span><\/strong><\/p>\n

                  All the fractions become \\frac{1}{2}<\/span> <\/span>after simplification.<\/span><\/p>\n

                  b. <\/strong>\\frac{2}{3}, \\frac{4}{6}, \\frac{6}{9}, \\frac{12}{18}<\/span><\/span><\/p>\n

                  All the fractions become \\frac{2}{3}<\/span> <\/span>after simplification.<\/span><\/p>\n

                  Multiplying both the numerator and denominator with the same number gives us an equivalent fraction of the given fraction.\u00a0<\/span><\/p>\n

                   <\/p>\n

                  Converting mixed fraction into an improper fraction<\/b><\/h3>\n

                  A mixed fraction is written in the form of\u00a0 ” a\\frac{b}{c}<\/span> “<\/span><\/b><\/p>\n

                  a = whole number <\/span>
                  <\/span>b = numerator <\/span>
                  <\/span>c = denominator<\/span><\/p>\n

                  The improper fraction form of this mixed fraction is written as \\frac{(a \\times c)+b}{c}<\/span>.<\/span><\/p>\n

                   <\/p>\n

                  Converting improper fraction into a mixed fraction<\/b><\/h3>\n

                  An improper fraction is written in the form of \\frac{p}{q}<\/span><\/span>(where p>q)<\/span><\/b><\/p>\n

                  p = numerator <\/span>
                  <\/span>q = denominator<\/span><\/p>\n

                  We have to then divide numerator by denominator<\/span><\/p>\n

                  Then the mixed fraction form of this improper fraction is written as:<\/span><\/p>\n

                  \u00a0” Quotient\\frac{Remainder}{ Divisor }<\/span> ”\u00a0<\/span><\/p>\n

                  <\/span><\/p>\n

                  Solved Examples<\/b><\/h2>\n
                    \n
                  1. Convert 1\u00a0\\frac{1}{7}<\/span><\/span>into an improper fraction.<\/span><\/li>\n<\/ol>\n

                    1 \\frac{1}{7}<\/span><\/span><\/p>\n