<h1><strong>FRACTIONS</strong></h1> CONTENT <ol> <li>Equivalent Fractions</li> <li>Ordering of Fractions</li> <li>Quantitative Reasoning</li> </ol>   <h2><strong>Equivalent Fractions </strong></h2> <h3><strong>When are fractions said to be equivalent?</strong></h3> Two or more fractions are said to be equivalent or exactly the same if they have the same quantity or have same value. In other words two or more fractions are equivalent if they can be reduced to the same lowest terms. <em>Examples</em>: \(\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8} = \frac{5}{10} = \frac{7}{14} = \frac{14}{28} =\)... These entire fractions are same, as they all have same amount, value or quantity. The same thing applies to these ones: \(\frac{3}{7} = \frac{9}{21} = \frac{12}{28} = \frac{15}{35} = \frac{21}{49} =\)... They are all equal and are therefore equivalent value.   <h2><strong>Test of Equivalent Fractions </strong></h2> If two fractions \(\frac{m}{n}\) and \(\frac{t}{k}\) are equivalent then, \(m × k = n × t\). So to test whether or not two fractions are the same we equate them and then cross multiply. If the two results of cross multiplying are exactly the same then it shows that the two fractions are equivalent. <strong>Examples</strong><strong>: </strong> (a) If \(\frac{3}{7} = \frac{9}{21}\), then 3 × 21 = 7 × 9 = 63. (b) If \(\frac{5}{10} = \frac{7}{14}\), then 10 × 7 = 5 × 14 = 70. (c) If \(\frac{9}{7} = \frac{18}{14}\), then 7 × 18 = 9 × 14 = 126.   <strong>ALTERNATIVELY:</strong> Each of the fractions can be reduced to its lowest term. If the lowest terms are equal to each other or to one another after the reduction, then it shows the equivalence. However, if after reduction the results are not the same, it then means the fractions are not equivalent. <strong>NOTE: </strong>Teacher to demonstrate this approach to students with few examples.

<h1><strong>BASIC OPERATIONS ON FRACTIONS</strong></h1> CONTENT <ol> <li>Addition and Subtraction of Fractions</li> <li>Multiplication and Division of Fractions</li> </ol>   <h2><strong>Addition of Fractions</strong></h2> <strong>Examples:</strong> 1. Add the fractions \(\frac{2}{3}\) and \(\frac{4}{5}\). <strong>Solution:</strong> \(\frac{2}{3} + \frac{4}{5} = \frac{5 × 2 + 3 × 4}{15} \\ = \frac{10 + 12}{15} = \frac{22}{15} = 1\frac{7}{15}\). 2. Add the fractions \(4\frac{3}{11}\), \(7\frac{1}{3}\). <strong>Solution:</strong> \(4\frac{3}{11} + 7\frac{1}{3} = \frac{47}{11} + \frac{22}{3} \\ = \frac{47(3) + 11(22)}{33} \\ = \frac{141 + 242}{33} = \frac{383}{33}\) = \(11\frac{20}{33}\) (in mixed fraction). (<strong>Note</strong>: In this method, we first change the mixed fractions to Improper fractions before adding).