<h1><strong>FRACTIONS </strong></h1> CONTENT <ol> <li>Definition and Types of Fractions</li> <li>Conversion of Fraction to Decimal and Vice Versa</li> <li>Conversion of Fractions to Percentages and Vice Versa</li> <li>Quantitative Aptitude on Fractions</li> </ol> <br> <h2><strong>What are fractions?</strong></h2> Fractions are portion or part of whole number that describes quantities. Examples Consider the shapes below: <img class="size-full wp-image-23522 aligncenter" src="https://classhall.com/wp-content/uploads/2018/06/fractions.jpg" alt="Fractions" width="490" height="150" /> <h2><strong>Types of Fractions</strong></h2> Fractions are divided into four basic types: (i) <strong>A Proper Fraction</strong> It is a fraction having both numerator and denominator. And such is said to be rational. In a proper fraction, its numerator is smaller in quantity than its denominator. We can use a funny example to explain. Suppose a 15 years old boy is made to carry on his head two small tubers of yam. We can see that he can comfortably and conveniently carry them without feeling the heaviness of the weight of the tubers, on his neck. If we let the boy be the denominator and the two tubers of yam to be numerator, we can reason or compare that the <strong><em>numerator</em></strong> (the yam tubers) and the 15 year-old boy (the <strong><em>denominator</em></strong>) are not equal in weight. Obviously in this example the numerator is lighter than the denominator. It is a proper thing for anyone to do when placing loads on a child’s head. The load on a child’s head should not be heavier than the body mass of that child. So, it is proper. That is exactly what a <strong>proper fraction</strong> looks like. Examples of <strong>proper fractions</strong> are : \(\frac{4}{19}, \frac{1}{13}, \frac{12}{13}, \frac{43}{81}, \frac{34}{43}, \frac{122}{123}, \frac{72}{144},\) etc. (ii)<strong> An Improper Fraction</strong>

<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.