If you have a division problem, you can use a fraction to represent it![br][br]For example, if you need to share some pizzas equally among 3 kids, you can cut each pizza into three slices and give a slice (one third of the pizza) to each kid. [br]Do the same for each pizza, count the number of slices (thirds) that each kid received, and you get the result as a fraction![br][br]In this model, a fraction [math]\frac{p}{k}[/math] represents the amount of pizza that an individual kid gets when [i]p[/i] pizzas are shared equally by [i]k[/i] kids.[br][br]Try a few division problems in the applet below and observe the results.
Select the example [math]2\div3[/math] in the app above, and animate to view the result.[br]Has each kid got more than 1 pizza?[br][br]Now try with [math]5\div2[/math]. Has each kid got more than 1 pizza?[br][br]Can you say when we can be sure that in a division (or fraction) the result is greater than 1?
In divisions, when the dividend is greater than the divisor as in [math]5\div2[/math], the result of the division is greater than 1.[br]In fact, if we evaluate [math]5\div2[/math], we get [math]2.5[/math].[br][br]In fractions, when the numerator is greater than the denominator as in [math]\frac{5}{2}[/math], the result is greater than 1.[br]These types of fractions are called [i]improper fractions[/i].