When 0 is in the denominator, the fraction’s value is undefined. This numerical investigation demonstrates that when 0 is in the numerator, the fraction’s value = 0. What happens as the denominator gets smaller? 2ĭividing by zero results in an “undefined” message in Desmos, the TI-84+ family, and TI-Nspire, while GeoGebra displays the symbol for infinity. As you decrease the numerator down to 0 what do you notice?
Begin with these fractions on your calculator or computer technology. Now, let’s look at fractions numerically by finding decimal equivalents. = undefined Looking at Fractions Numerically It doesn’t make sense: it is “undefined.” If we were dividing money, $10 divided into a certain number of piles (10 piles, 5 piles, 2 piles, or 1 pile, for example) can all be done, but we cannot divide $10 into ZERO piles.
But if the pizza delivery doesn’t show up, we have 0 pizzas divided among the 4 people in my house, so we each get 0: With pizzas, we can divide 1 pizza into 4 pieces, 10 pieces, or 1 piece, so those fractions can all be calculated. If you have $10, you can share that among 5 people: $10 5 = $2 each.īut if you have no money, zero dollars divided by 5 people means everyone gets $0.ĭisappointing, but mathematically sensible, and we can carry out the division. I like to use the idea of money or pizzas with my students. We can interpret a fraction as division of two numbers with a sharing metaphor 1. Let’s take a quick look at the “sharing” interpretation of division, then turn to technology for numerical and graphical representations of the amazing ZERO. How might we help students make sense of fractions containing zeros? The difference between and can be confusing.Įveryone knows from elementary school that you “can’t divide by zero” but that rule might not be enough to help learners interpret fractions and slopes that include a zero in the numerator or denominator. Understanding Zeros in Fractions & Slopes
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