A common point of confusion for Algebra 1 students is the slopes of horizontal and vertical lines, and how these relate to the fraction used for slope.īy graphing the line and changing the numerator and denominator values, we can visualize how slope is impacted when either number is zero. Slopes of lines give another window into how zero operates in a fraction. Students can also observe how the fraction’s value decreases when the numerator decreases, but the denominator has the opposite impact: the fraction’s value increases when the denominator decreases. 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. Still, college professors remain divided on the use of calculators in their classes.Understanding Zeros in Fractions & Slopes Are calculators still used?Ĭalculators are so commonplace in modern American education that a TI-84 or -89 can be found stashed away in many homes, mementos from taking the SAT or computing integrals on the Advanced Placement calculus exam. The two different types of TI-NSpire-the CX II and the CX II CAS-are both great options for math students handling coursework or about to tackle national exams (SATs and ACTs). The TI-NSpire by Texas Instruments is arguably the most powerful and reliable calculator you can buy. … The equation for fairness is simple: You know it when you see it, and this calculator inequity isn’t it. The ACT, which competes with the College Board for test-takers, prohibits calculators with CAS functionality. Seven models of the TI-Nspire CAS are on the College Board’s list. HP used reverse Polish notation on every handheld calculator it sold, whether scientific, financial, or programmable, until it introduced the HP-10 adding machine calculator in 1977. The HP-35, the world’s first handheld scientific calculator, introduced the classical four-level RPN in 1972. Texas Instruments Incorporated (TI), American manufacturer of calculators, microprocessors, and digital signal processors with its headquarters in Dallas, Texas. Where Are Texas Instruments Calculators Made?
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