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• Author or Editor: Laurence Sherzer
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## Expanding the Limits of the Calculator Display

The decimal expansions of 1/7 or 5/13 can be found immediately on the average electronic calculator. These decimal expansions are limited to six digits before they begin to repeat. But what do we say to students who want to explore the repeating properties of rational numbers? What would we answer if they asked for the decimal expansion of 1/17 or 3/23? Do we just say, “Keep dividing and you'll find the answer”? Hardly. Long decimal expansions are usually left to actuaries who don't want to mismanage thousands of dollars over the life of an annuity or mortgage table, or to spacecraft engineers who don't want to miss their targets in outer space.

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## McKay's Theorem

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## An Arithmetic Method for Converting Repeating Decimals to Fractions

Students can easily use calculators to convert fra ctions to decimal numbers. But students who have studied the algebraic method of changing a repeating decimal to a fraction often find the method tedious and tend to avoid it. This difficulty raises questions about students' under standing of the nature of repeating decimal numbers. Do they know that all repeating decima ls are shown as a pproximations on the ca lculator display?

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## Adding fractions using the definition of addition of rational numbers and the Euclidean algorithm

Adding fractions by first finding the lowest common denominator has for a long time been assumed to be the best approach to this operation. Is this really the most efficient approach? Is it pedagogically the most practical?

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## A simplified presentation for finding the LCM and the GCF

Given the prime factors of two positive integers, the least common multiple (LCM) of these two numbers is the product of the union of these prime factors, and the greatest common factor (GCF) is the product of the intersection of these prime factors. If we could just state this fact to our students and be understood, our job of teaching them to find the LCM or the GCF of two numbers would be greatly simplified. Unfortunately, as in most teaching, simple verbal statements do not suffice.

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## Adding integers using only the concepts of one-to-one correspondence and counting

The following is a method for teaching the addition of integers which requires only that the students have developed the concepts of one-to-one correspondence and counting. This means that the student need not be familiar with the operations of whole numbers.