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Title: Proper Fraction Fury Problem Statement: Suppose you start with a proper fraction (where the numerator is less than the denominator), and you add 1 to the numerator and to the denominator. For example, if you started with 2/ 3, then you'd get Is this procedure of adding 1 to the numerator and the denominator the same as adding the number 1 to the original fraction? Explain your reasoning. Try several examples (with proper fractions), comparing the sizes of the original fraction and the new fraction. What do you notice? Give a general explanation for what you observe. In other words, compare the sizes of Problem Setup: This problem compares adding 1 to the entire fraction versus adding 1a to the numerator and denominator separately. Plans to Solve/Investigate the Problem: The problem will be setup using Microsoft excel. The strategy is to come up with a way to express by adding one to the numerator and the denominator, as well as adding one to the whole fraction and compare my findings. Investigation/Exploration of the Problem: Four Columns were created in Microsoft Excel, which were as follows: Numerator Denominator 2 1 1 1 1 2 2 2 3 3 4 4 new Fraction 3 2 3 4 5 3 4 5 4 5 5 6 3/4 2/3 1/2 2/5 1/3 3/4 3/5 1/2 4/5 2/3 5/6 5/7 Fraction+1 1 2/3 1 1/2 1 1/3 1 1/4 1 1/5 1 2/3 1 1/2 1 2/5 1 3/4 1 3/5 1 4/5 1 2/3 5 5 6 7 6/7 3/4 1 5/6 1 5/7 I proceeded to plug in various numerators that were smaller than the denominator. I continued to do this until I could develop a pattern. In working the problem, I discovered that adding one to a problem causes the problem to increase in value by 1 whole number. In adding 1 to the numerator and denominator separately causes the value of the fraction to increase but not by an increase to exceed the value of one. Extensions of the Problem: The problem can extended to teach students the impact of adding whole numbers to fraction versus adding it to each part of a fraction. Author and Contact: LaTonya Beeman, [email protected] Martin Luther King Jr. Middle School, Atlant+a, GA