Download Proper Fraction Fury

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