Simplifying and/or Reducing Fractions?

[Mr. Tarzan]

I have always taught that when simplifying fractions, having the answer as an improper fraction is correct, even preferred over mixed numbers. I have always accepted mixed numbers as correct, but encouraged my students to be comfortable with improper fractions since they are used more frequently than mixed numbers in mathematics. I require mixed numbers only when students are stating a measurement in a real world situations.

My question to everyone out there is: What is the correct definition of Simplifying Fractions? Should the answer be as an improper fraction or mixed number? AND.... What is the difference between Simplifying Fractions and Reducing Fractions?

Thank you all for your responses.

[stapel_eliz]

What is the correct definition of Simplifying Fractions?

Whatever the teacher in your class is using, I suppose.

As far as I know, there is no standard meaning to "simplifying". In general, it refers to "reducing". In the lower grades, it often also refers to "converting improper fractions to mixed number", because that is, for some reason, often the preference at that level of study. This extra step is dropped, or even actively discouraged, in higher-level study.

[sdbielz]

This is just my opinion, I wouldn't take it as fact.

Reducing a fraction is reducing it... like, 9/12=3/4.

Simplifying it means to put it in simpler terms. That could mean to reduce it, or it could mean to rephrase it. The term 3 and 1/4 has more componants than 13/4, thus it is technically more complex. Therefore, Simplest form should be displayed as an improper fraction.

[eappelbaum]

In mathematical textbooks, answers are usually given as improper fractions rather than mixed numbers. Students get a brief exposure to mixed numbers in middle school and then never encounter them again. But mixed numbers are important both in applications and mathematics. Few people buy 7 half-pound packages of ground beef. You buy 3 and ½ pounds. Suppose you are graphing the equation 7x + 3y = 11. The fastest way to do so is find the intercepts. If x = 0, y = 11/3 = 3 2/3. If y = 0, x = 11/7 = 1 4/7. It is not hard to plot the corresponding points, connect with a straight edge, and draw a graph. But if you do not change the improper fractions to mixed numbers, you will not know where to plot the points. Of course you could also write the intercepts as decimals; this action is time-consuming and inaccurate. You could solve for y as a function of x and use a graphing calculator, also time-consuming and inaccurate. The graphing calculator does not display a scale. Because mixed numbers are so important, I usually ask students to answer problems with mixed numbers instead of improper fractions. Also, paper-grading is faster if answers are in a standard form, rather than getting some papers as fractions and others as mixed numbers. The teacher's instructions to students should state whether the answer is a mixed number or a fraction. Because "simplify" is vague, I prefer the old-fashioned terminology: reduce all fractions to lowest terms.