Admittedly fractions are trouble for most students. In my previous article I talked about why this is so. Percents and decimals too present their share of problems to young students-adults as well. There is an interesting connection between these three mathematical entities and here it is: fractions, percents, and decimals are variations of one and the same thing.
That is correct! These three curious mathematical objects, which go parading around as though they had independent identities, are really one and the same. It's like Clark Kent and Superman: you take off the glasses and suit, and you get Superman. Learn about the personality of one, and you've mastered the intricacies of the other.
Recip Saw
When I pointed this relationship out during one of my lessons, one student looked at me in amazement and said that he never realized that. This boy had gone through school for twelve years-he was a senior in high school-and never saw that connection. When I would stress this relationship throughout my different classes, I would get similar reactions from many students: they just never made the connection that linked these three seemingly different ways of expressing a mathematical idea.
Now this is a problem with mathematics education in this country. Connections are not made between topics in this difficult discipline. For this reason, students are left scratching their heads wondering when in the world they will ever use something like a decimal, a fraction, or a percent, even though these basic things are literally encountered everyday. This failure to connect math to reality harks back to questions like "Why are manhole covers round?", which I presented in my article Why Study Math - The Circle
For those educators reading this, they know that a common rebuttal of the math student is "When am I ever going to use this?" In fact, a common gripe I would hear is "This is totally useless stuff." In preparation for these questions, I worked diligently so that I could show students that there actually was a connection-a reason-why they were studying the particular lesson at hand.
For the topic in question-fractions, percents, and decimals-students must be made aware that a fraction is a percent and that a percent is a decimal. Once students know that they are dealing with one and the same thing, and not three separate ones, they feel less overwhelmed from having to know all about percents, all about fractions, and all about decimals. When students now see 1/8, they know that this is a mathematical synonym for 12.5% or 0.125. Similarly 1/4 is 0.25 which is 25%; 3/8 is 37.5% or 0.375; ½ is 50% or 0.5; 5/8 is 62.5% or 0.625 and 3/4 is 75% or 0.75.
As obvious as the previous mathematical synonyms are to those who understand them, these relationships elude many students, and they end up in ignorance, much like the senior of mine mentioned earlier-and this can be a life-long ignorance, unfortunately. Yet once connections like that among fractions, percents, and decimals are made, connections and cross links are made in other areas as well. When this is done, mathematics is no longer the formidable bugbear that many take it to be.
See more at Help with Fractions