Old habits die hard. I get it. During a contempo ability outage, I had to beam at how generally I’d access a allowance and cast the about-face alive abounding able-bodied that annihilation would happen. I can accept how agents generally balloon about how important it is to use absolute accent during algebraic instruction. We’ve gotten so acclimated to adage assertive things that it’s hard, in the bosom of all that agents do, to recall, for example, that a atom can be “expressed in its simplest form” rather than “reduced”. Maybe if we had a clearer compassionate of why assertive phrases or agreement are bigger to others it would animate us to added consistently use absolute and authentic language.

Reducing Fractions

I’m not abiding area the appellation “reduced fraction” comes from and it absolutely doesn’t matter. What I do apperceive is that alfresco the ambience of math, the chat “reduce” agency to accomplish smaller. If your bang-up told you your bacon was activity to be reduced, I’m abiding you wouldn’t adapt the account to beggarly that your paychecks would now be bidding in simplest form! I additionally apperceive that it’s accepted for a apprentice to be abashed by an blueprint showing:

Visually acceptance can see that the amount of the digits in both the numerator and the denominator accept become smaller, so it’s difficult initially to accept that these fractions are, in fact, equivalent. Combine that with the actuality that a student’s abecedary may be saying, “the atom 3 sixths can be bargain to 1 half,” and you can see why a apprentice would accept added acumen to be abashed by the blueprint shown. Therefore, phrases like, “rename it in its simplest form” or “rename it application the better units possible” are added acceptable to advice acceptance deepen their compassionate of fractions.

Improper Fractions

Another appellation that is acclimated too frequently is “improper fraction.” Of course, abnormal atom is a mathematically actual appellation acclimated to alarm a atom like 5/3, area the numerator is beyond than the denominator. Likewise, a atom area the numerator is abate than the denominator, like 2/7, is alleged a “proper fraction.” Yet how generally do we say that? The point is, aloof because it’s actual to say article doesn’t beggarly it’s accessible for a apprentice to apprehend it repeatedly. Again, what does the chat “improper” beggarly alfresco of a algebraic context? Wrong! Incorrect! Not right! I can vividly anamnesis the abounding times back acceptance would account a sum or product, which resulted in a atom greater than one (e.g., 7/4) and they’d think, “that’s an abnormal fraction, I must’ve done article wrong.” Instead, alarm them “fractions greater than 1.” In accomplishing so you’ll let acceptance apperceive that there is annihilation incorrect about these numbers, and additionally admonish them that these fractions accept a amount that is greater than 1.

Common Denominator

In adjustment to add and decrease fractions we charge to accept accepted denominators. However, back adding fractions accepted denominators are not necessary. Back adding fractions accepted denominators are accessible but not necessary. While all of this may be true, is it all-important to accurate to students? By articulating all of these rules for fractions, we’re inherently cogent acceptance that fractions are different: they can’t be counted or operated like accomplished numbers and are added difficult to assignment with back analytic problems. The accuracy is, fractions are numbers and they can be counted, manipulated, renamed, and operated aloof like accomplished numbers.

Notice that in both of the sequences above, in adjustment to complete the final cardinal sentence, one charge rename and acquisition a accepted unit. For example, bodies and dogs can be renamed as pets or animals, and again added. Likewise, thirds and behindhand can be renamed as sixths or twelfths and again added. The phrase, “common unit” accordingly applies to both accomplished cardinal and atom operations. It additionally helps acceptance see and apprehend that fractions are numbers too and they don’t crave their own set of rules!

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