Traditionally, the teaching of fractions in handling numbers provides
the basis for handling fractions in algebra. All sorts of techniques
carry over. This follows the Piaget line of reasoning of working from
the concrete to the abstract.
Some examples:
2/3 + 2/5 = 10/15 + 6/15 = 16/15
a/x + b/y = ay/xy + bx/xy = (ay + bx)/xy
4 3/5 = 20/5 + 3/5 = 23/5
x + a/y = xy/y + a/y = (xy + a)/y
(2/3)/(3/4) = (2 x 4)/(3 x 3) = 8/9
(a/x)/(b/y) = ay/bx
I have even taught "long division" in algebra by first reviewing "long
division" with numbers. Recently I heard a horror story of public school
systems no longer teaching long division of numbers. Argh!
I am sadly certain that public schools no longer teach how to take
square roots and cube roots of numbers by the method emulating long
division! And as for checking one's arithmetic by casting out nines....
Jim
Martin Vlietstra wrote:
Fractions DO have a role – in algebra when one is manipulating symbols,
but I agree with Pat, they do not have a role when one is manipulating
numbers.
....
--
James R. Frysinger
632 Stony Point Mountain Road
Doyle, TN 38559-3030
(H) 931.657.3107
(C) 931.212.0267
