but for the sake of equations, inequalities, functions, radicals, quadratic equations, and other algebra concepts.
Most frequently, it is the familiarity
with the rule for denominators that determines how well addition and subtraction are handled. Simply stated, denominators must be the same for all fractions
involved in addition or subtraction. If denominators are not the same, then learners must find the LCD (Least Common
Denominator) and change the fractions
before proceeding with the operation.
Recognition 2: Rules for adding
or subtracting fractions remain
important in algebraic expressions
of any kind, in equations, and in
Look again: Multiplication or division of
fractions takes strong footing on algebra’s
mountains of equations, inequalities, and
other concept valleys.
If you consider a simple equation
which you were solving for one variable,
your strategy probably led you to do
the same to both sides of the equation
in order to isolate the variable to one
side of the equation. This means that
you added, subtracted, multiplied, or
divided the same number on both sides
of the equation. The number might be
a fraction. If the learner already knows
how to use these fraction operations, his
attention will bend toward finding the
variable. He will not veer off the path to
learn or relearn the how-to of operating
5X + 3/5 = 30 3/5
5X + 3/5 – 3/5 = 30 3/5 – 3/5
Here, you subtracted 3/5 from both
sides of the equation.
5X = 30 > Result of subtracting—it’s a
simple multiplication problem.
5X/5 = 30/5 > Here, both sides of the
equation divided by 5.
X = 6 > Here, the variable isolated to
one side of the equation. Equation solved.
Recognition 3: Multiplication and
division of fractions are critical to
problem solving in algebra.
In essence, whether determining how to
make equivalent fractions in any type of
algebra problem, simplifying polynomial
expressions through addition or subtraction, or solving for one variable in
an equation that may use multiplication
and division, we come to see that understanding fractions improves our understanding of algebra.
Vivian Owens is the author of Create a
Touchable Math Environment and Parenting for Education: Revised Edition.
Her books have received awards and selection as “Resources in Education.” Other
books written by Owens include children’s
literature. After a long career as a classroom teacher, Vivian now consults and
writes books. She and her husband are the
parents of three adult children. Learn more
about books by Vivian Owens at www
Although grouping and simplifying like terms highlights the algebra, a learner
may be thrown off path by the need to add or subtract fractions.