lESSON
Simplifying
Algebraic
Fractions
Lab Gear
1.
IM!.!fiii.J.i
What
happens
if
you
add
or
subtract equal amounts to or from the nu-
merator and the denominator
of
a fraction?
How can you tell whether the value
of
the
fraction will increase, decrease, or remain
the same? Make up several examples to
see what happens, then make a
generalization.
To
model fractions with the Lab Gear, you can
use the workmat turned on its side. Instead
of
representing an equals sign, the straight line in
the middle now represents the fraction
bar.
4x +
16
Edith and Anna modeled the fraction 4x
with the Lab Gear,
as
shown below.
D
'This
is
an
easy problem," said Edith. "There's
a 4x in both the numerator and the denomina-
14.2 Simplifying Algebraic Fractions
tor, so I can get rid
of
them. The simplified
fraction is 16."
Anna didn't think Edith's method was right.
She decided to check Edith's answer by
substituting.
2. Calculate the value
of
the expression
4x +
16
for several different values for x.
4x
Do all values
of
x make this fraction equal
to 16? Does any value
of
x make it equal
to 16? Explain.
3.
<1>-
Explain why you cannot simplify a
fraction by subtracting the same number
from the numerator and the denominator.
Give examples.
As you know, to simplify a fraction, you divide
numerator
and
denominator
by
the same num-
ber. This is still true
of
algebraic fractions.
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