Bell Work
2
3
Find the LCM of 4x y and 6x y
Answer:
3
12x y
Lesson 44:
Addition of Rational Expressions
with Equal Denominators, Addition
of Rational Expressions with
Unequal Denominators
If we add one eleventh to two
elevenths, we get three elevenths.
1 + 2 = 1+2 = 3
11 11
11
11
This is a demonstration of the rule for
adding fractions whose denominators
are the same.
Rule for Adding Fractions with Equal
Denominators:
Fractions with equal denominators are
added by adding the numerators
algebraically and recording the sum over
a single denominator.
Here is another demonstration of the rule
for adding fractions with equal
denominators. This rule also applies if the
fractions are rational expressions with
equal denominators.
5 + a+b + 2
a+6 a+6
a+6
We see that the denominators are the
same, so we can add the numerators
and record the sum over a single
denominator.
5 + a+b + 2 = 5+a+b+2 = 7+a+b
a+6 a+6 a+6
a+6
a+6
Example:
Add
4
- 6ax
2
2
2x + y
2x + y
Answer:
4 – 6ax
2
2x + y
Example:
Add
5
3
+
z
2
2
2
a + 7y a + 7y
a + 7y
Answer:
2+z
2
a + 7y
Example:
Add 5x + 7 - 3x – 2
2
2
5a x
5a x
Answer:
2x + 9
2
5a x
There are three rules of algebra that
some people believe are more
important than all the rest of the rules
put together. Two of them are the
addition rule for equations and the
multiplication rule for equations. We
have used these many times.
1. The same quantity can be added to
both sides of an equation.
2. Every terms on both sides of an
equation can be multiplied (or
divided) by the same quantity.
The other important rule is that
3. The denominator and
numerator of a fraction can
be multiplied by the same
quantity.
This is called the DenominatorNumerator Same-Quantity Rule.
The denominator and numerator
of a fraction may be multiplied by
the same nonzero quantity
without changing the value of the
fraction.
We cannot find the sum of
¼+½
In this form because the denominators are
not the same. But if we use the
denominator-numerator same-quantity
rule and multiply both the numerator and
the denominator of ½ by 2, we get
¼ + 2/4 = 3/4
If the fractions to be added have
different denominators, the
procedure shown can be used to
rewrite the fractions as
equivalent fractions that have the
same denominator.
Example:
Add 3 + 2
4
b
(we will use a 3-step procedure to
solve this)
Answer:
Step 1: we write the fraction lines with
the proper sign between them:
_______ + ________
Answer:
Step 2: we write the least common
multiple of the denominators as the
new denominators. In other words we
are finding the common denominator.
_______ + _______
4b
4b
Answer:
Step 3: Now we use the denominatornumerator same-quantity rule to find what
is in the numerator.
3b + 8
4b
4b
3b + 8
4b
Example:
Add
4 + 1 + 1
b
c
2
Answer:
1. _____ + _____ + _____
2. _____ + _____ + _____
2bc
2bc
2bc
3.
8c + 2b + bc
2bc
2bc
2bc
= 8c + 2b + bc
2bc
Example:
Add m + 4 - 6
3
2
c
c
Answer:
3
m + 4c – 6c
3
c
Example:
Add p - a + c
4
2
b
Answer:
pb – 2ab + 4ac
4b
Practice:
Add
a + 3 + m
2
3
4
c
4c
3c
Answer:
2
12ac + 9c + 4m
4
12c
HW: Lesson 44 #1-30