Download Notes: Adding and Subtracting Fractions and Mixed

Notes: Adding and Subtracting Fractions and Mixed Numbers
(For more examples or a more detailed explanation, look at chapter 5 in the textbook.)
With Like Denominators: If the denominators in two fractions are the same, just add or subtract the
numerators.
Example:
REMEMBER: The final step to any problem when you
are adding and subtracting fractions and mixed
+ =
Then simplify: =
numbers is to simplify the answer.
With Mixed Numbers with Like Denominators: If you have mixed numbers in which the fractions have
like denominators, add or subtract the fractions
and add or subtract the whole numbers.
Example:
3 + 4 = 7 Simplify: 7
Sometimes the fraction in your answer is an improper fraction. Turn it in to a mixed number and add it
to your whole number.
Example:
How to simplify 5
2 + 3 = 5 Simplify: 5 = 6
Notice that 5 = 5 +
Change the improper fraction to a mixed number
=1
Then, add the mixed number to the whole number from your
problem: 5 + 1 = 6
With Unlike Denominators: If the denominators in two fractions or mixed numbers are NOT the same,
make equivalent fractions using the least common denominator (LCD). Example: +
First: Write
the problem
vertically:
+
Next: Rename
using the LCD, 15
x
=
x
=
Finally: add
the fractions.
+
While you are getting used to doing all of these steps, the “tic-tac-toe” framework is helpful.
Example:
+ =
x
+
x
With Mixed Numbers and Unlike Denominators: If you have mixed numbers in which the fractions
have unlike denominators, add or subtract the fractions and add or subtract the whole numbers.
Example:
5 – 3 =
5
x
5
– 3
x
3
2
Don’t forget to simplify, if necessary.
This example is already in simplest form.
Subtracting Mixed numbers with Renaming: Just like when we subtract whole numbers, sometimes
we have to “regroup” or “borrow” when we subtract fractions.
Example: Subtract from
a whole number
REALIZE:
5 is the same as 4 + 1,
Rename 5 as
4
and subtract
– 2
AND: 1 can be expressed as
5 – 2
SO:
Example: Subtract from
a mixed number
4 –1
5= 4
REALIZE:
2
4 is the same as 3 + 1 ,
AND: 1 can be expressed as
Rename 4 as 3
and subtract
– 1
SO: 4 = 3
2
Example: Subtract from a mixed number where the fractions have unlike denominators.
Use the “tic-tac-toe” graphic organizer to find equivalent fractions.
5
x
5 = 4+1
= 4
–2
x
2
–2
2
In this step you are renaming 5 as 4
Don’t forget to simplify, if necessary.
This example is already in simplest form.
As you get more familiar with the process, you will eventually be able to drop the framework and do
some of the work in your head. Your work might look like this:
5 =5 =4
–2 =
–2
2
However, until you have a complete understanding of
the process, please show all your work in using the
“tic-tac-toe” graphic organizer.