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ADDING AND SUBTRACTING FRACTIONS
Jump right to the exercises!
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The concepts for this exercise are summarized below.
For a complete discussion, read the text.
Fractions have lots of different names, and renaming is often needed
to add or subtract fractions.
Here's how you'd add 12
and
13
:
12
+13
=
1
2⋅3
3+
13⋅
22
= 36
+26
= 5
6
Notice that 36
is just another name for
12
, and
26
is just another name for
13
.
However, these are better names when you need to add these two numbers.
The next few paragraphs discuss the ideas in this example.
ADDING FRACTIONS WITH A COMMON DENOMINATOR
When fractions have the same denominator (called a common denominator),
it's easy to add them:
For all real numbers A and
B , and for
C≠0 ,
AC
+BC
=A+
BC .
That is, to add two fractions with the same denominator,
just add the numerators, and keep the denominator the same.
When fractions to be added don't have a common denominator,
you need to find one, and then rewrite the fractions with this common denominator.
In general, you'll want to use the least common multiple of the individual denominators
as the new denominator.
This is called the least common denominator.
Subtraction works the same way, because subtraction is just a special kind of addition.
EXAMPLES:
13
+25
=1
3⋅5
5+
25⋅
33
=1115
(Note that the least common multiple
of 3 and 5 is 15 .)
16
+12
=1
6+1
2⋅
33=
46=
23
(Note that the least common multiple
of 6 and 2 is 6 .)
(You may input your answer in either form, simplified or not.)
13
-25
=1
3⋅5
5-
25⋅
33
=515
-615
=-1
15
Use the least common denominator.
You must input your answer as a diagonal fraction (like "2/5"), since you can't input horizontal fractions.
You'll probably want to use paper-and-pencil to solve each problem; key in your answer when you're done.