Page 230 - Basic College Mathematics with Early Integers

ADDING AND SUBTRACTING LIKE FRACTIONS, LEAST
Objectives
3.4 COMMON DENOMINATOR, AND EQUIVALENT FRACTIONS
Add or Subtract Like Fractions.
Fractions with the same denominator are called like fractions. Fractions that have Add or Subtract Given Fractional
different denominators are called unlike fractions. Replacement Values.
Like Fractions Unlike Fractions
Solve Problems by Adding or
2 3 2 3 Subtracting Like Fractions.
and and
5 5 5 4
same denominator Î Î different denominators Find the Least Common
Î
Î
Denominator of a List of
5 16 7 5 5
, , and and Fractions.
21 21 21 7 9
same denominator Î Î different denominators Write Equivalent Fractions.
Î
Î
Î
Objective Adding or Subtracting Like Fractions
To see how we add like fractions (fractions with the same denominator), study one
or both illustrations below.

1 3
Add:
5 5
Figures Number Line
Q E To add 1 + 3 , start at 0 and draw an arrow
5 5
1
of a unit long pointing to the right. From
5
3
the tip of this arrow, draw an arrow of a
5
unit long also pointing to the right.The tip
4
Q E R of the second arrow ends at their sum, .
5
Start End
Q E

0 R 1

Q E R

1 3 4
Thus, + = .
5 5 5

Notice that the numerator of the sum is the sum of the numerators. Also, the
denominator of the sum is the common denominator. This is how we add fractions.
Similar illustrations can be shown for subtracting fractions.

Adding or Subtracting Like Fractions (Fractions
with the Same Denominator)
If a, b, and c are numbers, and b is not 0, then
a c = and also a c a - c
a + c
+ - =
b b b b b b
In other words,to add or subtract fractions with the same denominator,add or subtract
their numerators and write the sum or difference over the common denominator.
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