Download Adding or Subtracting Like Fractions

Math 64
4.4 "Adding and Subtracting Like Fractions"
Objectives:
*
Add or subtract like fractions.
*
Add or subtract given fractional replacement values.
*
Solve problems by adding or subtracting like fractions.
*
Find the Least Common Denominator of a list of fractions.
*
Write equivalent fractions.
Adding or Subtracting Like Fractions
Fractions with the same denominator are called like fractions. Fractions that have di¤erent denominators are called
unlike fractions.
Like Fractions
Unlike Fractions
Adding or Subtracting Like Fractions (Fractions with the Same Denominator)
and also
If a; b; and c; are numbers and b is not 0, then
In other words, to add or subtract fractions with the same denominator, add or subtract their numerator
and write the sum or di¤ erence over the common denominator.
Note:
a
a
=
=
b
b
a
b
as long as b is not 0.
Example 1: (Adding or subtracting like fractions)
Add or subtract the following fractions and reduce to lowest terms.
3
7
12 11
5
a)
+
b)
+
+
10 10
15 15 15
c)
7
5
+
16 16
d)
Page: 1
4
11
6
11
3
11
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
c)
3
16w
15
16w
4.4
d)
9y 2y 5y
+
+
8
8
8
3
8
Adding and Subtracting Given Fractional Replacement Values
Example 2: (Adding or subtracting like fractions)
Evaluate each expression for the given replacement values.
3
2
a) x + y; x =
and y =
4
4
b) x
y; x =
1
and y =
5
3
5
Solving Problems by Adding or Subtracting Like Fractions
Example 3: (Applications)
Find the perimeter of the following …gure.
Example 4: (Applications)
7
3
of a mile and from home to the post o¢ ce is of a mile. How much farther
8
8
is it from home to the World Gym than from home to the post o¢ ce?
The distance from home to the World Gym is
Page: 2
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
4.4
Finding the Least Common Denominator
In the next section, we will add and subtract fractions that have di¤erent, or unlike, denominators. To do so, we …rst
write them as equivalent fractions with a common denominator.
De…nition:
Least Common Denominator
The least common denominator (LCD) of a list of fractions is the smallest positive number
divisible by all the denominators in the list.
The least common denominator is also the least common multiple (LCM) of the denominators.
Finding the LCD: Method 1
Method 1:
Finding the LCD of a List of Fractions Using Multiples of the Largest Number
1: Write the multiples of the largest denominator (starting with the number itself) until a multiple common
to all denominators in the list is found.
2: The multiple found in Step 1 is the LCD.
Example 5: (Finding the LCD: Method 1)
Find the LCD of each list of fractions.
7
11
a)
and
8
32
b)
2
6
and
9
15
Finding the LCD: Method 2
Method 2:
Finding the LCD of a List of Denominators Using Prime Factorization
1: Write the prime factorization of each denominator.
2: For each di¤erent prime factor in Step1, circle the greatest number of times that factor occurs
in any one factorization.
3: The LCD is the product of the circled factors.
Example 6: (Finding the LCD: Method 2)
Find the LCD of each list of fractions.
3 1
13
a)
;
, and
4 14
20
b)
Page: 3
7
3
5
;
; and
20 24
45
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
c)
4.4
7 2
3
;
; and 2
y 11
y
d)
2
3
5
;
; and
25 15x
6x3
Writing Equivalent Fractions
Writing Equivalent Fractions
To write an equivalent fraction,
where a; b; and c are nonzero numbers.
Example 7: (Writing equivalent fractions)
Write each fraction as an equivalent fraction with the given denominator.
a)
14
=
17
68
b)
3
=
5
100
c)
19z
=
21
126
d)
7
=
6
36a
Page: 4
Notes by Bibiana Lopez