Add and Subtract Fractions with Common Denominators
Read this text. Pay special attention to the sections on fraction addition and subtraction. They provide an overview of how to add and subtract fractions with the same denominator. Complete the practice questions and check your answers.
Answers
EXAMPLE 4.53
Solution
Add the numerators and place the sum over the common denominator. | |
Simplify. |
EXAMPLE 4.54
Solution
Note that we cannot simplify this fraction any more. Since and
are not like terms, we cannot combine them.
EXAMPLE 4.55
Solution
We will begin by rewriting the first fraction with the negative sign in the numerator.
EXAMPLE 4.56
Solution
Add the numerators and place the sum over the common denominator. | |
Combine like terms. |
EXAMPLE 4.57
Solution
Add the numerators and place the sum over the common denominator. | |
Add. | |
Simplify the fraction. |
EXAMPLE 4.59
Solution
Subtract the numerators and place the difference over the common denominator. | |
Simplify the numerator. | |
Simplify the fraction by removing common factors. |
Example 4.60
Solution
Subtract the numerators and place the difference over the common denominator. |
The fraction is simplified because we cannot combine the terms in the numerator.
Example 4.61
Solution
Remember, the fraction can be written as
.
Subtract the numerators. | |
Simplify. | |
Rewrite with the negative sign in front of the fraction. |
Example 4.62
Solution
Combine the numerators over the common denominator. | |
Simplify the numerator, working left to right. | |
Subtract the terms in the numerator. | |
Rewrite with the negative sign in front of the fraction. |