Add and Subtract Fractions with Common Denominators
Site: | Saylor Academy |
Course: | RWM101: Foundations of Real World Math |
Book: | Add and Subtract Fractions with Common Denominators |
Printed by: | Guest user |
Date: | Saturday, September 7, 2024, 7:44 PM |
Description
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.
Add and Subtract Fractions with Common Denominators
Model Fraction Addition
How many quarters are pictured? One quarter plus 2 quarters equals 3 quarters.
Remember, quarters are really fractions of a dollar. Quarters are another way to say fourths. So the picture of the coins shows that
Let's use fraction circles to model the same example, .
So again, we see that
Add Fractions with a Common Denominator
Example 4.52 shows that to add the same-size pieces - meaning that the fractions have the same denominator - we just add the number of pieces.To add fractions with a common denominators, add the numerators and place the sum over the common denominator.
Model Fraction Subtraction
Subtracting two fractions with common denominators is much like adding fractions. Think of a pizza that was cut into 12 slices. Suppose five pieces are eaten for dinner. This means that, after dinner, there are seven pieces (or of the pizza) left in the box. If Leonardo eats 2 of these remaining pieces (or
of the pizza), how much is left? There would be 5 pieces left (or
of the pizza).
Let's use fraction circles to model the same example, .
Start with seven pieces. Take away two
pieces. How many twelfths are left?
Again, we have five twelfths, .
Subtract Fractions with a Common Denominator
We subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.
FRACTION SUBTRACTION
To subtract fractions with common denominators, we subtract the numerators and place the difference over the common denominator.
Source: Rice University, https://openstax.org/books/prealgebra/pages/4-4-add-and-subtract-fractions-with-common-denominators
This work is licensed under a Creative Commons Attribution 4.0 License.
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. |