Adding and Subtracting Fractions - Algebra II

Complete the following operations:

To complete this problem, we will need to make common denominators. Let's try 16, because it is the least common denominator.

So, we want the denominators of all our fractions to be 16. We get there by multiplying both halves of the fraction by the number which will get our denominator to 16. This sounds confusing, but makes more sense when we see it in action:

See how we multiply the first fraction by 2's and the second by 4's?

Next, complete the problem by combining the fractions by adding/subtracting along the top:

So our answer is:

When adding fractions, the first thing we need to do is get a common denominator.

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

When adding fractions, the first thing we need to do is get a common denominator.

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

When adding fractions, the first thing we need to do is get a common denominator, but for this question, we do not need to do this because their denominators are already the same. Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

When adding fractions, the first thing we need to do is get a common denominator.

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

When subtracting fractions, the first thing we need to do is get a common denominator.

Then when subtracting, only subtract the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

When subtracting fractions, the first thing we need to do is get a common denominator.

Then when subtracting, only subtract the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

When subtracting fractions, the first thing we need to do is get a common denominator.

Then when subtracting, only subtract the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

When adding fractions, the first thing we need to do is get a common denominator.

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

To add these fractions, first identify the common denominator, which is the product of the two: . Then, multiply each numerator by what you multiplied its respective denominator by. . Add the numerators: . Then, your answer is: .

Both fractions have the same denominator, so you can combine the terms in the numerator so that it looks like

After you combine like terms, you are left with in the numerator. The next step is to see what will cancel out. . The in the denominator can be canceled out, and you are left with in the numerator.

If you are having trouble visualizing this it would look like . You can cross out the two x's on the bottom, and two of the x's on the top. Therefore the answer is

When adding fractions, the first thing we need to do is get a common denominator.

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

To simplify this you need to find a common denominator of all the fractions which is "24"

You must multiply the numerator and the denominator by the value that gave you "24" on the bottom.

So you will get:

which equals

The rules for adding fractions containing unknowns are the same as for fractions containing explicit numbers, so you can guide yourself by recalling how you would proceed adding fractions such as,

As you know you need to write them with a common denominator. In this case the least common denominator is . So simply multiply the numerator and denominator of each fraction by the denominator of the other fraciton.

Notice that and are equal to one, this ensures that we are not changing the value of the fractions, we are changing only the representation of the value.

Similairily, the procedure for an algebraic expression containing unknowns parallels this idea,

Now we can add the numerators directly since we now have both terms expressed with a common denominator, .

When adding fractions, the first thing we need to do is get a common denominator.

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

When adding fractions, the first thing we need to do is get a common denominator.

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

When adding fractions, the first thing we need to do is get a common denominator.

Then when adding, only add the numbers on the top, while leaving the common number on the bottom the same. Once we get a final answer, simplify accordingly.

Find the least common denominator (LCD) and convert each fraction to the LCD and then add. Simplify as necessary.

The result is an improper fraction because the numerator is larger than the denominator and can be simplified and converted to a mix numeral.

Since the denominator is the same in both expressions, we can perform the subtraction in the numerator. The result will have the same denominator of 6x3y.

Simplify the expression:

Multiply all the nominators and the denominators separately.

Then, simplify the solution untill you get an answer that is an option on the exam.

An alternate, quicker solution would be to cancel out any matching denominators and nominators.

Once that is done, the equation simpifies to