Algebra II : Adding and Subtracting Fractions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #58 : Fractions

Add the fractions: 

Possible Answers:

Correct answer:

Explanation:

To add fractions we must find a common denominator. In this example we do so by multiplying each side by the denominator of the other fraction:

Add the numerators:

Example Question #61 : Fractions

Complete the following operations:

Possible Answers:

Correct answer:

Explanation:

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:

Example Question #62 : Fractions

Possible Answers:

Correct answer:

Explanation:

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: .

Example Question #63 : Fractions

Simplify the expression:

Possible Answers:

None of these

Correct answer:

Explanation:

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 

Example Question #64 : Fractions

Simplify the following:

Possible Answers:

Correct answer:

Explanation:

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  

Example Question #6 : Partial Fractions

Add:

 

 

 

Possible Answers:

Correct answer:

Explanation:

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, .

 

 

Example Question #65 : Fractions

Add the fractions:

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #66 : Fractions

Add the fractions:

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #67 : Fractions

Add the fractions:

Possible Answers:

Correct answer:

Explanation:

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. 

Example Question #68 : Fractions

Add the fractions:

Possible Answers:

Correct answer:

Explanation:

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. 

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