Algebra II : Adding and Subtracting Fractions

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #131 : Adding And Subtracting Fractions

Add the fractions:  

Possible Answers:

Correct answer:

Explanation:

Change the first fraction so that both denominators are common.  This will allow us to change the numerator.

Simplify the fractions.

The answer is:  

Example Question #132 : Adding And Subtracting Fractions

Subtract the fractions:  

Possible Answers:

Correct answer:

Explanation:

Convert the fractions so that all fractions have the least common denominator. 

The least common denominator is 81 since this number is the least number that can be divided by all three denominators.

Rewrite the fractions.

The answer is:  

Example Question #133 : Adding And Subtracting Fractions

Add the fractions:  

Possible Answers:

Correct answer:

Explanation:

We can start by reducing the fractions to break down the denominator.

Cancel out the common terms.

The answer is:  

Example Question #134 : Adding And Subtracting Fractions

Add the fractions:  

Possible Answers:

Correct answer:

Explanation:

Convert all fractions to a common denominator.

The LCD is 28 since this number is the least possible number divisible by all three denominators.

The answer is:  

Example Question #135 : Adding And Subtracting Fractions

Add the fractions:  

Possible Answers:

Correct answer:

Explanation:

Solve by changing all fractions to a common denominator.

Write the multiples of each term.  Note that the largest denominator will start with 27, so we would consider the factors that are above this value.  

The value of 54 is divisible by all four denominators.

Simplify the fractions.  With common denominators, the numerators can be added.

The answer is:  

Example Question #136 : Adding And Subtracting Fractions

Add the fractions:  

Possible Answers:

Correct answer:

Explanation:

In order to add the numerators of the fraction, we will need to determine the least common factor, or LCD.

Write out the multiples of each denominator.

We can see that 40 is the LCD.

Convert the fractions.

Simplify the terms.

The answer is:  

Example Question #137 : Adding And Subtracting Fractions

Subtract the fractions:  

Possible Answers:

Correct answer:

Explanation:

Reduce all fractions that can be reduced. 

Determine the least common denominator by multiplying all the new denominators together.

Convert all fractions to this LCD.

Subtract the numerators.

The answer is:  

Example Question #138 : Adding And Subtracting Fractions

Add and simplify, 

 

Possible Answers:

 

Correct answer:

Explanation:

                                                                 (1)

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Adding fractions with unknown or unspecified numbers  and  works very much the same way as adding fractions composed of ordinary numbers. If we were to add the fractions, 

 

We would first write them both with a common denominator by cross multiplying before combining the numerators. 

 

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Cross multiply to add the first two terms under a common denominator:

 

Add the two remaining terms by again cross multiplying to write both terms under a common denominator:

 

Factor the  2nd and 3rd terms in the numerator: 

 

 

Example Question #139 : Adding And Subtracting Fractions

Add  

Possible Answers:

Correct answer:

Explanation:

1) In order to add fractions you want to find the lowest common denominator. Look at the numbers 16 and 4 and ask what could each number be multiplied by to give the other number. The simplest solution is multiply 4 by 4. 

2) Knowing that you would need to multiply 4 by 4 to get 16 you want to multiply one fourth by four over four so that each fraction now has a common denominator of 16. The reason why it is four over four is because you want to multiply it by something equivalent to one over one so it doesn't change the math by interfering with your results

3) Now that each of these fractions have the same denominator you can now add them together. This is done by just adding the numerators together. Do not add the denominators together as you'll get a totally different result.

This leaves   as your final answer.

Example Question #131 : Adding And Subtracting Fractions

Subtract: 

Possible Answers:

Correct answer:

Explanation:

1) In order to subtract fractions you want to find the lowest common denominator. Look at the numbers  and  and ask what could each number be multiplied by to give the other number. The simplest solution is multiply   by .

2) Knowing that you would need to multiply  by  to get  you want to multiply  by  so that each fraction now has a common denominator of . The reason why it is  is because you want to multiply it by something equivalent to   so it doesn't change the math by interfering with your results

3) Now that each of these fractions have the same denominator you can now subtract them together. This is done by just subtracting the numerators from each other. Do not subtract the denominators together as you'll get a totally different result.

This leaves   as your final answer.

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