Algebra II : Elementary Operations

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #101 : Addition And Subtraction

Add the numbers:  

Possible Answers:

Correct answer:

Explanation:

Add the ones digits.

Add the tens digits with the one as the carryover.

Repeat the process for the hundreds digit.

There is no carryover for this step.

Add the thousands digits.

Combine this number with the ones digits of the previous steps.

The answer is:  

Example Question #102 : Addition And Subtraction

Add the numbers:  

Possible Answers:

Correct answer:

Explanation:

Add the ones digits.

The carryover is the tens place.

Add the tens place with the carryover from the last step.

Repeat the process for the hundreds digits.

Combine this number with the ones digits of the previous steps.

The answer is:  

Example Question #103 : Addition And Subtraction

Add the following numbers:  

Possible Answers:

Correct answer:

Explanation:

Add the ones digits.

Add the tens digits with the one as the carryover.

Repeat the process with the hundreds digit.

Combine this number with the ones digits of the previous calculations.

The answer is:  

Example Question #1 : Multiplication And Division

Let x and y be complex numbers

Evaluate the product .

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Multiplication And Division

Solve for  if .

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

The most important part of this problem is to remember the order of operations: PEMDAS

First: Perform any calculations that are within parentheses.

Second: Perform any calculations that are raised to an exponent.

Third: Working from left to right, perform any multiplications or divisions.

Fourth: Working from left to right, perform any additions or subtractions

 

For this problem:

First we do all of the calculations inside parentheses:   and .

Therefore, the expression becomes .Now working from left to right, we perform any multiplications and/or divisions:  and .

Therefore, the expression becomes  and we simply add the remaining numbers to get 

Example Question #3 : Multiplication And Division

Solve for  if .

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we simply follow our order of operations, PEMDAS:

 

First: Perform any calculations that are within parentheses.

Second: Perform any calculations that are raised to an exponent.

Third: Working from left to right, perform any multiplications or divisions.

Fourth: Working from left to right, perform any additions or subtractions.

 First, we evaluate our parentheses:  and .

The original expression then becomes .

Example Question #1 : Multiplication And Division

Find the Prime Factorization of .

Possible Answers:

Correct answer:

Explanation:

To find the prime factorization of 40, write 40 as a combination of its prime factors.

Example Question #1 : Multiplication And Division

Using the distributive property, simplify the following:

Possible Answers:

Correct answer:

Explanation:

The distributive property is handy to help get rid of parentheses in expressions. The distributive property says you "distribute" the multiple to every term inside the parentheses. In symbols, the rule states that 

So, using this rule, we get 

 

Thus we have our answer is .

Example Question #2 : Multiplication And Division

Simplify the following: 

 

Possible Answers:

Correct answer:

Explanation:

We are dividing the polynomial by a monomial. In essence, we are dividing each term of the polynomial by the monomial. First I like to re-write this expression as a fraction. So,

So now we see the three terms to be divided on top. We will divide each term by the monomial on the bottom. To show this better, we can rewrite the equation. 

 

Now we must remember the rule for dividing variable exponents. The rule is So, we can use this rule and apply it to our expression above. Then,

 

 

Example Question #101 : Elementary Operations

Multiply: 

Possible Answers:

Correct answer:

Explanation:

The first two factors are the product of the sum and the difference of the same two terms, so we can use the difference of squares:

Now use the FOIL method:

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