### All Algebra II Resources

## Example Questions

### Example Question #5 : Addition With Fractions

Simplify

**Possible Answers:**

**Correct answer:**

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.

### Example Question #1 : Adding And Subtracting Fractions

Simplify the expression.

**Possible Answers:**

**Correct answer:**

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 6x^{3}y.

Simplify the expression:

### Example Question #2 : Adding And Subtracting Fractions

Suppose a recipe calls for cup of flour, cup of cinnamon, and cup of sugar.

How many cups of ingredients total does the recipe call for?

**Possible Answers:**

**Correct answer:**

To solve, we must first find a common denominator between 3, 4, and 12. All 3 numbers are factors of 12 and therefore 12 can be the common denominator. Then the numerators must be multiplied by the same factor as the demominator was.

This gives us our new fractions:

Next, we add the numerators, but our denominators stay the same:

.

Lastly, we simplify to get as our answer.

### Example Question #4 : Addition With Fractions

Simplify the following fraction:

**Possible Answers:**

**Correct answer:**

Determine the factors of both the numerator and the denominator:

We notice that 3 is a factor of both 12 and 39 so we can simplify by dividing both 12 and 39 by 3.

The result is therefore,

### Example Question #7 : Addition With Fractions

Find the **simplified** result:

**Possible Answers:**

**Correct answer:**

Start by making both fractions into the same denominator. One option is

Then adjust the numerators by multiplying each fraction's numerator by the other fraction's denominator:

Then add the adjusted numerators:

Then we simplify by dividing both numerator and denominator by 2:

which gives us the final result.

### Example Question #3 : Adding And Subtracting Fractions

Find the result. (**It does not need to be simplified)**.

**Possible Answers:**

**Correct answer:**

We start by adjusting both equations to the same denominator.

Notice that the denominator of the second term is a factor of the denominator of the first term. Therefore we only need to adjust the second term by multiplying both numerator and denominator by 2:

Now we need to subtract the numerators:

### Example Question #4 : Adding And Subtracting Fractions

Find the solution:

**Possible Answers:**

**Correct answer:**

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

### Example Question #5 : Adding And Subtracting Fractions

What is the sum of and ?

**Possible Answers:**

**Correct answer:**

Convert the mixed number to an improper fraction.

Then add the numerators together and keep the common denominator.

Finally, simplify.

### Example Question #1 : Partial Fractions

Add:

**Possible Answers:**

**Correct answer:**

To add rational expressions, you must find the common denominator. In this case, it's .

Next, you must change the numerators to offset the new denominator.

becomes and becomes .

Now you can combine the numerators: .

Put that over the denomiator and see if you can simplify/factor further. In this case, you can't.

Therefore, your final answer is:

.

### Example Question #2 : Partial Fractions

Subtract:

**Possible Answers:**

**Correct answer:**

To subtract rational expressions, you must first find the common denominator, which in this case is . That means we only have to adjust the first fraction since the second fraction has that denominator already.

Therefore, the first fraction now looks like:

.

Now that the denominators are the same, combine numerators:

.

Now, put that over the denominator and see if you can simplify any further.

In this case, you can't, so your final answer is:

.

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