# Algebra II : Multiplying and Dividing Fractions

## Example Questions

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### Example Question #1 : Multiplying And Dividing Fractions

Solve the following equation to find

Explanation:

The first step in solving this equation is to add the fractions, giving us:

To solve for , we need to divide both sides by .

Remember: When we divide a number by a fraction, we "switch" (find the reciprocal) of the fraction and mulitply it to the number.

The right side of the equation cancels out leaving  alone:

Notice: Both the numerator and denominator are divisble by  so we can simplify this further.

### Example Question #2 : Multiplying And Dividing Fractions

Simplify .

Explanation:

The problem can be made easier by first simplifying each fraction:  and

This brings our new problem to .

Now, the numerators are multiplied by each other then the denomenators are multiplied by each other: .

### Example Question #3 : Multiplying And Dividing Fractions

Simplify .

Explanation:

To solve, we must turn the division problem into a multiplication problem by "flipping" the second fraction (dividing by a fraction is the same as multiplying by its reciprocal):

.

Then, we multiply the numerators followed by the denomenators:

.

Lastly, the fraction must be simplified by a factor of 3:

, which gives us our final answer.

### Example Question #4 : Multiplying And Dividing Fractions

Multiply:

Explanation:

To multiply fractions, just multiply the numerators, then the denominators, and then simplify.

### Example Question #5 : Multiplying And Dividing Fractions

Multiply:

Explanation:

To multiply fractions, multiply the numerators and denominators together, then simplify.

### Example Question #6 : Multiplying And Dividing Fractions

Multiply:

Explanation:

Multiply the numerators and denominators. Then, simplify.

### Example Question #7 : Multiplying And Dividing Fractions

Multiply:

Explanation:

Multiply the numerators and denominators, then simplify.

### Example Question #8 : Multiplying And Dividing Fractions

Simplify:

Explanation:

In order to divide fractions, you need to multiply the first fraction by the reciprocal of the second one.

Now, multiply the numerators and denominators together, then simplify.

### Example Question #9 : Multiplying And Dividing Fractions

Simplify:

Explanation:

To divid fractions, you need to multiply the first fraction by the reciprocal of the second.

Now, multiply the numerators and denominators together, then simplify.

Simplify: