# Algebra II : Adding and Subtracting Fractions

## Example Questions

### Example Question #90 : Fractions

Explanation:

Find the least common denominator to these fractions.

Multiply both denominators together.

Convert the fractions using this denominator.

### Example Question #61 : Adding And Subtracting Fractions

Subtract the fractions:

Explanation:

In order to subtract the fractions, we must find the least common denominator of the three fractions.

Multiply all three numbers together to find the common denominator.

Convert all the fractions to this denominator, and multiply the numerators with what was multiplied to the denominator to get the new numerator.

Simplify the numerators.

### Example Question #62 : Adding And Subtracting Fractions

Explanation:

To be able to add the fractions, we will need to determine the least common denominator.

The least common denominator is  since this is the minimal term that is both divisible by  and itself.

Convert only the first fraction with the denominator of .

### Example Question #63 : Adding And Subtracting Fractions

Explanation:

In order to add the fractions, we will need a common denominator.

Notice that the largest denominator is divisible by seven.  We can change just the first fraction to the least common denominator.

Rewrite the fraction.

Reduce this fraction by writing out the common factors of the numerator and denominator.

### Example Question #64 : Adding And Subtracting Fractions

Determine the sum as a mixed fraction:

Explanation:

The denominators are not common.  Convert the denominators to a least common denominator.

To obtain the LCD, we can multiply four times three.

This value is the least possible value divisible by four and three.

Convert the fractions.  Multiply the numerators by what was multiplied on the denominator to get the LCD.

Simplify the fractions and add the numerators.  The denominator stays the same.

Forty three goes into twelve three times.  The remainder is seven, which can be written as seven-twelves.

### Example Question #65 : Adding And Subtracting Fractions

Explanation:

In order to add these fractions, we will need a common denominator.  Notice that the least common denominator is nine since it's the least number divisible by both denominators.

Convert the second fraction to the correct denominator.

Simplify the fractions.

### Example Question #66 : Adding And Subtracting Fractions

Subtract the fractions:

Explanation:

The least common denominator is 12.  Convert the first fraction to this denominator in order to subtract the numerators.  The denominators will remain the same.

Simplify the fractions.

### Example Question #67 : Adding And Subtracting Fractions

Subtract the fractions:

Explanation:

To subtract the fractions, we will need to find the least common denominator.

Write out the factors for both denominators.

Multiply four by 15 to get the least common denominator.

The least common denominator is .

Convert both fractions.

### Example Question #68 : Adding And Subtracting Fractions

Explanation:

Determine the least common denominator.  Expand the factors for each denominator.

The least common denominator is .

### Example Question #69 : Adding And Subtracting Fractions

Subtract the fractions: