Perform the indicated operations. See Examples 11 through 23.ExampleExample 11 Multiply:...

Perform the indicated operations. See Examples 11 through 23.

Example

Example 11 Multiply: Simplify the product if possible.

Solution:

To simplify the product, we divide the numerator and the denominator by any common factors.

Example 12 Divide and simplify.

Example 13 Divide and simplify.

Example 14 Divide and simplify.

Example 15 Add or subtract as indicated. Then simplify if possible.

Example 16 Add or subtract as indicated. Then simplify if possible.

Example 17 Add or subtract as indicated. Then simplify if possible.

Example 18 Add or subtract as indicated. Then simplify if possible.

Example 19 Add:

Solution: We first must find the least common denominator before the fractions can be added. The least common multiple of the denominators 5 and 4 is 20. This is the LCD we will use.

We write both fractions as equivalent fractions with denominators of 20. Since

then

Example 20 Subtract and simplify:

Solution: The LCD is 12. We write both fractions as equivalent fractions with

denominators of 12.

Example 21 Divide:

Solution: First write each mixed number as an improper fraction.

Now divide as usual.

The fraction is improper. To write it as an equivalent mixed number, remember that the fraction bar means division, and divide.

Thus, the quotient is or .

Example 22 Add:

Solution: 

Example 23 Subtract:

Solution: