This document provides an overview of operations with algebraic fractions that may be included on high school equivalency tests, including multiplying, dividing, and adding or subtracting fractions. While arithmetic fractions are generally not tested, algebraic fractions are more difficult for most adult learners and high school algebra students. The document demonstrates multiplying, dividing, adding and subtracting algebraic fractions through examples and explains that getting a common denominator is a complex process when adding or subtracting fractions.

1. Skill 25 Algebraic Fractions page 139 in the book
Operations with fractions from arithmetic are not generally tested
on the high school Equivalency test. However, there may be a
problem using fractions with algebra which may include
multiplying or dividing and adding or subtracting.
These are hard problems for most adult learners and most high school
algebra students too. I have included just a few with similar problems
from arithmetic on the next several slides.

2. Multiplying Fractions
Look at the arithmetic fractions on the right. Multiply across the top and then
across the bottom. Do the same thing with the algebraic fractions at the left. As you
multiply, divide out any common factors in the top and bottom.

3. Dividing Fractions
Remember that to divide fractions, write the first fraction, change to multiplying, and invert
the second fraction. (Multiply by the reciprocal.) Then, multiply as usual.

4. Adding and Subtracting Fractions
To add or subtract, we must have like denominators. Keep the “like” denominator
and add or subtract the numerators. Getting a common denominator is a complex
Process illustrated by problems 7 and 8 below.