How to Simplify Fractions When Multiplying Using the Distributive Property

Algebra problems require a special order of operations.

Frequently used algebraic properties include the communicative property, the associative property, the additive property and the distributive property. The distribute property is used to multiply a single term and two or more terms that are enclosed by parenthesis. For instance, 5(x +2). Importantly, the rules of the distributive property apply whether the terms inside the parenthesis require addition or subtraction, as in 5(x-2). The distributive property follows certain rules if a fraction is present.

Instructions

1. Find a common denominator between fractions inside the parenthesis by multiplying each numerator and denominator by the denominator of the other fraction. For instance, if given the fractions 1/2 and 3/4, multiply 1/2 by 4 to get 4/8 and multiply 3/4 by 2 to get 6/8.

2. Add or subtract fractions inside the parenthesis only once they share a common denominator. As in the above example, 4/8 and 6/8 can be combined to equal 10/8 or subtracted to equal -2/8.

3. Simplify the fraction, if possible. 10/8 is reduced to 5/4, since the numerator and the denominator are divisible by 4. Likewise, -2/8 is reduced to -1/4. The fraction 3/8 may not be reduced since the numerator and the denominator do not share a common denominator.

4. Use the distributive property to get rid of parenthesis by multiplying each term inside the parenthesis by the term outside the parenthesis. For instance, if given 5(3/2 + x), multiply 5 by both 3/2 and x to get 15/2 + 5x.

References

• Purple Math: Simplifying with Parenthesis
• Capitan: Solving Simple Alegebra Equations