In algebra, the distributive property states that x(y + z) = xy + xz. This means multiplying a number or variable at the front of a parenthetical set is equivalent to multiplying that number or variable to the individual terms inside, then carrying out their assigned operation. Note this also works when the interior operation is subtraction. A whole number example of this property would be 3(2x + 4) = 6x + 12.
Follow the rules of multiplying and adding fractions to solve distributive property problems with fractions. Multiply two fractions by multiplying the two numerators, then the two denominators and simplifying if possible. Multiply a whole number and fraction by multiplying the whole number to the numerator, keeping the denominator and simplifying. Add two fractions or a fraction and a whole number by finding a least common denominator, converting the numerators and performing the operation.
Here is an example of using the distributive property with fractions: (1/4)((2/3)x + (2/5)) = 12. Rewrite the expression with the leading fraction distributed: (1/4)(2/3x) + (1/4)(2/5) = 12. Perform the multiplications, pairing numerators and denominators: (2/12)x + 2/20 = 12. Simplify the fractions: (1/6)x + 1/10 = 12.
Subtract 1/10 from both sides: (1/6)x = 12 - 1/10. Find the least common denominator to perform the subtraction. Since 12 = 12/1, simply use the 10 as the common denominator: ((12 * 10) / 10) - 1/10 = 120 / 10 - 1/10 = 119 / 10. Rewrite the equation as (1/6)x = 119/10. Divide the fraction to simplify: (1/6)x = 11.9.
Multiply 6, the inverse of 1/6, to both sides to isolate the variable: x = 11.9 * 6 = 71.4.