Solving Equations with Fractions

Property To solve an equation with fractions, first use addition or subtraction to isolate the term with the variable. Then, multiply by the reciprocal of the variable's coefficient to find the final answer.

Examples To solve $\frac{1}{2}n \frac{1}{3} = \frac{3}{4}$, first add $\frac{1}{3}$ to both sides to get $\frac{1}{2}n = \frac{13}{12}$. Then multiply by $2$ to find $n = \frac{13}{6}$. To solve $\frac{1}{8}m + \frac{3}{4} = \frac{7}{12}$, first subtract $\frac{3}{4}$ (or $\frac{9}{12}$) to get $\frac{1}{8}m = \frac{2}{12}$. Then multiply by $8$ to find $m = \frac{16}{12} = \frac{4}{3}$.

Explanation Fractions in equations look tough, but the rules don't change! First, get the variable term alone using addition or subtraction. Then, to get rid of the fraction coefficient, multiply both sides by its reciprocal—its flipped version. This clever trick turns the coefficient into a simple 1, leaving your variable solved.