Grade 12 Multi-step Fraction Equations Worksheet

Multi-step Fraction Equations

Carefully solve each multi-step fraction equation. Show all your work for full credit. Simplify all answers to their lowest terms.

1. Solve for x: \(\frac{3}{4}x - \frac{1}{2} = \frac{5}{6}\)

2. Solve for y: \(\frac{2}{3}(y + 5) = \frac{1}{6}y + 2\)

3. Find the value of z: \(\frac{z}{5} + \frac{z}{10} = \frac{3}{4} - \frac{1}{20}\)

4. Which of the following is the solution to the equation \(\frac{1}{3}(2x - 1) = \frac{1}{2}x + \frac{1}{6}\)?

5. To eliminate fractions in an equation, multiply all terms by the   of the denominators.

6. If an equation has a variable in the denominator, you must check for   solutions.

7. The equation \(\frac{x}{2} + \frac{x}{3} = 5\) is equivalent to \(3x + 2x = 30\).

8. Solve for m: \(\frac{m+1}{2} - \frac{m-2}{3} = \frac{1}{4}\)