Grade 12 Multi-step Fraction Equations Worksheet
Solve multi-step equations involving fractions, combining algebraic techniques with fraction arithmetic.
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Multi-step Fraction Equations
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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 \(\frac{1}{3}(2x - 1) = \frac{1}{2}x + \frac{1}{6}\)?
\(x = 1\)
\(x = 2\)
\(x = 3\)
\(x = 4\)
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 \(3x + 2x = 30\).
True
False
8. Solve for m: \(\frac{m+1}{2} - \frac{m-2}{3} = \frac{1}{4}\)