Algebra: Fractional Basic Practice 2
In this practice set, students will work through 6 targeted questions that focus on combining algebraic fractions into one simplified expression. The exercises guide students to identify common denominators, rewrite each fraction accurately, and simplify step by step.
Related Lessons:
Practice 2 - Question 1
Simplify into a single fraction \(\frac{3x}{2}-\frac{2x-1}{3}\)
Solution:
\(\frac{3x}{2}-\frac{2x-1}{3}\)
\(=\frac{3}{3}\times\frac{3x}{2}-\frac{2x-1}{3}\times\frac{2}{2}\)
\(=\frac{9x-2\left(2x-1\right)}{6}\)
\(=\frac{9x-4x+2}{6}\)
\(=\frac{5x+2}{6}\)
Practice 2 - Question 2
Simplify as a single fraction -\(\frac{x}{2}+3y-2\left(4y-x\right)\)
Solution:
\(-\frac{x}{2}+3y-2\left(4y-x\right)\)\(=-\frac{x}{2}+\frac{2}{2}\times\frac{3y}{1}-\frac{2}{2}\times\frac{2\left(4y-x\right)}{1}\)
\(=\frac{\left(-x\right)+\left(2\right)\left(3y\right)-4\left(4y-x\right)}{2}\)
\(=\frac{-x+6y-16y+4x}{2}\)
\(=\frac{3x-10y}{2}\)
Practice 2 - Question 3
Simplify as a single fraction \(\frac{2x-3y}{2}-\frac{3x-2y}{3}\)
Solution:
\(\frac{2x-3y}{2}-\frac{3x-2y}{3}\)
\(=\frac{3}{3}\times\frac{2x-3y}{2}-\frac{3x-2y}{3}\times\frac{2}{2}\)
\(=\frac{3\left(2x-3y\right)-2\left(3x-2y\right)}{6}\)
\(=\frac{6x-9y-6x+4y}{6}\)
\(=-\frac{5y}{6}\)
Practice 2 - Question 4
Simplify into a single fraction \(1+\frac{u-2}{2}+\frac{4u-5}{3}\)
Solution:
\(1+\frac{u-2}{2}+\frac{4u-5}{3}\)
\(=\frac{6}{6}\times1+\frac{3}{3}\times\frac{u-2}{2}+\frac{2}{2}\times\frac{4u-5}{3}\)
\(=\frac{6+3\left(u-2\right)+2\left(4u-5\right)}{6}\)
\(=\frac{6+3u-6+8u-10}{6}\)
\(=\frac{11u-10}{6}\)
Practice 2 - Question 5
Simplify as a single fraction \(\frac{3\left(x-3\right)}{2}-\frac{2x}{5}\)
Solution:
\(\frac{3\left(x-3\right)}{2}-\frac{2x}{5}\)
\(=\frac{5}{5}\times\frac{3\left(x-3\right)}{2}-\frac{2x}{5}\times\frac{2}{2}\)
\(=\frac{15\left(x-3\right)-\left(2x\right)\left(2\right)}{10}\)
\(=\frac{15x-45-4x}{10}\)
\(=\frac{11x-45}{10}\)
Practice 2 - Question 6
Simplify into a single fraction 4x-\(\frac{2\left(5x-7\right)}{6}-\frac{3\left(x-3\right)}{4}\)
Solution:
\(4x-\frac{2\left(5x-7\right)}{6}-\frac{3\left(x-3\right)}{4}\)
\(=\frac{12}{12}\times\frac{4x}{1}-\frac{2}{2}\times\frac{2\left(5x-7\right)}{6}-\frac{3}{3}\times\frac{3\left(x-3\right)}{4}\)
\(=\frac{\left(12\right)\left(4x\right)-4\left(5x-7\right)-9\left(x-3\right)}{12}\)
\(=\frac{48x-20x+28-9x+27}{12}\)
\(=\frac{48x-20x+28-9x+27}{12}\)
\(=\frac{19x+55}{12}\)
Step By Step Full Solution
Below are six fractional algebra questions, each accompanied by complete step-by-step solutions. Watching the video explanations offers a different learning experience compared to reading written solutions, as students can clearly see how each step is developed and how the overall solution is structured, deepening students’ conceptual understanding and strengthen skills and techniques.