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:
\(4x-\frac{2\left(5x-7\right)}{6}-\frac{3\left(x-3\right)}{4}\)
\(=\frac{12}{12}\times\frac{4x}{1}-\frac{2}{2}\times\frac{2\left(5x-7\right)}{6}-\frac{3}{3}\times\frac{3\left(x-3\right)}{4}\)
\(=\frac{\left(12\right)\left(4x\right)-4\left(5x-7\right)-9\left(x-3\right)}{12}\)
\(=\frac{48x-20x+28-9x+27}{12}\)
\(=\frac{48x-20x+28-9x+27}{12}\)
\(=\frac{19x+55}{12}\)