Algebra: Fractional Basic Practice 1
This section includes 6 carefully structured practice questions designed to strengthen students’ understanding of the rules and techniques for combining algebraic fractions into a single simplified fraction. Each question provides focused practice to help students apply common denominators, organise their working clearly, and simplify their final answers with confidence.
Related Lessons:
Practice 1 - Question 1
Simplify into a single fraction \(\frac{3g+4h}{8}-\frac{7g-2h}{3}\)
Solution:
\(\frac{3g+4h}{8}-\frac{7g-2h}{3}\)
\(=\frac{3}{3}\times\frac{3g+4h}{8}-\frac{7g-2h}{3}\times\frac{8}{8}\)
\(=\frac{3\left(3g+4h\right)-8\left(7g-2h\right)}{24}\)
\(=\frac{9g+12h-56g+16h}{24}\)
\(=\frac{-47g+28h}{24}\)
Practice 1 - Question 2
Simplify into a single fraction \(\frac{x}{2}+\frac{x-1}{3}-\frac{3x}{4}\)
Solution:
\(\frac{x}{2}+\frac{x-1}{3}-\frac{3x}{4}\)
\(=\frac{6}{6}\times\frac{x}{2}+\frac{4}{4}\times\frac{x-1}{3}-\frac{3x}{4}\times\frac{3}{3}\)
\(=\frac{6x+4\left(x-1\right)-\left(3x\right)\left(3\right)}{12}\)
\(=\frac{6x+4x-4-9x}{12}\)
\(=\frac{x-4}{12}\)
Practice 1 - Question 3
Simplify into a single fraction \(\frac{3a+11}{5}-\frac{a+2}{10}\)
Solution:
\(\frac{3a+11}{5}-\frac{a+2}{10}\)
\(=\frac{2}{2}\times\frac{3a+11}{5}-\frac{a+2}{10}\)
\(=\frac{2\left(3a+11\right)-\left(a+2\right)}{10}\)
\(=\frac{6a+22-a-2}{10}\)
\(=\frac{5a+20}{10}\)
\(=\frac{5\left(a+4\right)}{10}\)
\(=\frac{a+4}{2}\)
Practice 1 - Question 4
Simplify into a single fraction \(\frac{1}{2}\left(\frac{11x}{15}+\frac{8}{5}\right)-\frac{2+x}{2}-\frac{2x-3}{5}\)
Solution:
\(\frac{1}{2}\left(\frac{11x}{15}+\frac{8}{5}\right)-\frac{2+x}{2}-\frac{2x-3}{5}\)
\(=\frac{11x}{30}+\frac{3}{3}\times\frac{8}{10}-\frac{15}{15}\times\frac{2+x}{2}-\frac{2x-3}{5}\times\frac{6}{6}\)
\(=\frac{11x+\left(3\right)\left(8\right)-15\left(2+x\right)-6\left(2x-3\right)}{30}\)
\(=\frac{11x+24-30-15x-12x+18}{30}\)
\(=\frac{12-16x}{30}\)
\(=\frac{4\left(3-4x\right)}{30}\)
\(=\frac{2\left(3-4x\right)}{15}\)
Practice 1 - Question 5
Simplify as a single fraction \(\frac{x}{5}+\frac{1-2x}{3}\)
Solution:
\(\frac{x}{5}+\frac{1-2x}{3}\)
\(=\frac{3}{3}\times\frac{x}{5}+\frac{1-2x}{3}\times\frac{5}{5}\)
\(=\frac{3x+5\left(1-2x\right)}{15}\)
\(=\frac{3x+5-10x}{15}\)
\(=\frac{5-7x}{15}\)
Practice 1 - Question 6
Simplify as a single fraction \(3-\frac{2\left(x-2\right)}{3}+\frac{x}{4}\)
Solution:
\(3-\frac{2\left(x-2\right)}{3}+\frac{x}{4}\)
\(=\frac{12}{12}\times\frac{3}{1}-\frac{4}{4}\times\frac{2\left(x-2\right)}{3}+\frac{x}{4}\times\frac{3}{3}\)
\(=\frac{\left(12\right)\left(3\right)-8\left(x-2\right)+3x}{12}\)
\(=\frac{\left(12\right)\left(3\right)-8\left(x-2\right)+3x}{12}\)
\(=\frac{36-8x+16+3x}{12}\)
\(=\frac{52-5x}{12}\)
Step By Step Full Solution
In this section, you will work through six fractional algebra questions presented with detailed, step-by-step guidance. The solutions walk you through the thinking process behind each step — how the fractions are combined, and how the expression is simplified correctly. By following the explanations closely, you will learn how to approach similar questions with confidence, avoid common mistakes, and apply the correct techniques systematically.