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:
\(3-\frac{2\left(x-2\right)}{3}+\frac{x}{4}\)
\(=\frac{12}{12}\times\frac{3}{1}-\frac{4}{4}\times\frac{2\left(x-2\right)}{3}+\frac{x}{4}\times\frac{3}{3}\)
\(=\frac{\left(12\right)\left(3\right)-8\left(x-2\right)+3x}{12}\)
\(=\frac{\left(12\right)\left(3\right)-8\left(x-2\right)+3x}{12}\)
\(=\frac{36-8x+16+3x}{12}\)
\(=\frac{52-5x}{12}\)