Algebra: Fractional Basic
In this introductory lesson on algebraic fractions, students will learn through 4 examples how to combine multiple fractions into one simplified expression. They will practise finding a common denominator, rewriting each fraction correctly, and combining like terms carefully. Clear working and checking for cancellation are emphasised to build a strong foundation for advanced algebra.
Related Lessons:
Example 1 Of 4
Simplify into a single fraction \(\frac{7x-5}{6}-\frac{3\left(x-2\right)}{4}\)
Solution:
\(\frac{7x-5}{6}-\frac{3\left(x-2\right)}{4}\)
\(=\frac{2}{2}\times\frac{7x-5}{6}-\frac{3\left(x-2\right)}{4}\times\frac{3}{3}\)
\(=\frac{2\left(7x-5\right)-3\left(3x-6\right)}{12}\)
\(=\frac{14x-10-9x+18}{12}\)
\(=\frac{5x+8}{12}\)
Example 2 Of 4
Simplify into a single fraction \(\frac{2x+3}{6}-\frac{x-5}{2}\)
Solution:
\(\frac{2x+3}{6}-\frac{x-5}{2}\)
\(=\frac{2x+3}{6}-\frac{x-5}{2}\times\frac{3}{3}\)
\(=\frac{2x+3-3\left(x-5\right)}{6}\)
\(=\frac{2x+3-3x+15}{12}\)
\(=\frac{-x+18}{12}\)
Example 3 Of 4
Simplify into a single fraction \(\frac{2\left(x+3y\right)}{5}-\frac{3\left(y-2x\right)}{4}+\frac{5x-y}{2}\)
Solution:
\(\frac{2\left(x+3y\right)}{5}-\frac{3\left(y-2x\right)}{4}+\frac{5x-y}{2}\)
\(=\frac{4}{4}\times\frac{2\left(x+3y\right)}{5}-\frac{5}{5}\times\frac{3\left(y-2x\right)}{4}+\frac{10}{10}\times\frac{5x-y}{2}\)
\(=\frac{4\left(2x+6y\right)-5\left(3y-6x\right)+10\left(5x-y\right)}{20}\)
\(=\frac{8x+24y-15y+30x+50x-10y}{20}\)
\(=\frac{88x-y}{20}\)
Example 4 Of 4
Simplify into a single fraction \(\frac{2\left(x-4\right)}{3}+\frac{\left(3-5x\right)}{2}-\frac{4x-1}{5}\)
Solution:
\(\frac{2\left(x-4\right)}{3}+\frac{\left(3-5x\right)}{2}-\frac{4x-1}{5}\)
\(=\frac{10}{10}\times\frac{2\left(x-4\right)}{3}+\frac{15}{15}\times\frac{\left(3-5x\right)}{2}-\frac{6}{6}\times\frac{4x-1}{5}\)
\(=\frac{10\left(2x-8\right)+15\left(3-5x\right)-6\left(4x-1\right)}{30}\)
\(=\frac{20x-80+45-75x-24x+6}{30}\)
\(=\frac{-79x-29}{30}\)
Watch Full Concept Breakdown
Combining multiple fractional algebraic expressions into a single fraction is an essential algebraic technique. When applied correctly, the common denominator method is reliable, ensuring students arrive at the correct answer if each step is followed carefully. Below is the complete explanation of the common denominator for the four examples above.