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:
\(\frac{2\left(x-4\right)}{3}+\frac{\left(3-5x\right)}{2}-\frac{4x-1}{5}\)
\(=\frac{10}{10}\times\frac{2\left(x-4\right)}{3}+\frac{15}{15}\times\frac{\left(3-5x\right)}{2}-\frac{6}{6}\times\frac{4x-1}{5}\)
\(=\frac{10\left(2x-8\right)+15\left(3-5x\right)-6\left(4x-1\right)}{30}\)
\(=\frac{20x-80+45-75x-24x+6}{30}\)
\(=\frac{-79x-29}{30}\)