Resources for Equations with Fractions
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Equations with Fractions Theory
![For equations with fractions, you can find the lowest common denominator (LCD) for all the fractions and then multiply both sides of the equation by the LCD or simply find the LCD and multiply each term by the LCD and thus remove all fractions and then proceed with the solution\\ \begin{multicols}{2} \textbf{Example 1}\\ Solve \(\dfrac{2 x}{3}+\dfrac{1}{4}=5\)\\ \textbf{Example 1 solution}\\ \(\begin{aligned} \text { LCD } & =3 \times 4 \\ & =12 \end{aligned}\)\\ \(\begin{aligned} \frac{4}{4} \times \frac{2 x}{3}+\frac{3}{3} \times \frac{1}{4} & =5 \\ \frac{8 x}{12}+\frac{3}{12} & =5 \\ \frac{8 x+3}{12} & =5 \\ 12 \times\frac{(8 x+3)}{12} & =12 \times 5 \\ 8 x+3 & =60 \\ 8 x+3-3 & =60-3 \\ 8 x & =57 \\ \frac{8 x}{8} & =\frac{57}{8} \\ x & =7 \frac{1}{8} \end{aligned}\) \columnbreak \textbf{Example 2}\\ Solve \(\dfrac{3 x}{5}+\dfrac{x}{15}=7\)\\ \textbf{Example 2 solution}\\ \(\text { LCD }=15\)\\[3pt] \(\begin{aligned} \cancel{15}^{3} \times \frac{3 x}{\cancel{5}}+15 \times\frac{ x}{15} & =15 \times 7 \\ 9 x+x & =105 \\ 10 x & =105 \\ \frac{10 x}{10} & =\frac{105}{10} \\ x & =10.5 \end{aligned}\) \end{multicols}](/media/tv4fziyf/6911.png)
NSW Y8 Maths Equations Equations with Fractions
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