Question

$\frac{1}{4} x \: + \frac{1}{5} y - \frac{1}{6} x \: - \frac{1}{10} \: y$
You have to Simplify each of the following expressions.​

Answer 1

★Question:

$\\ frac \: {1}{4} x \: + \frac{1}{5} y - \frac{1}{6} x \: - \frac{1}{10} \: y \\ </p><p>You \: \: have \: \: to \: \: Simplify \: \: each \: \: of \: \: the \: \: following \: \: expressions.$

★Answer:

$\frac{1}{4} x \: + \frac{1}{5} y - \frac{1}{6} x \: - \frac{1}{10} \: y \\ \\ = \frac{x}{4} + \frac{y}{5} - \frac{x}{6} - \frac{y}{10} \\ = \frac{25x + 12y - 10x - 6y}{60} \\ = \frac{15x - 6y}{60} \\ = \frac{3(5x - 2y)}{60} \\ = \frac{5x - 2y}{20} (ans)$

Answer 2

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To simplify the expression, we can first combine like terms. Like terms are terms that have the same variable(s) raised to the same power(s).

For the given expression, we can combine the terms that contain x and the terms that contain y:

$\begin{aligned} \frac{1}{4} x - \frac{1}{6} x + \frac{1}{5} y - \frac{1}{10} y &= \frac{3}{12} x - \frac{2}{12} x + \frac{2}{10} y - \frac{1}{10} y \ &= \frac{1}{12} x + \frac{1}{10} y \ \end{aligned}$

Therefore, the simplified expression is:

$\begin{aligned} \frac{1}{4} x + \frac{1}{5} y - \frac{1}{6} x - \frac{1}{10} y &= \frac{1}{12} x + \frac{1}{10} y \ \end{aligned}$

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