Clearing Fractions in Equations

Sometimes, having fractions in an equation can be a little intimidating, but we can remove the fractions by multiplying both sides of the equation by the smallest number both denominators divide evenly into.



To remove the fractions from an equation, you multiply every term in the equation by the common denominator of the fractions.


Now let’s try the problem:

\[ \tfrac{x}{2} + 5 = \tfrac{x}{3} + 8 \]

First, we need to find the smallest number both 2 and 3 go into (or the LCD), which would be 6. Then we multiply both sides of the equation by that number.

\[6\left(\tfrac{x}{2} + 5\right) = 6\left(\tfrac{x}{3} +8\right)\]

Using the distributive property, simplify the equation.
\left(6 * \tfrac{x}{2}\right) + \left(6 * 30\right) &= \left(6 * \tfrac{x}{3}\right) + (6 * 8) \\
3x + 30 &= 2x + 48 \end{align*}\]

Now solving the equation as usual, we get

\[x = 18\]

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