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.

 

Remember:

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.
\[\begin{align*}
\left(6 * \tfrac{x}{2}\right) + \left(6 * 30\right) &= \left(6 * \tfrac{x}{3}\right) + (6 * 8) \\
3x + 30 &= 2x + 48 \end{align*}\]

Now solving the equation as usual, we get

\[x = 18\]


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