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How do you solve basic fraction equations?

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Quick Answer

To solve equations involving fractions, the main step is to isolate the variable, convert the fractions into whole numbers, and then solve the equations as normal. When solving algebraic equations, treat both sides equally. Removing all the extra information on one side of the equation provides the solution. Other types of equations with fractions can be solved with the cross-multiplication method.

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Full Answer

For a simple fraction example, take x/3 + 3/5 = 4. The first thing to do is convert 3/5 to a decimal for easier calculations; it converts to 0.6. This leaves the equation as x/3 + 0.6 = 4. Subtracting 0.6 from 4 leaves 3.4, so the equation is now x/3 = 3.4. Multiply both sides by 3, leaving the solution as 10.2. Remember that if the denominators of fractions are the same, you can work with the numerators as normal.

To solve proportional equations, use the cross-multiplication method of multiplying numerators by opposite denominators, then solving for the variable. For example, the equation 3/5 = 9/x is solved by multiplying 5 by 9 to yield 45, also multiplying 3 by x. The reduced equation is 3x = 45. Dividing both sides by 3 shows x to be 15.

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