## Example 1: Multiply by Each Denominator

Let's suppose the following equation is presented to you. You see several fractions, and you may be tempted to run and hide. Don't be too hasty! There is a rather quick and easy modification that you can make to ease your concerns.

(3/4)*n* + 2 - (4/3) = (1/6)

Multiply each term by all of the denominators: 4, 3, and 6. This will cause each original denominator to be canceled leaving only multiplication. The result of the multiplication will not have any fractions in it.

(3/4)*n* (4)(3)(6) + (2) (4)(3)(6) - (4/3) (4)(3)(6) = (1/6) (4)(3)(6)

(3)*n*(3)(6) + (2)(4)(3)(6) - (4)(4)(6) = (1)(4)(3)

54*n* + 144 - 96 = 12

54*n* + 48 = 12

54*n* = -36

*n* = (-36/54) = -2/3

Notice that the answer can still be a fraction, but the equation changed into one without any fractions. The only down side to this method is that the resulting equation has the potential for rather large numbers. Even so, it should still be easier than working with the fractions along the way.

## Example 2: Multiply by Each Denominator

Here is another example.

(-11/4)*x* - (5/3)*x* = (53/9)

Each term will be multiplied by 4, 3, and 9.

(-11/4)*x* (4)(3)(9) - (5/3)*x* (4)(3)(9) = (53/9) (4)(3)(9)

(-11)*x*(3)(9) - (5)*x*(4)(9) = (53)(4)(3)

-297*x* - 180*x* = 636

-477*x* = 636

*x* = (636/-477) = -4/3

Let me be clear on this. The numbers can get quite large. If you would prefer not to deal with numbers so large, there is another method closely related to this one.

## Example 3: Multiplying by the LCM

Instead of multiplying each term by each of the denominators, multiply each term by the least common multiple of the denominators. In the first example, this LCM would be 12. The result would look like this.

(3/4)*n* + 2 - (4/3) = (1/6)

(3/4)*n* (12) + (2) (12) - (4/3) (12) = (1/6) (12)

The factor of 12 will simplify with each denominator.

(3)*n*(3) + (2)(12) - (4)(4) = (1)(2)

9*n* + 24 - 16 = 2

9*n* + 8 = 2

9*n* = -6

*n* = (-6/9) = -2/3

The answer is the same as we expected, but this time the values were smaller and therefore easier to work with.

## Lesson Summary

We cannot always avoid problems that contain fractions, but we can manipulate them so that fractions aren't a stumbling block. Multiply each term by either all of the denominators or by the least common multiple of the denominators. Reduce each term. Solve the remaining equation by getting the variable isolated on one side of the equal sign with a coefficient of a positive one.