Sometimes it will be the case that we have a fraction of an unknown and we are asked to solve the equation. The best way to solve the equation when this is the case is to multiple all of the terms in the equation by the denominator of the fraction (you may find it easier to tidy up the equation first; collect like terms). We are then able to solve the equation in the usual way.

The examples in this section build on the content that was discussed in “linear equation – multiples of unknowns”; make sure that you have gone through that section before doing this section (click here to be taken through to that section).

The examples in this section build on the content that was discussed in “linear equation – multiples of unknowns”; make sure that you have gone through that section before doing this section (click here to be taken through to that section).

**Example 1**

Find the value of

*d*.

Before we multiply all of the terms in the equation by the denominator of the fraction, we may want to tidy up some of the terms. For example, we can move the 7 from the left side to the right side. By doing this, we have less terms that we need to multiply by 3 and this reduces the chance of making an error/ missing a term out.

To move the 7 from the left side of the equation to the right, we take 7 from both sides of the equation.

To move the 7 from the left side of the equation to the right, we take 7 from both sides of the equation.

The equation above states that we have a third of d. There are two ways that we are able to find out what the value of d is. The first method is to divide both sides by the coefficient of d; we divide by ^{1}/_{3}. The second method it to multiply both sides by the denominator of the coefficient; multiply both sides by 3. Both of these methods will give you the same answer. Personally, I believe that it is much easier to multiply both sides by 3.

This tells us that

We can check that this value is correct by subbing it into the first equation.

*d*is 12.We can check that this value is correct by subbing it into the first equation.

This works, which means that

*d*is 12.**Example 2**

Find the value of

*e*.

The first step in answering this question is to get rid of the fraction. We do this by multiplying every term/ both sides of the equation by the denominator of the fraction, which is 4. You may find it easier to write the right side of the equation with a bracket; this is so that we ensure that we multiply all of the terms on the right side of the equation by 4.

The next step is to expand the bracket on the right side of the equation, which we do by multiplying all of the terms inside the bracket by 4.

We now solve in the usual way. There are more

We need to move 3

*e*’s on the right side of the equation than the left side. This means that we will get all of the*e*’s to the right side of the equation and all of the numbers to the left.We need to move 3

*e*from the left of the equation to the right, which we do by taking 3*e*from both sides.We now need to move the -28 from the right to the left, which we do by adding 28 to both sides.

We want to find the value of

*e*and not 17*e*, which means that we divide both sides of the equation by 17.Therefore,

*e*is 2. We can check that this value is correct by subbing*e*as 2 into the original equation. I am not going to do this, but feel free to check for yourself.