Solve Equations with Fractions

"I think of a number, divide by 5, then add 4 and the answer is 7. What number am I thinking of?"

 

From your previous work on equations, you will be familiar with this sort of puzzle and how to express it algebraically.

 

So what is different about this one?

 

Well, this includes division, which is important when we think about how to write it as an equation.

When writing algebra we do not use the '÷' symbol, as we write a division sum as a fraction. 

 

So in order to write this puzzle as an equation, with x as the unknown number, we need to write:

 

Other than this, there is no difference between this and other two-step equations.

 

In this case, x has been divided by 5 then had 4 added.

To solve this, we must apply the inverse operations in the reverse order.

So first we subtract 4 then we multiply by 5, remembering to do the same to both sides. 

 

We can set out our working as like this:

 

 

So the number we started with was 15.

 

 

 

Here is another equation, which is slightly different:

 

Notice here that the line goes under the x - 12, not just the x.

This changes the order, meaning that starting with x first, we subtract 12 then divide by 3.

 

So when we apply the inverses in reverse order, we must multiply by 3 then add 12.  

 

Here is our working:

 

 

 

 

Are you getting the hang of this?

 

In this activity, we will solve equations involving fractions to find the value of a variable represented by a letter. 

You will want to have a piece of paper and pen handy to record your working, as this is a great way to maximise your marks in an exam.