Lesson video

Hi, I'm Miss Davies.

In this lesson we're going to be solving algebraic fraction equations.

We're going solve this equation to work out the value of y.

To begin with we're going to multiply both sides by 11.

At the left-hand side of the equation is 3y add eight divided by 11.

This gives 3y add eight is equal to 77.

We can then subtract eight from both sides to give 3y is equal to 69.

Finally, divide both sides by three to give y equals 23 as the solution.

In this next example we have got a y value on each side of the equation.

We're going to start off in the same way by multiplying both sides by 11.

This gives us 3y add eight is equal to 11y subtract 44 as I have multiplied both y and negative four by 11.

We can then subtract 3y from both sides to collect our y terms on one side of the equal sign.

Next, we're going to add 44 to both sides, and then divide both sides by eight.

This gives a solution of 6.

5 is equal to y, or we can write this as y is equal to 6.

5.

Here is a question for you to try.

Pause the video to complete your task and we'll see you once you're finished.

Here are the answers.

Always multiply by the denominator first, and when you're expanding a bracket make sure that you are multiplying all of the terms within the bracket by whatever is outside of the bracket.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Always multiply by the denominator first, then ensure that you are multiplying all of the terms in a bracket when you're expanding it.

In this next equation we have got a fraction on both sides of the equal sign.

We're going to start off by multiplying both sides by 2y add one.

This gives five is equal to seven multiplied by 2y add one all divided by 3y add five.

Next, we're going to multiply both sides by 3y add five.

This will remove the denominator.

Next we can expand both of the brackets.

We can now solve this as a normal equation.

We're going to subtract 14y from both sides of the equation, and then subtract 25 from both sides.

This gives a solution of y is equal to negative 18.

In our next example, we have got two fractions again, with the y terms and an expression on the numerator.

We're going to complete this in the same method.

Start by multiplying both sides by 11.

Then multiplying both sides by six.

Now that we've removed the denominators, we can expand both of these brackets and solve as we usually would do.

We'll start by subtracting 18y from both sides to give 48 is equal to 37y subtract 11.

We can then add 11 to both sides of the equation and then divide both sides by 37.

This gives us 59 divided by 37 is equal to y.

We're going to leave this as a fraction, as it would give a recurring decimal.

We can also write this as y is equal to 59 over 37.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here are the answers.

Multiply by one denominator, then the other, before you expand any brackets.

In this next example we've got a fraction on either side of the equal symbol.

Both of these fractions have an expression in both the numerator and the denominator.

We're going to multiply both sides by y subtract one to begin with.

This gives y add five is equal to y add seven multiplied by y subtract one all divided by y subtract nine.

Next, we're going to multiply both sides by y subtract nine.

We can then expand both of the bracket to give us y squared subtract 4y subtract 45 is equal to y squared add 6y subtract seven.

We're now going to subtract y squared from both sides of the equation.

Next, we can add 4y to both sides and add seven to both sides.

Finally, we can divide both sides of the equation by 10 which gives negative 3.

8 is equal to y which we can write as y is equal to negative 3.

8.

Here are some questions for you to try.

Pause the video to complete your task and resume once you're finished.

Here and the answers.

You should be multiplying by one denominator, then the other, and then expanding out the brackets.

That's all for this lesson.

Thanks for watching.