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Hi everyone, I'm Mr. Lund.

And in this lesson, we're going to be solving equations where we have algebraic fractions either side of our equal sign.

Hi everyone, take your time to read this question.

How do we show that these two equations are the same? Here I have two fractions which equal each other.

One has a denominator two and on the right hand side, the denominator is 11.

By multiplying both sides of the equation by two, I find that the numerator of three b plus one is equal to two lots of six b plus seven over 11.

Multiply both sides of the equation by 11, I find that 11 lots of three b plus one is equal to two lots of six b plus seven.

What would happen if I multiplied both sides by 11 to start? Here, I would find that 11 lots of three b plus one over two is equal to the numerator on the right hand side of six b plus seven.

Multiply both sides by two, finds me exactly the same answer.

So using that skill, can you match these pairs of equivalent equations? Pause the video and return to check your answers.

Here is the solutions to question number one.

There is a quick method called cross multiplication.

If I multiply the denominator here by the numerator here, and then the same on the other side, denominator by the numerator, I end up with two lots of a minus two, equals three a.

That is a really quick method.

So if you haven't seen that, give that a go.

So let's use the skill we learned previously to help us solve this equation.

We can rewrite our equation to look like this, by expanding both sides of the equation, then we can start to solve.

Subtract 12b from both sides.

Subtract 11 from both sides.

That finds a 21b is equal to three.

Dividing both sides by 21, finds you a solution of b is equal to three over 21.

Here are some examples for you to try.

Pause the video and return to check your answers.

Did you use the cross multiplication method? I'll quickly show you how I would cross multiply question two a.

Here we go.

There we go.

Cross multiply there.

This is where I would start to solve my equation and the cross multiplication process makes it a lot easier to get started with this part.

In these questions can you find the missing values? Pause the video and return to check your answers.

Here is the solutions to question number three.

How did you do, finding the missing numbers? So here are the final questions.

Take your time with these, pause the video and return to check your answers and well done for getting this far.

Here is the solution question number four.

Well done for getting this far.

There's been a lot of work involved here.

Hopefully the cross multiplication method, just makes things a little bit easier for you.