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Hello, everyone.

I'm Mr. Lund, and in this lesson, we're going to be solving equations with algebraic fractions which are equal to a number.

Hello, everyone.

We're going to use a bar model to visualise what happens when we solve equations involving fractions.

We want to find the value of b.

b has been divided into five equal parts.

Each of those parts is equal to 12.

Let's have a look at the notation.

b over five equals 12.

If I multiply both sides of this equation by five, I find that b equals 60.

By rearranging the equation, I can also find that b over 12 is equal to five.

b equals 60.

Here are some examples for you to try.

See if you can solve these equations.

Pause the video and return to check your answers.

Here's the solutions for questions one and two.

Hopefully, in question one, you've found that a was equal to 12.

I think of a number, add eight, and then divide by five.

The answer is five.

How can I form an equation to represent this statement? I have an unknown number and I'm going to use algebra.

I'm going to use the letter n to represent that unknown number.

Add on five and then divide all of that expression by five.

That is equal to five.

Solve the equation to work out the number that I thought of.

By solving the equation, first multiplying both sides by five, and then subtracting eight from both sides, I can find that the number I originally thought of was 17.

Here are some questions for you to try.

Pause the video and return to check your answers.

Here's the solutions to question three and four.

In questions 4a, b, c, and d, the first step that you had to take was to multiply both sides by three.

Let's look at how to solve this equation.

In this example, two s divided by seven is equal to six.

By multiplying both sides of the equation by seven, I will find the numerator of the fraction, two s equals 42.

Finally, I need to divide both sides by two to find the solution that s is equal to 21.

Here's another example.

How is it different from the last example? Well, the first step that we need to take is exactly the same.

We're going to multiply both sides of this equation by seven.

The numerator of two s plus five is on one side of the equation, and 42 is on the other side of the equation.

By subtracting five from both sides, we find the two s is equal to first seven, therefore s is equal to 18.

5.

Here are some questions for you to try.

Pause the video and return to check your answers.

Here's the solutions to questions five and six.

Maybe some of you may have ended up with, for example, question 6a, you might have ended up with two p is equal to 18.

You haven't quite solved at that point.

You must then divide through by two to find p on its own, and that gave you an answer of nine.

Let's give question seven a go.

Pause the video and return to check your answers.

Well done.

Great stuff for getting this far.

It's quite a lot of questions there and quite complex ones as well.

So we got to question seven.

Hopefully you are getting into the flow of what you're doing now.

Well done for getting as far as question seven.

There was lots of work there in that worksheet.

Question 7a, two t plus t minus seven plus t plus two would find you an expression of four t minus five if you collected all your like terms together.