Lesson video

Hi, I'm Miss Davies.

In today's lesson, we're going to be solving equations that involve adding algebraic fractions.

We've been asked to solve this equation.

Before we start the process of solving it, we need to add the algebraic fractions.

As the denominators are already the same, it is simply a case of adding the numerators.

Three w add two w is five w.

So, the left hand side of our equation simplifies to give five w over two.

That is still equal to 25.

To solve the equation, we're going to multiply both sides by two.

This gives five w equals 50.

Five w means five multiplied by w.

The inverse of multiplying by five is dividing by five.

So, let's divide both sides by five.

This gives us w is equal to 10.

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.

Make sure that you have added the algebraic fractions before solving the equations.

A equals four u over three, B equals two u over three.

A plus B is equal to seven, so we need to calculate the value of A.

Let's start by substituting the values of A and B into the equation.

We're then going to simplify that left hand side of the equation.

This gives us six u divided by three.

This is still equal to seven.

Six u over three means six u divided by three.

And the inverse of dividing by three is multiplying by three.

So, let's multiply both sides of our equation by three.

This gives us six u is equal to 21.

Six u means six multiplied by u.

The inverse of multiplying by six is dividing by six.

21 divided by six is 3.

5.

That is the value of u.

We've been asked to calculate the value of A.

A is equal to four u divided by three.

To work this out, we need to substitute 3.

5 in for u.

This is four multiplied by 3.

5, divided by three.

That is 14 divided by three, or 14 thirds.

We could also write this as four and two thirds.

Here is a question for you to try.

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

Here is the answer.

The perimeter is 20 a add four, all over four.

We can then write this equals 31 and solve to find that a is equal to six.

Then, substitute this in to find the length BC.

This gives three multiplied by six, divided by four, which is 4.

5 centimetres.

We've been asked to solve this equation.

What is different about this equation, compared to all the ones we've seen before? Well done if you noticed that the denominators are different.

To add fractions, we need to make our denominators the same.

The lowest common denominator of these two fractions is six.

Using our equivalent fractions, we can rewrite this equation as nine w over six add four w over six is equal to eight.

This simplifies to 13 w over six equals eight.

We can now solve the equation.

First thing we're going to do is multiply both sides by six.

This gives three w equals 48.

We can then divide both sides by 13.

13 isn't a factor of 48.

Think about how we might write w.

Well done if you said 48 over 13.

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.

Make sure that you've added the algebraic fractions before going on to solve the equations.

Here is a question for you to try.

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

Here is the answer.

To start this question, you needs to say that x plus five over three, add three x minus two over six, is equal to five.

You can then solve this to find that x is equal to 4.

4.

To find the length from A to B, you need to do 4.

4 divided by two, which is 2.

2 centimetres.

That's all for this lesson.

Thanks for watching.