Lesson video

Hi, I'm Ms. Davis.

In this lesson, we're going to solve equations that involve subtracting algebraic fractions.

In order to solve this equation, we need to simplify the left hand side of the equation first.

Seven w over two subtract two w over two simplifies to five w over two.

This is still equal to 20.

The first step in solving this equation is to multiply both sides by two.

This gives five w equals 40.

Our next step is to divide both sides by five.

This gives us a solution of w equals eight.

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 simplified by subtracting those algebraic fractions before you solve the equation.

What is different about this equation compared to the ones in the previous set of questions? Well done if you noticed that the denominators are different.

The first thing we're going to do is simplify the left hand side of the equation.

Before we do that, we need to use our equivalent fractions to make our denominators the same.

The lowest common multiple of two and three is six.

So the lowest common denominator of these two fractions is six.

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

This then simplifies to five w over six.

And this is still equal to eight.

To start solving this equation, the first thing we're going to do is multiply both sides by six.

This gives five w equals 48.

Because five w means five multiplied by w, we're going to divide both sides by five as this is the inverse of multiplying my five.

This gives us a solution of two equals 48 over five.

This could also be written as 9.

4, or as a mixed number of nine and 2/5.

What's different about this equation? We've got an integer as well as fractions.

Let's start by finding the lowest common denominator.

The lowest common multiple of two and three is six.

So the lowest common denominator is six.

How many six are there in two wholes? There's 12.

Using our equivalent fractions, let's rewrite this equation with a common denominator.

We can simplify the left hand side of this equation to nine x subtract 12 all over six.

We can now multiply both sides by six to remove the fractions.

We're now going to add 12 to both sides.

That gives us nine x equals eight x, add 12.

We can then subtract eight x from both sides.

Leaving us with a solution of x equals 12.

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 equation formed from this diagram is eight x plus 12 over 16, subtract three x plus one over eight, is equal to two.

This simplifies to two x plus 12 all over 16, is equal to two.

You can then solve this to find that x is equal to 11.

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.

In part a, you've got a decimal a fractional answer, and that is absolutely fine.

Here is a question for you to try.

You need to find two mistakes that Jess has made.

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

Here are the answers.

Jess has incorrectly multiplied 0.

5 by 12.

She has said that it is 24, but it should be six.

She's also written nine divided by seven incorrectly.

Nine should be the numerator, and seven should the denominator.

That's all for this lesson, thanks for watching.