# Lesson video

In progress...

Hi, I'm Mrs. Dennett, and in this lesson, we're going to be looking at recurring decimals where one digit repeats.

We're going to be changing these decimals into fractions.

We're going to start this lesson by recapping solving equations.

We want to solve this equation nine X equals 42.

We want to find the value of X.

We use inverse operations to help us to do this.

So, first of all, we divide by nine and we get 42 over nine, which we can write as a fraction.

Then we need to simplify our answer.

We get X equals 14 thirds.

Here are some questions for you to try.

Pause the video to complete the task and restart when you finished.

Notice that sometimes you can simplify.

In part A dividing both numerator and denominator by five.

And in part C, 15 and nine have a common factor of three.

So 15 ninths becomes five thirds.

So three over two is also one and a half.

We're going to write 0.

7 recurring as a fraction.

We use algebra to help us to do this.

X is equal to recurring decimal.

In this case, 0.

7 recurring.

We want to eliminate the recurring part of the decimal.

There's only one digit is recurring.

That's one place value.

We multiply X by 10 to get 10 X and 0.

7 recurring by 10 to get 7.

7 recurring.

How does this help us to eliminate the recurring part of the decimal? We used subtraction to help us to do this.

So 10 X take away X, leaves us with nine X.

And 7.

7 recurrent take away 0.

7 recurring leaves us with seven.

So we have nine X equals seven.

We have eliminated the recurring part of the decimal and can now solve using the skills we practised earlier.

Divide both sides by nine to get X equals seven ninths.

So 0.

7.

recurring is equivalent to seven ninths.

Here's a question for you to practise.

Pause the video, to complete the task and restart when you finished.

Did you remember all the steps involved? We multiply by 10 because we have only one digit recurring.

So 10 X takeaway X leaves us with nine X, 4.

4 recurring takeaway 0.

4 recurring leaves us with four and we've eliminated the recurring decimal.

Now we just have an equation to solve.

We use inverse operations to find the value of X.

Four divided by nine is four ninths and it cannot be simplified.

So 0.

4 recurring is equivalent to four ninths.

Here are some questions for you to try.

Pause the video to complete the task and restart when you finished.

I hope you weren't put off by the fact that question C and D are decimals greater than one.

There is still only one recurring digit.

So you just multiply by 10 and subtract as with all the previous questions.

Here is the final question for you to try.

Pause the video to complete the task and restart when you finished.