Lesson video

Hi, everyone.

My name is Ms. Cou.

I hope you enjoy the lesson today and I'm really happy you've chosen to learn with me.

There may be some easy or hard parts of the lesson, but don't worry, I am here to help.

You'll also come across some new keywords and maybe some keywords you've already come across before.

I do hope you'll like the lesson, so let's make a start.

In today's lesson from the unit Comparing and Ordering Fractions and Decimals: Positive and Negative Numbers, we'll be converting fractions with technology, and by the end of the lesson, you'll be able to convert from fractions to decimals and back again using the converter key on a calculator.

So let's have a look at some keywords.

A proper fraction is a fraction where the numerator is less than the denominator, for example, 2/3.

You'll notice the numerator is two and the denominator is three.

Two is less than three, so this is a proper fraction.

An improper fraction is where the numerator is greater than or equal to the denominator.

For example, 7/5.

Seven is greater than the five.

And a mixed number is an improper fraction written as its integer parts plus the fractional part where the fractional part is a proper fraction.

For example, 3 1/2.

Today's lesson will be broken into three parts.

The first part will be using a calculator to simplify fractions, the second part will be converting between fractions and decimals, and the third part will be using mixed numbers on a calculator.

So let's have a look at the first part.

We'll be using a calculator to simplify fractions, and in this lesson, we'll be focusing on the Casio fx 991 classwiz.

Now the Casio 991 classwiz can do so much, including simplifying fractions effortlessly.

So let's have a look.

For example, we're going to simplify 245/1000.

All we need to do is press 245, the fraction button, and 1000, and then press execute.

The great thing is the calculator will automatically simplify it for you with no extra work, so we know our answer is 49/200.

This works for proper and improper fractions, too.

So let's have a look at an improper fraction.

We have 455/50.

I want you to simply input it into your calculator by pressing 455, the fraction button, and 50 and then press execute, and what you'll find is the calculator will automatically simplify it to 91/10.

So scientific calculators will simplify both proper and improper fractions.

Let's have a look at a quick check question.

Sam wants to work out 25/30 multiplied by 45, so Sam does this on the calculator.

What did Sam do wrong? See if you can explain why, and press pause if you need more time.

Well, hopefully you spotted Sam needed to press the scrolling to the right key to exit that denominator, and failing to do so has meant Sam has multiplied the denominator by 45 as opposed to multiplying the fraction by 45.

So the keys to press would be 25, that fraction button, and then 30, scrolling to the right, press multiply, 45, and then execute.

And the great thing is the calculation will look exactly the same as what is displayed on your calculator.

So now what I want you to do is use your calculator to work out the answers to the following, giving your answer as an improper fraction.

I'm going to do the first one and then you can do the next one.

4/11 multiplied by 265.

Well, we're going to press the following buttons, four, fraction button, 11.

Then we need to scroll to the right to leave that denominator.

Then we need to multiply by 265 and press execute.

What you'll notice on your calculator screen is the same calculation as we displayed here, and our answer is 1060/11.

Well done if you got that one right.

Now your question is, using your calculator, work out the answers to the following, giving your answer as an improper fraction.

See if you can give it a go, and press pause if you need.

Great work, so let's see how you got on.

All the buttons that you needed to press were 48, fraction button, 65.

Then you need to scroll to the right to leave that fraction, multiply by 40 fraction 12, and then press execute.

The great thing is the calculation will look exactly the same in your calculator display, thus giving you a final answer of 32/13.

Fantastic work if you got that one right.

Now it's time for your task.

What I want you to do is use your calculator to write the simplified fractions to the following, 24/40, 88/120, 88/40, 78/1000, 2834/5000, and 95/90.

So you can give it a go and press pause if you need more time.

Well done, so let's move on to question two.

Question two wants you to use your calculator again and work out the answers to the following, ensuring to give your answer as a proper or improper fraction.

We have 3/162 multiplied by 12/33, and we have 39/20 multiplied by 389.

See if you can give it a go and press pause if you need more time.

Great work, so let's move on to question three.

Question three wants you to figure out the missing digits on the calculator screen to make the calculations correct.

Use your calculator as this will really help you out.

See if you can give it a go, and press pause if you need more time.

Great work, everybody, so let's see how you got on.

Well, for question one, hopefully you spotted 24/40 simplifies to 3/5, 88/120 simplifies to 11/15, 88/40 simplifies to 11/5, 78/1000 simplifies to 39/500, 2834/5000 simplifies to 1417/2500, and 95/90 simplifies to 19/18.

Well done if you got those right.

For question two, remember the calculation should appear the same on your calculator display.

So we should have 2/297 for the answer to question 2A, and for B, we should have 15171/20 for your answer for B.

Well done if you got those right.

For question three, you had to figure out those missing digits, so let's see how you got on.

Well for A, it's 25/7, and for B it was 5/25 multiplied by 92/4.

For C, 24/12 divided by 35/4 give you 8/35, and for D, 3/12 subtract 15/4 gives us -7/2.

Great work if you got that one right.

Fantastic work, everybody, so let's look at the second part of our lesson.

We'll be converting between fractions and decimals.

Now, converting from fractions to decimals is really easy with the Casio fx 991 classwiz, so let's have a look at an example.

We're going to look at the fraction 5/8 and convert it into decimal form.

All you need to do is press five, that fraction button, and eight, and then press execute.

But what you'll notice is the calculator will give it as a fraction, so to convert it into a decimal, we simply need to press the format key, scroll down 'til you'll see decimal, and then press execute, and what the calculator will do, it will convert the 5/8 into the decimal equivalent of 0.

625.

So scientific calculators are fantastic as it allows you to change the format of a given number.

So now what I'd like you to do is I'm going to check your understanding and I want you to use your calculator to work out the equivalent decimals of these fractions.

See if you can give it a go, and press pause if you need more time.

Great work, everybody, so let's see how you got on.

6/5 is equivalent to 1.

2, 25/30 is equivalent to 0.

83 recurring, and using that correct mathematical notation, it's 0.

83 with a little dot above the three.

98/11 is 8.

9090, so on and so forth, but using that correct notation, it's 8.

90 with a dot above the nine and a dot above the zero.

Well done if you got these right.

The Casio fx 991 classwiz also allows you to change a terminating decimal into a fraction easily.

For example, let's have a look at 0.

8392 into a fraction.

All we need to do is insert 0.

8392 and then press execute.

What it does, it gives us that fractional equivalent automatically.

Now if it doesn't give you that fractional equivalent automatically, then you press format and ensure that you select standard and then execute, and it will give you that fractional equivalent.

So now let's have a look at a quick check.

What I want you to do is use your calculator to match the decimal to the fractional form.

See if you can give it a go, and press pause if you need more time.

Well done, so let's see how you got on.

0.

78 is 39/50, 0.

982 is 491/500, 3.

568 is 446/125, and 3.

244 is 811/250.

Well done if you got those right.

So now we know some basics associated with our scientific calculator.

Converting recurring decimals into fractions does take a little bit more inputting, and what we need to do is insert at least 18 decimal places when the number is less than one.

For example, if we want to find the equivalent fraction to the recurring decimal 0.

929292, so on and so forth, what we have to do is input that 0.

9292 so we have at least 18 decimal places.

See if you can give it a go and convert that 0.

92 recurring into a fraction.

What did you get? Well, you can see it on my calculator screen.

I've put in at least 18 decimal places, and I finally get 92/99, so it's important to remember to convert with recurring decimals into fractions, it does take a little bit more inputting.

So let's have a look at a check.

Aisha needs to find the fractional equivalent to 0.

871871871, so on and so forth, so she puts this into a calculator and presses execute.

Now, why did the calculator not give the decimal as a fraction, and why is the last digit nine? Have a little think and press pause if you need more time.

Well, hopefully you spotted Aisha did not put in enough decimal places for the calculator to recognise it's a recurring decimal, and the reason why the last digit is a nine is because the calculator has rounded the decimal to the 10th decimal place.

These are important things to remember about your scientific calculator as there are limitations to using a scientific calculator.

Now let's have a look at your task.

What I want you to do is use your calculator to fill in the table below, identify the decimal and its simplified fractional equivalent.

See if you can give it a go and press pause if you need more time.

Well done, so let's move on to question two.

Question two wants you to find the missing values on the calculator displays.

There are lots of different ways that you can find these missing values.

See if you can give it a go, and press pause if you need more time.

Great work, so let's go through our answers.

Well, we're asked to use our calculator for question one.

0.

982 as a simplified fraction is 491/500.

298/125 as a decimal is 2.

384.

0.

78 recurring with the 78 recurring is 26/33.

59/9 is 6.

5 recurring, and 9.

8, the seven and one are the only digits that recur, gives us a fractional equivalent of 9773/990.

Well done if you got this one right.

Question two is a nice little puzzle.

For 2a, you should have got 106/45, for 2b, it should be 0.

1486, which gives you the fractional equivalent of 743/5000, and for C, we should have had the missing digit was four before the 5656 recurring, giving us the fraction 113/2475.

For D, it was 47/180 to give you 0.

261 where the one is recurring.

Great work if you got that one right.

Fantastic work, everybody, so let's have a look at the last part of our lesson.

We'll be looking at mixed numbers on a calculator.

Continuing to use the Casio fx 991 classwiz, when an answer is found, pressing that format button allows you to change how you want to see your answer.

For example, there are different formats that you might be able to spot, standard, decimal, improper fraction, and also mixed fraction.

So let's change our improper fraction into a mixed number.

We're going to look at 25/3 first, so let's input it into our calculator.

25, fraction button, three, and then execute, and what you should get is 25/3 displayed on your calculator screen.

Now to convert it to a mixed number, simply press format, and you'll have these options available to you.

Scroll down using the cursor key to identify mixed fraction, and press execute, and what the calculator has now done is change that improper fraction into a mixed number.

So now we know the answer is 8 1/3.

So now we know how to change an improper fraction into a mixed number, let's do a quick check.

I want you to change the following improper fractions to mixed numbers using your calculator.

Press pause for a little bit more time.

Great work, so let's see how you got on.

84/5 gives us the mixed number of 16 4/5, 157/12 gives us the mixed number of 13 1/12, and 98/12 gives us the mixed number of 8 1/6.

Well done if you got those right.

So now we know the Casio classwiz can help us change the format, let's see if we can change the mixed number into a decimal and improper fraction.

So to access the mixed number button, you have to access it via the shift key and then the fraction button, and this is so important to do whenever you're inputting in a mixed number.

So press the shift key and the fraction button.

What will be displayed on your screen are these three little boxes.

From here, you can then insert the integer and the improper fraction.

So let's give it a go.

We have to convert 5 7/8 into a decimal.

So first of all, let's access that mixed number button on our calculator.

Press shift and the fraction key, and it'll come up on the screen, and I want you to insert the digits 5 7/8 using the cursor keys to navigate around the integer and the proper fraction, and what you'll see is when you press execute, it'll automatically convert it into an improper fraction.

So we know 5 7/8 is equivalent to the improper fraction of 47/8.

Now to convert this to a decimal, simply press format, and then select decimal.

From here, it's now converted our mixed number into a decimal, 5.

875.

Great work if you managed to do this.

So now let's have a look at quick check.

I'm going to do the first question and I want you to do the second question.

So the first question wants us to use our calculator to convert the mixed number into an improper fraction and decimal.

We have 5 3/4, so remember, to access that mixed number, press shift, then the fraction button, four, scroll to the right so we can access the proper fraction, input 3/5 as our proper fraction.

Then you press execute.

Once you've done that, you'll be able to see 4 3/5 as our mixed number and 23/5 as our improper fraction.

Then to convert it to a decimal, we simply press the format, select decimal, and you can see it's 4.

6 as a decimal equivalent.

Fantastic work if you got that one right.

Now it's your turn.

I want you to convert the mixed number into an improv fraction and a decimal, so I'm gonna give you 8 7/11.

See if you can give it a go, and press pause if you need more time.

Well done, so let's see how you got on.

Well, don't forget to press the shift and the fraction button to access that mixed number button.

Then you input the eight, scroll to the right to access the numerator of our proper fraction, scroll down to access the denominator of our proper fraction and then press execute.

The great thing is it'll always display the calculation or the number that you have in front of you.

So we know 8 7/11 is the same as 95/11.

This is a decimal.

Well, we need to press that format button, select decimal, and it will convert it.

So our decimal equivalent is 8.

6363, so on and so forth.

Massive well done if you got that one right.

Now it's time for your task.

I want you to fill in the table below, identifying the mixed number, the equivalent improper fraction and the equivalent decimal.

See if you can give it a go, and press pause if you need more time.

Great work.

So let's have a look at question two.

Question two wants you to work out the following calculations using your calculator, giving your answer as a mixed number, and D is a fantastic question where you need to create your own questions where the answer is 3 1/2.

See if you can give this a go, and press pause if you need more time.

Well done, so let's see how you got on.

For question one, the equivalent improper fraction to the mixed number 24 3/8 is 195/8, and as a decimal, it's 24.

375.

The equivalent mixed number to the improper fraction 38/9 is 4 2/9, and as a decimal, it's 4.

2 recurring.

The equivalent improper fraction to the mixed number 2 12/19 is 50/19, and the equivalent decimal is 2.

631578947, so a huge well done if got this one right.

For question two, remember to access that mixed number button.

For A, you should have got 9 1/6, for B, 4 43/72, and for C, -3 3/12.

Really well done if you got these right.

So in summary, scientific calculators are excellent tools and allow us to successfully and easily convert between fractions and decimals using that format button.

The fraction button is really helpful when when we're inputting proper fractions or even improper fractions, and remember, to insert a mixed number, you have to access that mixed number button, and to access it, you simply press shift and that fraction button.

Don't forget to use those cursor keys for scrolling around and you use these arrows to navigate around the calculation.

A huge well done.

It was great learning with you today.