Lesson video

Morning and welcome to today's lesson on finding Decimal Equivalent of Fractions.

Today will be learnig how to convert the fraction into a decimal.

Are you ready for the lesson? You need a pencil and a piece of paper.

Pause the video now and get your equipment, if you don't already have it.

Now, we're looking straight into our procedure of converting a fraction to a decimal.

I have the fraction 4/5.

There are two strategies for converting a fraction to a decimal.

First of all, strategy one.

This is where we convert it to an equivalent fraction with a denominator of 10 or 100, and we use our place value chart to help us.

So if I'm looking at 4/5, I'll write it out over here.

I can see because five is a factor of 10, that I can convert this to an equivalent fraction with a denominator of 10.

I've multiplied five by two.

I do the same to my numerator.

So, 4/5 is equivalent to 8/10.

Thinking back to our previous lesson and using our place value chart, I know that 8/10 means that there are eight in the 10ths column and a place holder in the one's column, therefore 8/10 is equivalent to 0.

8 and also 4/5 is equivalent to 0.

8 because 4/5 is equivalent to 8/10.

So there was strategy one.

Now this is a great strategy, but it doesn't always work.

So for example, if I'm looking at the fraction 3/8, I have a problem here because the denominator eight is not a factor of 10 or 100.

I can't look at 3/8 and multiply my denominator by any whole number to get to 10 or 100.

So this does not work.

We need a different strategy.

So let's look at our strategy two.

In strategy two, we are using division.

4/5 literally means four divided by five.

Here's some new vocabulary.

Listen really carefully because these are some very advanced words.

The number that is being divided here, which is four, is called the dividend.

The number by which a number is being divided, in this case five, is called the divisor and then the quantity produced by the division of these numbers gives us the quotient.

So dividend divided by divisor is equal to quotient.

I'll be using this vocabulary when I'm talking you through strategy two.

So strategy two literally means four divided by five.

Numerator divided by denominator.

So, I'm going to show you how to do this division using the bus stop method.

So, I'm going to draw my bus stop and now I think about how might different numbers go into my bus stop.

So I know that my dividend, which is four, the number that I am dividing, goes under the bus stop and my divisor, five, goes outside of the bus stop.

Now I'm being asked, first of all, how many groups of five are there in four? How many lots of five ones go into four ones? Well, I know that five one does not go into four ones.

Therefore I need to put a place holder zero above the bus stop in the ones column.

Now I need to regroup these four ones to four tenths.

So I need to put in my decimal point, my place holder in the tenths column.

And I'm regrouping four ones into the tenths column.

So now I have 40 tenths.

So I'm being asked now how many groups of five are there in 40 tenths? Now, it's really hard to think about it in terms of tenths.

So, for now I'm going to think about it just as 40.

So how many times does five go into 40? Use my times tables knowledge.

I know that there are eight groups of five in 40.

So my eight goes above my bus stop into the tenths column.

So now I can see that there are 0.

8 groups of five in 40 tenths.

So, four divided by five is equal to 0.

8.

This is my quotient.

And in this case, the quotient is a decimal quotient.

Okay that's tricky.

Let's try another one together.

3/8 so our strategy is three divided by eight.

I draw my bus stop.

I put my dividend three under the bus stop and my devisor eight outside of the bus stop.

How many eights are there in three ones? There are zero.

So I draw my decimal point, my place hold in the tenths column and I regroup three ones into 30 tenths.

How many groups of eight are there in 30 tenths? Now I need to think of it as 30 because it's too complicated to think of it in terms of tenths.

So how many groups of eight are there in 30? I know that three eights are 24 with six remaining.

So they're regrouped into my hundreds column.

How many eights are there in 60? I know that seven eights are 56.

So there are four remaining.

So I regroup my four into my thousands column.

How many eights are there in 40? There are five and I'm done.

So three divided by eight is equal to 0.

375.

3/8 is equivalent to 0.

375 as a decimal.

Now it's your turn.

Pause the video and convert the fraction 7/8 into a decimal using division.

So you will have drawn a bus stop and put your dividend, seven, under the bus stop and your divisor, eight, outside of the bus stop.

How many eights are there in seven? There are zero.

So we're regrouping into the tenths column.

How many eights are there in 70? There are eight.

Eight times eight is 64.

So there are six remaining.

How many eights are there in 60? There are seven.

Seven times eight is 56 with four remaining.

How many eights are there in 40? There are five.

So 7/8 is equivalent to 0.

875 as a decimal.

Now we're going to look up answers where our quotient, I should say, is decimal quotient that is recurring.

You may not have heard of this, but let's have a look at what this looks like.

So for converting with the fraction 1/3 to a decimal, I need to use strategy two because the denominator three is not a factor of 10 or 100.

So 1/3 one divided by three.

Draw my bus stop, dividend one underneath, divisor three outside.

How many groups of three in one? There are zero.

I regroup that one into the tenths column.

How many threes are in 10? There are three.

Three times three is nine.

I have one remaining.

I regroup into my hundreds column.

How many groups of three are there in 10? There are three with one remaining.

Regroup into my thousands column.

Now you will see the pattern here.

This is called recurring.

Okay? Which means that the answer is going to go on and on and on and on and on.

So the answer would be 0.

333333 and I will be bored before I can carry on.

So this is a recurring decimal quotient and the way we write there is like this, 0.

3, we put a dot on top of the digit in the tenths column, which means recurring.

O.

3 recurring.

So, 1/3 is equivalent 0.

3 recurring.

Okay, you are going to have a go at this one.

Pause the video and convert a fraction to a decimal.

You will end up with a recurring decimal quotient.

So you will have drawn you bus stop.

One, the dividend inside.

Six, the devisor outside.

How many sixes in one? There are zero.

I need to regroup into the tenths column.

How many six are 10? There are one with four remaining.

Regroup.

How many sixes in 40? There are six, because six times six is 36 with four remaining.

How many sixes in 40? There are six, because six times six is 36 and four remaining.

So we have another recurring answer.

This time, you need to be careful here because it's not 0.

1 recurring because there's a different number after the one.

It is 0.

16 recurring.

So, 1/6 is equivalent to 0.

16 recurring.

Okay.

It's time for your independent task.

Pause the video and complete the task.

Come back here when you finished and we can go through the answers together.

Okay.

Now question one.

You were asked to convert the fractions to decimals, starting with 3/8.

So you will have noticed that you needed to use strategy two because eight is not a factor of 10 or 100.

So three divided by eight.

How many eights are in three? There are zero.

We regroup.

Put my decimal point, don't forget that.

3/8 in 24, so three here with six remaining.

Seven eights in 56, so a seven there with four remaining.

And five eights in 40, so a five there.

3/8 is equivalent to 0.

375.

3/4, I'll do the same.

Four into three doesn't go, so I regroup.

Four into 30 goes seven times, because four times seven is 28 with two remaining.

Four into 20 goes five times.

You may have noticed that four is a factor of 100.

I know that four multiplied by 25 is 100 and three multiplied by 25 is 75.

75/100 is equivalent to 0.

75.

So you could have used strategy one or two there.

3/4 is a good one to remember though, if you have that one in your head, that's a good one because it comes up a lot of times in fractions.

Especially relating to things like time.

Moving on to 5/6.

So, we're using strategy two.

How many sixes in five? There are zero.

We regroup.

Trying to be a bit tidier with my writing.

How many sixes, in fact, that's just really messy.

Let me do that again.

So, how many sixes are there in five? There are zero.

I regroup.

I put my decimal point in there.

How many sixes are there in 50? There are eight, because six times eight is 48 with two remaining.

How many sixes are there in 20? There are three, because three times six is 18 with two remaining.

How many sixes in 20? There are three with two remaining.

So I have a recurring answer.

So, 5/6 is equal to 0.

83 recurring.

My final question, I could use strategy one, because five is a factor of 10.

2/5 is equivalent to 4/10, which is equal to 0.

4.

I hope you can read that.

I'm sorry it's a bit messy.

On to question two.

You were asked to convert the mixed numbers to decimals.

So, for now we can just leave the whole number and look at the fraction.

So, we're looking at 1/4.

Now if you think back to the previous question, we knew that three quarters could be using either strategy four is a factor of 100 by multiplying by 25.

So 1/4 is equal to how many hundreds multiplied by 25.

Do the same to the top.

1/4 is equal to 2500.

So 2500 is 0.

25.

Don't forget your whole number.

So 3 1/4 is 3.

25.

Just a side note, I set it 3 1/4 was one worth remembering 3 1/4 is equal to 7500 which is equal to 0.

75.

1/4 or so really handy one, just to remember, it's 2500, which is 0.

25.

Okay, on to the next one, park the whole number four a sec and look at the 4/5, 4/5 can be converted to an equivalent fraction with 10 as the denominator by multiplying by two, and that gives us four and eight tenths 4.

8 39 4/20 I can actually see that 4/20 is not a fraction in its simplest form.

It can be simplified into tenths by dividing by two, so it actually becomes 2/10 39 2/10 is 39.

2.

Last one, 1/2 I'm looking at first, I can use strategy one, because two is a factor of 10.

By multiplying by five, which gives me 5/10 7 5/10 is 7.

5.

On to the last question, we're now vies the following lengths of ribbon in different colours to wrap the present.

So what I want to do first before I can find out how much ribbon he has all together, and need them all to be in the same unit, so I'm going to convert them all into decimals.

So remember, I said to think about a 1/4 having that in our head, a 1/4 as we worked out here is 0.

25.

So 2 1/4 is 2.

25 1.

08 is already as a decimal, 3 4/5 remember the 4/5 is a factor sorry.

4/5 is equivalent, 8/10.

So that's 3.

8 and then 4/20 is actually equivalent to 2/10.

So that's 4.

2.

Now all we need to do is to add those decimals together.

So we need to make sure that we line them up in our correct columns, okay? So you may want to label them ones, tenths and hundreds.

And we know that addition can be done in any order, but just to be systematic, I'm going to work from left to right 2.

25 plus 1.

08 plus 3.

8.

I'll put a placeholder there just to be tidy, and 4.

2.

Another placeholder, they're adding them together.

Five plus eight is 13.

Two plus eight is 10, plus two is 12, plus one is also 13.

And then two plus one is three, plus three is six plus four is 10 plus one is 11.

All together, he had 11.

33 metres of ribbon.

Okay, it's time for your final knowledge quiz.

Pause the video and complete the quiz to see what you've remembered.

You've worked so well today.

That was quite a tricky lesson.

And I was stumbling over my words quite a lot because it was hard to keep track of what we were doing.

So that's why it's really important to make really clear and careful notes as you're going along.

I'm looking forward to meeting you back here for our next lesson.

We're going to be learning how to add fractions with different denominators.

And that is a fun lesson.

I'll see you then bye.