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Hello, my name's Mrs. Hopper, and I'm excited to be working with you in this lesson from the unit on Comparing Fractions Using Equivalents and Decimals.
I love fractions, and I hope you do too.
And I hope during this lesson you'll be able to see and understand a little bit more about them and how they link to decimals.
So if you're ready, let's make a start.
So in this lesson, we're going to be using our knowledge of equivalents to compare fractions and decimals.
We've got three key words today: equivalent, tenth, and hundredth.
I'm sure you're familiar with them, but let's just rehearse them.
They're gonna be useful to us.
So my turn, equivalent, your turn.
My turn, tenths, your turn.
My turn, hundredth, your turn.
Well done, let's just check those definitions just so we're really sure we know what these words are going to be helping us with today.
So numbers are equivalent if they have exactly the same value.
And when one whole is divided into 10 equal parts, each part is one tenth.
This can be expressed as a fraction or as a decimal.
And when one whole is divided into a hundred equal parts, each part is one hundredth, and this can be expressed also as a fraction or a decimal.
So let's make a start on the lesson.
There are two parts in our lesson today.
In the first part, we're going to be converting between decimals and fractions.
And in the second part, we're going to be using fraction and decimal equivalents to compare.
And we've got Lucas and Sam helping us in the lesson today.
So we've got some decimals here.
How would you read them? Do you wanna have a go? And I wonder what the value of each digit is.
I won't read them out to you, we're gonna be reading them as we go through and look at them.
And finally, how would you write the decimal as a fraction? So we're going to be thinking about reading them what the value of each digit is, and how we would write the decimal as a fraction.
So where should we start? Let's start here.
So we've got 0.
1 and 0.
01.
And we can represent 0.
1 on a place value chart.
We've got zero 1s, our decimal point, and one 10th.
0.
1 is the same as one-tenth.
And that's gonna give us a clue as to how to write it as a fraction, isn't it? Ah, Sam says, "I can write that as 1/10th as a fraction." 0.
01 is the same as one-hundredth.
So we've got zero in the 1s, zero in the 10ths, and one in the 100ths column.
And Sam says, "I can write that as 1/100 as a fraction." So knowing how our place value headings look as fractions can help us to turn decimals into fractions.
Over to you to check your understanding.
How would you read this decimal? What's the value of each digit? And how would you write the decimal as a fraction? You've got the place value chart and some stem sentences that Lucas and Sam are giving you to help.
So fill in those gaps and then we'll look at the answers together.
How did you get on? So 0.
2 is the same as two-tenths.
Zero in the 1s, decimal point, and a two in the tenths column.
And the decimal point tells us that that is our tenths column.
And Sam says, "I can also write that as 2/10 as a fraction." Okay, time to check again.
What about this decimal? Again, pause the video and complete the gaps on the slide and we'll get together for some feedback.
How did you get on? So 0.
02 is the same as two-hundredths, and that's how we write that as a decimal.
Zero 1s, zero tenths, and two in the hundredths column.
And Sam's gonna write it as a fraction, it's 2/100 as a fraction.
And what would 0.
25 be as a fraction? That's how we read it.
Well, Lucas says, "0.
25 is the same as 25 hundredths." Let's have a look at that.
Oh, so it's 0.
25.
But if we read to the hundredths column, we've got 25 hundredths.
Sam says, "I can write that as 25 out of 100, 25/100 as a fraction." But Lucas says, "Can you simplify 25 hundredths? Can you write that fraction in a simpler form?" "Yes, says Sam, "25 is a factor of the numerator and the denominator." So when we simplify a fraction, we find a common factor to the numerator and the denominator, and hopefully the highest one possible.
But 25 must be because 25 is the value of the numerator.
So if we divide both the numerator and the denominator by 25, scale them down by the same factor, we get the equivalent fraction of 1/4.
And you may already have known that 0.
25 is equivalent to 1/4 as a fraction.
What about 0.
75 then as a fraction? Well, Lucas says, "That's the same as 75 one-hundredths." So we can see that 75, we don't read it as that, do we? But if we're reading it as a number of hundredths, we can say there are 75 hundredths.
So Sam then can record that as 75/100 as a fraction.
And Lucas again says, "Can you simplify 75 one-hundredths?" "Yes, 25 again is a factor of both 75 and 100, the numerator and the denominator." So 75/100 is equivalent to 3/4.
And you may have known that 0.
75 is equivalent to 3/4 as a fraction.
Time to check your understanding now.
What would 0.
5 be as a fraction in its simplest form? Use the place value chart and the stem sentences to help you work through it.
Pause the video, and we'll come back together for some answers.
How did you get on? So 0.
5 in the place value chart will be 0 ones, decimal point, and five tenths.
So 0.
5 is the same as 5 tenths.
And we can write that as 5/10 or 1/2.
So you might have spotted that with 5/10, the factor common to both was 5, so 5 divided by 5 is 1, 10 divided by 5 is 2.
So we can scale down the numerator and denominator by the same factor so that 5/10 is equivalent to 0.
5.
So 0.
5 is equal to 1/2 as a fraction.
So decimals have a fraction equivalent.
Let's have a look at this chart.
Are these fraction equivalents all in their simplest form? And Lucas is reminding us, "A fraction in its simplest form is when the numerator and denominator only share a factor of 1." So let's have a look.
Are the fractions here in their simplest form? Well, you possibly had a look, anything with a 1 as a numerator will definitely be in its simplest form because 1 only has a factor of 1.
So 0.
01 is equivalent to 1/100, that is in its simplest form.
0.
1 is equivalent to 1/10, and that is in its simplest form.
And 0.
25 is 1/4, and that is in its simplest form.
Any others there? Well, there is one more that is in its simplest form, and that's 0.
75 is equal to 3/4.
The 3 numerator and 4 denominator only share a common factor of 1.
3/4 is a fraction in its simplest form, even though it's not a unit fraction with 1 as a numerator.
What about the others though? I think all of those, we could simplify those fractions.
So can we write the remaining fraction equivalents in their simplest form? What about 2/100? Well, Lucas says, "The numerator and denominator share a factor of 2, 2/100 therefore must be equal to 1/50." So we can also say that 0.
02 is equal to 1/50.
What about 2/10? Well, yes, again the numerator and the denominator share a common factor of 2.
So 0.
2, which is 2/10, is equal to 1/5.
So 0.
2 as a decimal is equivalent to 1/5 as a fraction.
Lots of ways to think about this.
We can think about common factors of the numerator and denominator, but we can also think here that 5 is half of 10, so this fraction must be equivalent to 1/2.
0.
5 is equivalent to 1/2.
And what about 0.
6 and 6/10? Again, there's a common factor of 2 there, isn't there? And if we scale the numerator and denominator both down by a factor of 2, we get the fraction 3/5, so 0.
6 is equal to 3/5.
Time for you to check your understanding now.
The fractions have a decimal equivalent.
What are the decimal equivalents to these fractions? So can you think about tenths and maybe hundredths as well and think about how you would represent these fractions as a decimal? Pause the video, have a go, and we'll come back for some answers.
How did you get on? So 9/10 can be written as 0.
9 with a 9 in the tenths column.
So that's a fairly easy one to convert, 0.
9.
What about 4/5? Well, we could use our knowledge of equivalent fractions, couldn't we? And we could create an equivalent fraction with 10 as the denominator.
So 4/5 is equal to 8/10, which is equal to 0.
8 and 8 in the tenths column.
So we can work through an equivalent fraction to help us with this one.
What about 1/4? This may be one that you know, but 1/4, well, 4 isn't a factor of 10, is it? But it is a factor of 100, so we could create an equivalent fraction with a denominator of 100.
So 1/4, we could rewrite as 25/100, and we could record that as a decimal as 0.
25 to show those 25 hundredths.
And what about 1/20? Hmm, but we could also think about creating an equivalent fraction with 100 as the denominator.
So 1/20th is equal to 5/100, we've scaled both up by a factor of 5.
5/100 is 0.
05, so our equivalent decimal is 0.
05.
So we can really use our understanding of equivalent fractions to help us to convert fractions into decimals.
Using those denominators of 10 or 100 can really help you to do that.
Right, over to you for some practise.
So can you convert these fractions and decimals into their equivalent values? So find an equivalent fraction with a denominator of 10 or 100 to convert a decimal if you need to.
So pause the video, have a go, and we'll get together for some answers.
How did you get on? So here are our answers.
So 0.
4 we might have known was 4/10, but it's also equivalent to 2/5, so in its simplest form.
0.
04 is 4/100.
And we can simplify that, we might have done it all in one go, but we've done a halving and halving again or a scaling down by a factor of 2, so 4/100 is equal to 2/50.
And we can again scale both the numerator and denominator down by a factor of 2 to give 1/25.
So 0.
04 is equivalent to 1/25.
What about 0.
08? Well, that's 8/100, isn't it? And we could just leave it as 8/100, but if we simplify it, we can think that that is, well, we've halved again, scaled down by a factor of 2 and then done that again, 4/50 or 2/25.
And now we know that is in its simplest form because 2 only has factors of 2 and 1, and 25 does not have a factor of 2, it's an odd number so that fraction must be in its simplest form.
0.
75 you might have known was equivalent to 3/4, but we could also work that out by saying, "Well, that's the same as 75/100, which is the same as 3/4." Well, now E and F is slightly different because we've got decimals greater than 1.
So 1.
25 is equal to 1 and 25/100, which is also equal to 1 and 1/4.
And you might have seen that 0.
25 and thought, "That was equal to 1/4." And the same for F, you might have seen straight away that 2.
5 is equal to 2 and 1/2.
But if you hadn't spotted that, you could say it's 2 and 5/10 and then simplify your 5/10 to 1/2.
And for the second set here, well, 6/10 is equal to 0.
6.
2/100 is equal to 0.
02.
And for I, 2/5, well, you might have known that that was equal to 0.
4 as a decimal, but you might have converted it into a fraction with a denominator of 10, so 4/10 is 0.
4.
75/100 is equal to 0.
75.
1/4 is equal to 25/100 or 0.
25, and you may have known that straight away.
And then for L, 1 and 1/4, well, if we know that 1/4 is 0.
25, then 1 and 1/4 must be 1.
25.
But you could have used your fraction equivalences as well.
I hope you were successful with all of those.
And on into the second part of our lesson, using fraction and decimal equivalents to compare.
Sam is checking Lucas' work on comparing fractions and decimals, and she does not think that this is correct.
How could she help Lucas to correct his work? So Lucas has said that 0.
25 is greater than 2/5.
And Lucas says, "Well, 25 out of something must be bigger than 2 out of something." Hmm, I think he's forgotten about what his whole is and what his numbers are representing, hasn't he? Sam says, "I think we should find the equivalent decimal for 2/5 or the equivalent fraction for 0.
25." "Okay," says Lucas, "2/5 is equal to 4/10, which is equal to 0.
4." "Oh," he says, "When I look at the decimals, 0.
25 is smaller than 0.
4." Hmm.
And Sam says, "The equivalent fraction for 0.
25 is 1/4, and 1/4 is smaller than 2/5." Well, we've sort of proved that with the decimals, we might have to do a bit of drawing to sort that one out.
'Cause 1/4 and 2/5, we can reason that they probably should be, but we might need to prove that if we were going to use that as our route to the answer.
The decimals in this case help us because we can clearly see that 0.
25 is less than 0.
4.
So he's corrected his work.
Well done, Lucas.
It's often easier to compare numbers if they are written in the same form.
So convert a fraction to its equivalent decimal or the other way round to help you compare them.
Easier to compare things when they look the same.
Lucas is checking an answer for Sam.
Do you think she's correct? Sam has said 1.
5 is equal to 1/5.
And Sam says the 1 in the decimal is the numerator and the 5 is the denominator.
Ooh, do you agree with Sam? Is that right? Well Lucas says, "No, the 1 in the decimal represents 1 whole and the 5 is 5/10." That's not the same in the fraction, is it? "Oh!" says Sam, "So the fraction is 1 whole and 5/10, which is 1 and 5/10 or 1 and 1/2." "Yes," says Lucas, "So 1.
5 is bigger than 1/5, much greater than a 1/5." Well done, Sam, you corrected your work.
So thinking about the decimal as its fraction equivalent helped Sam to correct her work that time 'cause she could see straight away that that was going to be 1 and something, which was going to be bigger than 1/5 on its own.
Time to check your understanding.
Convert the decimal to its fraction equivalent or the other way round, decide if these are correct.
So pause the video, have a go, and then we'll come back and look at our answers.
So which one is correct do you think? Well that's not correct, is it? 1 and 1/2 as a decimal would be 1.
5, so that's got to be greater.
I think there's been a mistake there made by thinking that we can just use the numbers in the fraction to create the decimal, and that's not right, is it? What about B? No Bs not correct either, B is 1 and 3/100.
And in our decimal we've got 1 whole and 3/10, so that's going to be larger.
What about C then? Now that one is right, isn't it? 1 and 3/100 is equal to 1.
03 as a decimal.
The fraction represents 1 whole and 3/100, so the decimal equivalent is correct.
Ah, now can you use less than or greater than to correct A and B? Pause the video, have a go, and we'll look at the answers.
So in A, 1 and 1/2 is greater than 1.
12.
The whole in the decimal is correct, but the fraction represents 5/10 and should beat 1.
5.
And what about B? We did talk about this on the previous slide, didn't we? So the 1 whole in the decimal is correct, but the fraction represents 3/100 and should be 1.
03.
So 1.
3 must be greater than 1 and 3/100, or 1 and 3/100 is less than 1.
3.
And as we said, you can't always use all the numbers in the decimal in the fraction and the other way round.
Think of what the fraction would be as tenths or hundredths to help convert it if it's not a known fact or it's a fraction with a denominator that doesn't neatly convert into a decimal.
So there's a couple we haven't mentioned this time.
It's useful to remember these approximate equivalents.
Remember, we couldn't find an exact decimal to represent 1/3 and 2/3 because 3 is not a factor of 100, so therefore we can't get an accurate answer as a decimal.
But it's useful to remember these approximate equivalents.
1/3 is equal to 0.
3333333, and 2/3 is equal to 0.
6666666, which you might find rounded up to a 7 at some point when it's used.
So they're not easy to work out as 3 is not a factor of 10 or 100.
And so you can't create equivalent fractions of tens or hundreds to convert into decimals.
So Lucas and Sam are playing a pairs game with a set of fraction and decimal cards.
They take it in turns to turn over two cards, and if they are equivalent, they keep the pair.
If they're not, they use less than or greater than to compare them and then turn them back over and put them back in with the other cards.
So you keep them if they're a pair, otherwise you work out which one's greater and then return the cards to the pack.
Ha, Lucas has picked two cards.
He says, "I know that 0.
8 is equivalent to 8/10, and that's equal to 4/5." And he says that, "4/5 must be greater than 3/4.
It's only 1 fifth away from a whole, whereas 3/4 is a whole 1/4 away from a whole and 1/5 is smaller, so that must be right." Sam says, "I know that 3/4 as a decimal is 0.
75 because 3/4 is equal to 75/100.
And 0.
8 is greater than 0.
75." So they've both proved it correctly, but Lucas used the fractions route and Sam used the decimals route.
So Lucas puts the cards back and Sam picks two more.
Are they an equivalent pair? What do you think? Over to you to check.
Pause the video, have a go, and we'll get back together for some feedback.
How did you decide to check? Did you turn 3/5 into a decimal or did you turn 6/10 into a fraction, I wonder? Well Lucas says, "Let's find a fraction equivalent to 3/5 with a denominator of 10 to make it easy to turn it into a decimal." Sam says, "3/5 is equal to 6/10, which is 0.
6 as a decimal.
So 3/5 is equal to 0.
6.
I can keep the cards!" she says.
Well done, Sam, you get to keep those ones.
Over to you for some practise.
So for part 1, we'd like you to have a go at playing Lucas and Sam's matching card game, and you've got some cards there to help you.
If your cards are equivalent fractions and decimals, you keep them.
If not, you use a less than or a greater than sign to compare them.
For part 2, you're going to put the correct symbol between these expressions.
So are they less than, greater than, or equal to each other? And then for part 3, if you had any that were not equal, so where you use the less than or greater than card, can you create an equivalent fraction for the decimal or an equivalent decimal for each of the fractions? So pause the video, have a go at your tasks, and we'll come back together for some feedback.
I wonder which cards you picked for Sam and Lucas's matching game.
Here are two that we picked out.
We've got 2/5 and 0.
33333.
I wonder if you remembered anything about that one.
So you might know that 0.
33333 is roughly equivalent to 1/3 and 1/3 is equal to 2/6.
So 2/5 has to be greater than 2/6 'cause 6ths are smaller than 5ths.
Or you might have used the other strategy to go invert the fraction into the equivalent decimal.
And 2/5 is equivalent to 4/10, which is equal to 0.
4.
And 0.
4 is greater than 0.
3333333.
Doesn't matter how many 3s there are, it's still only got 3 in the tenths so it's always going to be smaller than 0.
4.
So here are the correct symbols in between these pairs of fractions and decimals.
So did you spot for the first one, 0.
06, that was hundredths, so that's got to be smaller than tenths.
Our 2/100 and our 2/100 were equal.
Oh, 2.
5, that's a whole number, 2 and 1/2 so it must be greater than 2/5.
75/100 is equal to 0.
75, 1 and 1/4 is equal to 1.
25, and 1/4 is less than 0.
4.
Hmm, I wonder how we could prove that.
Well, 1/4 as a decimal is 0.
25, isn't it? So that's got to be smaller than 0.
4.
That was a good way round of thinking about it.
And what about the equivalences for the ones that didn't have an equal sign? So 0.
06 is 6/100, which is equal to 3/50, and 6/10 is equal to 0.
6.
2.
5 is equal to 2 and 1/2 and 2/5 is equal to 0.
4.
And then finally, 1/4 is equal to 0.
25, and 0.
4 is equal to 4/10 or 2/5.
So lots of practise there at comparing and creating equivalents.
And we've come to the end of our lesson.
We've been using knowledge of common equivalents to compare fractions and decimals.
It's really useful to know some common fraction and decimal equivalents off by heart.
They're useful facts to have.
But you can convert many fractions to decimals by creating an equivalent fraction with a denominator of 10 or 100 so that you can read the fraction as a number of tenths or hundredths.
And we've got a couple of examples here.
4/5 is equal to 8/10, which is equal to 0.
8, and 0.
75 is 75/100, which we can simplify to 3/4.
It is useful though to know them, especially for 1/2, 1/4, 1/10, and 1/5, they're really useful to know.
Some fraction and decimal equivalents are harder to convert as the denominator is not a factor of 10 or 100.
And we saw that with some of our fractions earlier, and you may have come across it in previous lessons.
1/3 and 2/3 are useful ones to know.
3 is not a factor of 10 or 100, so these are ones that we really need to remember.
1/3 is 0.
33333 with the 3s going on forever, and 2/3 is 0.
6666666 going on forever, and you might find that rounded up to a 7.
It's useful to remember these equivalents though.
Thank you for all your hard work.
I hope you've enjoyed playing around with fractions and decimals and their equivalents, and ordering and comparing.
And I hope I get to see you again in a lesson soon.
Bye-bye.
