Recall and use equivalences between fractions, decimals and percentages

Key Stage 2

Maths

Percentages and statistics

What percentage of numbers between 1 and 100 are multiples of 10?

What percentage of numbers between 1 and 100 are both multiples of 5 and 10?

What percentage of numbers between 1 and 50 are odd?

What percentage of numbers between 1 and 50 are cube numbers? (1x1x1)

What percentage of numbers between 1 and 50 neither multiples of 2 or 7?

﻿Today, we'll be learning to recall and use equivalences between fractions, decimals and percentages. Just a pencil and a piece of paper today, so get your equipment together, if you haven't done so already. Here's our agenda for today's learning, so we're going to recall and use equivalence between fractions, decimals and percentages, or look at equivalent fractions, decimals, and percentages. We'll look at ordering them before you do some independent learning and a final quiz. So I'd like you to start off by having a look at all of these images on the screen, they all represent one quarter. And I'd like you to think about how else we could describe these images, thinking about the theme of today's lesson, fractions, decimals, and percentages, how else could we describe them. Pause your video now to make some notes. So here are some of the things you may have written. So we know that they represent one quarter and one quarter is equivalent to two eighths. And if we think a bit out of a whole of 100, it's equivalent to 25 hundredths. That is the same as 0.25 and 25%. And then I've got this random one in here, which we'll think about in a moment. So let's think about this 0.25 one, so if we look at the bead string, if the bead string has a value of one, the whole bead string has a value of one, then every individual bead has a value of 0.01 because it's 100th of the whole. Therefore, if we look at 25 beads that has a value of 0.25, which is a quarter of the whole or 25%. Now let's have a look at this one, this random fraction that's in there, 90, 360ths, now that applies to the circle. And what we're looking at here is one whole turn is 360 degrees, and the circle has got a quarter of a turn indicated, and we know that a quarter of 360 degrees is 90 degrees. And we can simplify this, as simplifies to 36, which simplifies to one quarter. And in a couple of weeks, we'll be looking at pie charts, when we go into our statistics topic and we'll be using this kind of fraction out of 360, quite a lot. So look out for that coming up in a few lessons time. Now, going to look at some more equivalent fractions. So let's think about what we can say about the relationship between these two Cuisenaire rods. Well, first of all, I can see that the yellow rod is half the length of the orange rod. So if the orange rod has a value of one, then the yellow rod has a value as 0.5 or one half. The yellow rod is 50% of the length of the orange rod. So I can see some really clear equivalences here, one half, which is equal to 50 hundredths is equal to 50% and also 0.5. So I've got my fraction, decimal and percentage equivalents. Now I want you to have a look at this next one independently. Think about what you can say about the relationship between one white rod and the brown rod, pause the video now while you make some notes. So you may have noticed that the white rod is one eighth of the length of the brown rod. Eighth white rods is equivalent to one brown rod. So if the brown rod has a value of one, then the white rod has a value of 0.125 or one eighth. And if you cast your mind back to when we looked at how to convert a fraction into a decimal, what you would do, one divided by eight, and that would give you 0.125. So therefore we think about this in terms of percentages, the white rod is 12.5% of the length of the brown rod. And if I also think about this in another way, I can think of if one white rod is one eighth, then two white roads are two eighths or one quarter, one quarter is equal to 25%. So half of that is 12.5%, half of 25% is 12.5%, so you can see the link there. Now I'd like you to have another go, so I'd like you to pause the video and match the pairs of equivalent fractions, decimals, and percentages. So I'm working systematically. I started my top left hand corner and I can see that 0.7, which is equal to seven tenths or 70 hundredths is also equal to 70%. So you can see that I worked my way through, making it into equivalent fractions and then an equivalent fraction over 100, which helped me to convert to a percentage. So then I look at my next one along, I'm looking at 100th. If I think of that as a decimal, I know that that is 0.01. So one in the hundreds column and as a percentage, 100th is 1%, so you can see those two, one tenth is equivalent to 1%. Moving on to 0.9, I made that 0.9 it has a nine in the 10ths column, therefore it's equivalent to nine tenths. And I can take that further, nine tenths is equivalent to 90 hundredths, which is 90%. And then I can use that to help me with the next one, 0.8, 0.8 is equivalent to eight tenths because the eight is in the 10ths column, which is the same as 80 out to 80 hundredths, sorry. So eight tenths is equivalent to 80 hundredths, which is the equivalent to 80%. So you can see those two in orange there. Onto the next one, so I'm looking here at the picture of the rod, where three out of four parts have been shaded, so I know three out of four parts, that's three quarters. I know that three quarters is equal to 75 hundredths, or 0.75 or 75%, so there I have my two matching pairs. And remember in our previous fractions topic, we talked about some of those fractions and decimals and percentages that are really worth remembering. It's worth remembering that three quarters is equivalent to 0.75 or 75%, you'll see that one coming up a lot. Next I move on to one half, one half is equivalent to five tenths, which is 0.5. So I can see my match there in grey and I'll take it further, so if one half is five tenths, which has 50 hundredths, which is 50%. Then onto my next picture, I've got three out of five parts shaded here. So that's three fifths, three fifths is equivalent to six tenths, which is equivalent to 0.6. So there, I've got my matching path and 0.6, which is six tenths, is equivalent to 60 hundredths, which is the same as 60%. So I've only got two left and I'll just check now. So this is one out of five parts shaded. So that's one fifth, which is equivalent to 20 hundredths or 20%, so they're my last to match up. So now we're going to use that knowledge to order some fractions, decimals, and percentages. So here's my first question, which is bigger, one fifth or 35%? Now I'd like you to do some thinking now, before we go into exploring this further, so use the bead string and use the hundred square to support your thinking and pause the video now to do some calculations as to which is bigger, one fifth or 35%? So we'll look at one fifth, first. We know that one fifth of the whole is equal to 20 beads. So I've split the whole, which is a hundred into five equal parts. So one fifth of the whole is 20 beads. So then if the whole has a value of one, one fifth is equivalent to 20 hundredths. So we're moving into equivalent fractions to help us to move into percentages. If we just go quickly back and you can see that we can't directly compare these two, because they're not in the same format, we need them to be either both fractions or both percentages in order to compare. So we're going back, so we had said that this section one fifth is 20 out of a hundred beads, so that's 20 hundredths. And therefore one fifth is equivalent to 20%, 20 out of 100. Let's have a look at all of those equivalences this together. So we turned one fifth into two tenths, which is equal to 20 hundredths. And then we can use our knowledge of decimal, two tenths is equal to 0.2. So two in the 10ths column and that's equal to 20%, 20 hundredths. So then we know, if we look at this, comparing our bead strings, we can see that one fifth is 20 of those beads or 20% or 20 out of 100, and 35% is 35 out of 100. Therefore 35% is greater than one fifth. So I'd like you to use that same strategy, to order these fractions, decimals, and percentages starting with the largest, and the first job is to convert them into equivalent fractions with a denominator of 100. Pause the video now and have a go. So let's have a look at this in detail. Here are my fractions, decimals and percentages, in order to compare, they need to be in the same form. So three twentieth, I'm going to multiply by five to give me 15 hundredths. Now, remember that whatever we do to the numerator, we must do to the denominator. So I multiplied 20 by five to get 100, 3 by five to get to 15. I know that 30%, I know percent means out of 100, so 30% literally means 30 hundredths. If I look at 0.03, I can see that it has a three in the hundredths column, that means that it's equal to three hundredths and then three 50th, if I multiply both numerator and denominator by two, then I find the equivalent fraction of six hundredths. Now I have equivalent fractions, I can compare them, I'm starting with the largest, I can see looking at the numerators that 30 hundredths is the largest, then 15 hundredths, then six hundredths, and finally three hundredths. So now you're going to apply all of that learning to some of your independent work. So I'd like you to pause the video and complete the tasks and then click restart once you're finished. So for question one, you were asked to complete the table to give the equivalent fractions, decimals, and percentages. So for the first one, we were given four fifths and I just converted that into a fraction over 10 to help me. So four fifths is equivalent to eight tenths, so the decimal version will have an eight in the 10ths column, that's 0.8. And I know that as a percentage, that is 80%. And if you're not confident to go straight from decimal to percentage, you can think back to what this is as a fraction, it's eight tenths, which is 80 hundreds, which is 80 out of 100, 80%. For the next one, I can see that there is a two in the hundredths column, so that's equivalent to two hundredths. And I know straight away as a percentage two hundredths, two out of a hundred, 2%. Onto the next one, 89% as a decimal, is 0.89, which is equivalent to 89 hundredths, and finally 0.5, that is five in the 10ths column, so that's five tenths, which we know is equivalent to one half. And there's a percentage is 50%. For question two, you were asked to order the fractions, decimals, and percentages in descending order, which means starting with the greatest. And again, your needed to have them in the same format, in order to compare them. So 0.6 has a six in the tenths column, it's six tenths or 60 hundredths. 1.6 is equivalent to 16 tenths or 160 hundredths. 78%, 78 out of a hundred, so 78 hundredths. 62 hundredths, and then this one always worth remembering one half 50%, 50 hundredths. Now I can get on with the ordering and I'm going to be using the numerators out where the fraction is out of 100. So I can actually see that this one is definitely the greatest. It's the only one that is a number greater than one, all of the others are less than one. So 160 hundredths is the greatest, then we've got 78 hundredths, then 62 hundredths or 62%, then 60 hundredths, so 0.6 and finally one half. Same again for the next question, so these needed to be in a similar format in order to compare, so 27% is 27 hundredths, one quarter 25 hundredths, 25%, 0.3 is three tenths, which is equivalent to 30 hundredths. 32% is 32 hundredths, and two fifths is equivalent to four tenths, which is 40 hundredths. Descending, again, we're starting with the greatest, these are all numbers that are less than one. And we can see that this one 40 hundredths or two fifths is the greatest. then it is 32%, then 0.3, then 27%, and finally one quarter. Another one where you would ordering them in descending order, so 65% is 65 hundredths, 18 twentieth, I multiplied numerator and denominator by five to give me 90 hundredths, which is 90%. Then I have 85 hundredths, 88 hundredths and nine hundredths. So I'm starting with the greatest, which is 18 twentieths or 90%. Then I go onto 88 hundredths or 88%, then 85%, 65%, and then nine hundredths, which is 9%. Next question you're matching the equivalent fractions, decimals, and percentages. So we start systematically at the top left with 90%. We know that that is equivalent to 90 hundredths, which simplifies to nine tenths. And then that converts to 0.9, which has a nine in the 10ths column. The next one we have is 33.3 recurring or 33.3% recurring, which we know is equivalent to one third or as a decimal 0.3 recurring. And then finally we'll just check our last one, we've got 15%, which is equivalent to three twentieths. And I know that it is because if I convert that to a fraction over a hundred, I multiply numerator and denominator by five, which gives me 15 hundredths or 0.15. Question four, you were asked what percentage of each shape is shaded? So we can see in the first sheet that two out of four parts are shaded, which is the same as one half or 50%. And then in the next one, if you put this grey part up into the top, that's one part. And if you put this grey part over here, that gives us two parts, so it's two out of five, two fifths, which is equivalent to four tenths or 40%. Last question you were asked to match each card to the percentage that is equivalent to the decimal or fraction. So we know that 2% as a decimal is 0.02, and as a fraction is two hundredths. We know that 22% as a decimal is 0.22, as a fraction is 22 hundredths, and then we know that 20% as a decimal is equivalent to 0.2, which is as a fraction two tenths or 20 hundredths or one fifth, so lots of equivalent fractions there. So it's time for your final quiz, pause the video and complete the quiz and then click restart once you're finished.

Recall and use equivalences between fractions, decimals and percentages

Recall and use equivalences between fractions, decimals and percentages

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