Lesson video

Good morning, welcome to today's lesson, where we're looking at the equivalence between decimals and fractions.

If you haven't done so already, get your equipment ready.

All you'll need is a pencil and a piece of paper.

Pause the video now and get your things together.

Let's look at today's lesson agenda.

Today, we're looking at the equivalence between decimals and fractions.

Equivalent decimals and fractions, then non-equivalent decimals and fractions before moving on to your independent task and then a final knowledge quiz.

Now, here is your do now.

You have these two numbers, what is the same, and what is different about them? Pause the video while you note down some ideas.

The first thing you will have noticed is that one of the numbers is a decimal while the other is a fraction.

Let's start off by looking at the decimal 0.

5.

The first thing to ask us is what is the value of each of the digits? The value of the zero is zero ones, the value of the five is five tenths.

Let's look at this using a place value chart.

So our zero ones go into the ones column and our five tenths go into the five, the tenths columns, sorry.

That means that 0.

5 is equivalent to 5/10.

Now, we know from our knowledge of equivalents that 5/10 is not a fraction in its simplest form.

Five is a factor of both five and 10, therefore the numerator and denominator can both be divided by five to have this fraction as an equivalent in its simplest form 1/2.

Therefore, 0.

5 is equivalent to 1/2.

Now, if you remember, we looked at the relationship between the numerator and the denominator between fractions, but also within fractions.

So we can see from this one that the denominator 10 is two times greater than the numerator to five.

So the numerator multiply by two gives us the denominator, that's the relationship.

The relationship should be the same here as well.

The denominator two is two times greater than the numerator one.

So the relationship between the numerator and denominators is equivalent between fractions and within fractions.

Let's look at this representation, pictorially.

We can use bar models to first of all show 0.

5 is five lots as 0.

1.

That's equivalent to five lots of 1/10, which is 5/10, which is also equivalent to 1/2.

Lets look at another one together.

This time, we're looking at 0.

2 and I've already shown you the equivalents using bar models.

Let's have a look at our place value chart, so the zero is representing zero ones.

And the two here represents the 2/10.

So we know that 0.

2 is equivalent to 2/10, and we can see that 0.

2 is two lots as 0.

1, which is 0.

2 put on there.

It's two lots of 1/10, which is 2/10, which is equivalent to 1/5.

We can see the equivalents in the bar model.

Let's just check the relationship between the numerator and the denominator between those two fractions.

So I know that two divided by two is equal to one and 10 divided by two is equal to five.

So they are equivalent fractions.

Now, it's your turn, pause the video and show the comparison of the decimals 0.

6 with the fraction 3/5, use the place value chart and show you're simplifying.

So we'll start with 0.

6 and put it into our place value chart, zero ones and 6/10.

So we can see that 0.

6 is equivalent to 6/10.

We know that this fraction is not in its simplest form.

We know that two is a factor of both six and 10, and if we divide six and 10 both by two, we get our equivalent fraction in its simplest form of 3/5.

And here's your representation pictorially.

Six lot is 0.

1 is equivalent to 0.

6, six lots of 1/10 is equivalent to 6/10, which is equivalent to three lots of 1/5, 3/5.

Now, let's look at some more advanced fraction and decimal comparisons.

Now, we're going to look at 0.

75 and 3/4.

These are equivalent fractions, but I want to prove it.

So I'm going to start by looking at 0.

75 and use my place value chart to help me.

My zero is in my ones column, it's representing zero ones.

My seven is in the tenths, and my five is in hundredths.

That means that 0.

75 is equivalent to 75/100, and I've shown it here using 100 square, which is divided into 100 lots of 100s.

So I can see that when I shaded 75 parts, this is what it looks like using my 100 square, okay.

Now, I can see that 0.

75 is equivalent to 75 out of 100 parts shaded in the 100 square.

I know from my knowledge of equivalent fractions, that 75/100 is not in its simplest form.

I know from my knowledge of times tables that as there is a seven, not seven, a five in the ones column and the zero and ones column that both definitely multiples of five.

So I could divide them both by five to find an equivalent fraction.

Now, 75 divided by five is equal to 15 and 100 divided by five is equal to 20.

Now, still using my knowledge of timetables, I can see that this is still not in its simplest form, so I can simplify them further by dividing them again by five.

15 divided by five is three and 20 divided by five is four.

Therefore, proving that 75/100 is equivalent to 3/4.

I could have done this simplifying in one jump.

I'll do it down at the bottom.

75/100, I know that the lowest common factor between 75 and 100 is 25.

So I could have divided both by 25 and in one step that gets me to 3/4.

Now, it's your turn, pause the video and show the comparison between the decimals 0.

65 and the fraction 13/20, use a place value chart and show your simplifying.

So when looking at this one, first of all, you're looking at 0.

65, and you can label the digits to show their value.

So we can see from this labelling, that 0.

65 is equivalent to 65/100.

I know that these numbers both have factor of five, so I can divide them both by five.

And that will get me the equivalent fraction 13/20.

I know that this is in its simplest form because I know that the only comment factor of 13 and 20 is now one, therefore it cannot be simplified any further.

And I've just drawn all over my place value chart.

Now, looking at comparing non-equivalent decimals and fractions, they include the inequality signs to make a statement correct, 0.

7 and 4/5.

The most important thing is to make sure that both of the numbers are in the same form.

So either I can meet both of them decimals, or I can make both of them fractions.

Today, we're working on converting decimals to fractions.

In our next lesson, we'll look at fractions to decimals.

So I'm going to convert them both to fractions, which means that I need to turn 0.

7 into a fraction.

I'll use my place value chart to support my working.

So I put my decimal into my place value chart, and I can see that the equivalent fraction for this decimal is 7/10.

Now, I'm looking at comparing 7/10 and 4/5.

You will notice that these have got different denominators, therefore they are very difficult to compare.

So I need to turn them into a equivalent fractions with the same denominators.

So I need to look at 4/5, I can see that a comment multiple of tenths and fifths is 10, so I'm going to convert this into an equivalent fraction with 10 as the denominator, which means that I'm multiply numerator and denominator by two.

So 4/5 becomes 8/10.

I'm now comparing 7/10 and 8/10.

I can see that 7/10 is less than 8/10, so I can insert this sign.

So 0.

7 is less than 4/5.

Let's do another one together.

This time, we're looking at 1.

6 and 9/2.

So again, I'm going to convert my 1.

6 to a fraction using my price value chart.

This time I have one in the ones and six in the tenths, 1.

6.

So I can see that this is equivalent to 1 6/10.

Now, it's difficult for me to compare a mixed number and an improper fraction.

Also, I have these with different denominators.

So I'm going to convert this one to improper fraction first, I know that 1 6/10 in six tenths is equivalent to 16/10.

Now, I need to make the 9/2 into an equivalent fraction with 10 as its denominator, so that I can compare these two fractions.

I know that two multiplied by five is equal to 10.

And then I multiply nine by five, which gives me 45.

So 9/2 is equivalent to 45/10.

Now, I'm comparing 16/10 and 45/10.

I can see that 16/10 is less than 45/10, so I can insert this symbol here.

So 1.

6 is less than 9/2.

Now, it's your turn.

Pause the video and insert one of the inequality signs to make this statement correct? Make sure you use your place value chart to support your working.

So you were converting 2.

6 into a fraction.

That's two ones and six tenths.

So that's 2 6/10, we want to deal with both improper fractions or both mix numbers, not a mixture.

So I'm going to turn 2 6/10 into an improper fraction.

And I know that that is equivalent to 26/10.

Now, I need to convert 7/5 into an equivalent fraction with a denominator of 10.

And I know that five multiplied by two is equal to 10 and seven multiplied by two is equal to 14.

So I'm comparing 26/10 and 14/10, so I can see that 26/10 greater than 14/10.

So 2.

6 is greater than 7/5.

Now, it's time for some independent learning, pause the video and complete your task and come back here when you finish so that we can go through the answers together.

Okay, good job.

Now, let's have a look at the answers to question one together.

You were asked to insert one of the inequality signs to make the statements correct.

So we want to deal with the same type of number, so we're going to convert the decimals into fractions.

We know that 0.

7 is 7/10, and we need to compare 3/4 and 7/10.

So our common denominator here will be 20.

So this will be 14/20 because we've multiplied by two.

And to get to 20 here, we're multiplying by five, so that's 15/20.

We can see that 15/20 is greater than 14/20.

Moving on to the second one, 0.

25 is equivalent to 25/100.

We need to make this an equivalent fraction with a denominator 100.

And I know that five multiplied by 20 is equal to 100.

Two multiplied by 20 is equal to 40, and therefore, 40 is greater, sorry, 40/100 is greater than 25/100.

Onto the last one, 0.

65 is 65/100 as a fraction.

Again, we need this to be an equivalent fraction with the denominator 100, I know that 20 multiply by five is 100, so I do the same to my numerator.

Seven multiplied by five is 35.

I can straight away see that 35/100 is less than 65/100.

Onto question two, we're writing these numbers in order, starting with the smallest.

So let's work on getting them into all fractions.

So 0.

6, 6/10 you may have labelled your digits to help you, or you may now be at the stage where you're looking at them and you feel like, you know, what's going on.

3/10, we leave.

0.

2 is 2/10, 9/10, we leave, go back to the question.

We're starting with the smallest, so we can see after this that 2/10 is the smallest, so this is our first one, then and 3/10, 6/10, and finally 9/10.

Onto question three, we're all doing these numbers now starting with the largest.

Okay, so we've just got one to convert to a fraction.

0.

45 is equivalent to 45/100.

Now, we've got to convert these fractions, so that they are equivalent fractions.

And we can see that these are all factors of 100.

So I can convert these to fractions with a denominator of 100.

Multiply this one by two, gives me 70/100, multiply this one by five, gives me 40/100, and multiply this one by 20, three times 20 is 60/100.

Oops, that looks like 66, there we go.

Okay, back to the question, we're starting with the largest this time.

So I can see that the largest is this one 70/100, and the next one is 60/100, followed by 45/100, and finally 40/100.

Onto question four.

Now, we need to circle the three numbers that add up to one.

Now, I'm looking at my decimals and I'm going to convert them into fractions.

5/10, 1/10, 15/100, and 2/10.

So I need to convert these two equivalent fractions with the same denominator.

I'm looking at all of my denominators and a common multiple is 100.

So I need to convert them all into fractions over 100.

So I know that four times 25 is 100, so I do the same to my numerator.

Then I need to multiply this by 10, so it's 50/100.

Again, multiply by 10, so it's 10/100, same here, 70/100.

This one is fine.

And then this one I multiply by 10 to give me 20/100.

Now, I'm looking for three numbers that add up to one.

If I think about that in terms of fractions, I'm looking at fractions out of 100 parts.

So one is equivalent to 100/100.

So which of these three numerators add up to make 100? I can see that 10, is a bit of trial and error here, but 10 and 70/100 make 80/100.

Add another 20, it gives me 100/100.

So it's 0.

1 plus 7/10 plus 0.

2 is equal to one.

Last question, Omar says that 0.

35 is smaller than three 3/5, we need to explain why he is correct.

So we can look at 0.

35 and we can look at 3/5.

Lets first of all look at this fraction.

If I think about this fraction as an equivalent fraction with the denominator of 10, I can start to think about what we're looking at in our next lesson, which is converting fractions to decimals.

6/10, well, I know that as a decimal, that is 0.

6, and I know that 0.

6 is greater than 0.

35, but let me also just look at it the other way.

0.

35 is equivalent to 35/100, 3/5 is equivalent to 6/10, which is equivalent to 60/100.

So I can clearly see that 3/5, 6/10, 60/100 is greater than 0.

5 or 35/100 And for your final knowledge quiz, pause the video and compete the quiz to see what you've remembered.

You've worked really well today, I'm really looking forward to meeting you back here tomorrow with our next lesson when we'll be learning the opposite, we'll be converting fractions to decimals.

See you then.