Lesson Video: Modeling Tenths | Nagwa Lesson Video: Modeling Tenths | Nagwa

# Lesson Video: Modeling Tenths Mathematics

In this video, we will learn how to represent tenths with a model, a fraction, a decimal, and words

14:57

### Video Transcript

Modeling Tenths

In this video, we’re going to learn how to represent tenths with a model, a fraction, a decimal, and words. Let’s start with a 10 frame. Now, often we use 10 frames to help us with counting. They represent 10, don’t they? But in this video, let’s think about them slightly differently. Let’s think about the 10 frame as representing one whole, one whole rectangle or one whole 10 frame.

Now, one thing we know about 10 frames is that they’re split into 10 equal parts. Now, what’s one of these parts worth? We can write this part as a fraction. The whole amount has been split into 10 equal parts. So we know the denominator for our fraction is 10. And we just want to know what the value of one of these is worth. So our numerator is one. We can read this fraction as one-tenth. And instantly, we’ve just represented one-tenth in three different ways: using a model, writing it as a fraction, and also using words. If we saw any of these three representations, we’d think to ourselves, “That shows one-tenth.” Let’s have a go at practicing showing tenths in these three different ways.

This table contains three columns, where we can show a number of tenths as a model, a fraction, and in words. In the first row, we can see a model, but nothing else has been completed. How would we show what we can see as a fraction? Well, we can see that our model is a rectangle that’s been split into 10 equal parts. So the denominator for our fraction must be 10. And if we count the number of shaded parts, there are five of them. Five out of 10 equal parts have been shaded. And how would we say this part using words? Of course it’s five-tenths, isn’t it?

In the second row, we’re only given a fraction. Again, the denominator is 10. So we know this shows a number of tenths, and the numerator is three. So we could represent this part with the words three-tenths. We could also show it using a model as long as our model shows 10 equal parts, with three of them having been chosen or selected. This tape diagram works well, 10 equal parts, and we’ve shaded three of them, three-tenths.

Hopefully, you’re getting the hang of this by now. In the final row, we’re given a part written in words: nine-tenths. As a fraction, we know this is going to have nine as the numerator and 10 as the denominator, nine out of a possible 10. And if we want to model this part again, we’re just gonna need to show something having been split up into 10 equal parts. And we need to show that nine of them have been chosen. So how about this? A 10 frame where nine out of the 10 squares have counters in them, nine-tenths.

So, so far, we know how to represent tenths in three different ways. But if you remember, at the start of the video, there were actually four different ways that were mentioned. We’re going to need to add another column to our table because the fourth way we can represent these parts is as a decimal. Now, it would be nice to complete our table. But we’re gonna have to come back to it in a moment because first we’re going to have to learn what a decimal is.

A decimal is a number that has a whole part and what we call a fractional part, separated by something called a decimal point. Let’s show what we mean. And I’m sure you’ve done work using a place value grid like this before. The column with the lowest value in this grid is the ones column. And as we move to the left, the value of each column gets 10 times greater. So after the ones, we have the tens. 10 times greater than a 10 is 100, and 10 times greater than 100 is 1000, and so on.

Now, if we move along our columns from left to right in the opposite direction, we can think about them getting 10 times smaller. 100 is 10 times smaller than 1000, a 10 is what you get when you split 100 into 10, and a one is 10 times smaller than a 10. But what if we carried on going?

So far, we’ve just been dealing with whole numbers, like ones, tens, hundreds, and thousands. But what if we start thinking about parts of a whole? What’s 10 times smaller than one? Or if we think about it another way, what do we get if we split up one into 10 equal parts? Well, we can’t do with our base 10 equipment, but it would probably look a little bit like this if we could. It’ll be a sliver of a ones block.

Well, we know from what we’ve talked about already in this video that when we split one whole into 10 equal parts, we call them tenths. And so the next column to the right of our ones column, which is a new column to learn about, is called the tenths place. And to separate the whole part of a number from this new part that shows less than a whole, we call it the fractional part, we simply use a little dot. And we call this the decimal point. So, for example, if we want to write one-tenth as a decimal, we put a zero in the ones place, because we don’t have any whole number at all. We’re talking about less than a whole, aren’t we? Then we need to draw our decimal point. And we put the digit one in the tenths place, one-tenth. Sometimes you might hear this read as 0.1.

So let’s finish off our table. The first row, we want to show five-tenths, so that’s zero ones, a decimal point, and a five in the tenths place, five-tenths or 0.5. To show three-tenths, we’ve still got zero ones because we’re showing less than a whole. Again, we need a decimal point and this time the digit three in the tenths place, three-tenths or 0.3. And I’m sure you can work out how to represent nine-tenths.

Now that we’ve found out how to represent tenths as a model, a fraction, using words, and as a decimal, let’s try practicing what we’ve learned. See if you can answer these questions.

Write a decimal to match the given model.

The model that our question is talking about is this shape here. It’s being divided into parts, and some of them have been shaded. Now, we might know how to describe this model using words, maybe even as a fraction. But our question asks us to write a decimal that matches the model.

Now, we know that a decimal is a type of number written using digits that has a whole part and then a part that shows less than a whole. It’s a way of showing amounts that are less than a whole. And to separate the whole part and the fractional part, we draw a dot, a decimal point. Now, before we write this as a decimal, perhaps it might be useful to think about what fraction we can see. Firstly, we can see that this shape has been divided into 10 equal parts. And it’s important that we can see that they are equal. This means that the denominator of our fraction is 10. And in this model, seven of those 10 parts have been shaded. So the numerator for our fraction is seven. Seven out of 10 parts are shaded. And we’d say this using words as seven-tenths.

Now that we know how many tenths our model shows, we can write the amount as a decimal. The whole part is going to be zero because we don’t have any whole shapes that have been shaded. It’s only part of a shape. Now, the column after the decimal point, this is the fractional part of our decimal, is worth tenths. And we know that our model shows seven-tenths. So we’re going to need to write the digit seven in the tenths place. We found the answer by first working out how many tenths our model shows and then by using this information to write the amount as a decimal. The correct answer is seven-tenths, which we write with a zero, a decimal point, and then the digit seven.

The given box can hold 10 counters. What fraction of the box is filled? Write this fraction as a decimal.

In the picture, we can see a box, and we’re told that it can hold 10 counters. This box looks a little bit like a 10 frame, doesn’t it? Although we’re told it can hold 10 counters, we can see that it only contains three at the moment. Only part of the box is filled. And in the first part of the question, we’re asked to write this as a fraction. What fraction of the box is filled?

Well, if we draw our horizontal line to begin with, we can start by completing the denominator, because we know that the whole box has been split up into 10 parts. They’re all equal parts because they can all contain one counter. So the denominator for our fraction is going to be 10. We’re talking about a number of tenths here. And the number of these 10 equal spaces that are filled with counters is three. Our box contains three out of a possible 10 counters. It’s three-tenths full.

You know, there’s another way we could represent this amount because in the second part of our question, we’re told to write this fraction as a decimal. We could use this place value table to help us. We can’t see any whole boxes that are full. So we need to put a zero in the ones place. But we can see that three-tenths of the box is full. And when we want to show a number of tenths, we draw a little decimal point after the ones place. And we write the number of tenths in the tenths place, which is the next place to the right, 0.3. When we see this, we can just say three-tenths.

Now, as we look back at this question, we can see a number of tenths shown in three different ways, firstly as a model, as part of the question, then as a fraction, and finally as a decimal. And they all represent the same value. The fraction of the box that’s filled is three-tenths. And to write three-tenths as a decimal, we simply write the digit zero, a decimal point, and then the digit three, 0.3.

Each square is one whole. James has colored one whole and four-tenths orange. Write this as a mixed number. Write the decimal shown by the model. Hint: Use a place value table to help you.

In the model, we can see two squares. And in the very first part of the question, we’re told that each square has a value of one whole. We’re then told that James has colored one whole and four-tenths orange. In other words, he’s colored a whole square and part of a square. Now, there are several ways that we could represent a whole and a bit more or a whole and a part. And one of these is as a mixed number.

A mixed number has a whole part and a fraction part. So if we were to represent what James has colored as a mixed number, we’d need to represent the whole square. So we’d write the number one, one whole square. And then part of a square, which is four-tenths of a square that is colored, we simply write as a fraction. James has colored one and four-tenths.

Another way we could represent a whole amount and a part is as a decimal. Now, to help us solve this part of the problem, we’re given a hint: to use a place value table. We know that the decimal point in a decimal number separates the whole part from the fractional part or the part that’s less than a whole. Now, often when we start learning about tenths, we put a zero in the ones place, because we’re only talking about a number of tenths. We’re not talking about any whole amounts. But in this example, James has colored in a whole square. So we’re going to need to write the digit one in the ones place. This represents his one whole square that he’s colored in. And we know that the column to the right of the decimal point shows the number of tenths. And in the second square, we know James has colored four-tenths. So we’re going to write the digit four in the tenths place.

In this question, we can see the same value represented in four different ways. It’s described in the actual question in words. We’re also shown a model. And we’ve had to work out answers which show it as a mixed number, which is a whole number and a fraction, and finally as a decimal, four different ways of saying exactly the same thing. As a mixed number, James has colored one and four-tenths. And we write this as a decimal as a one, then the decimal point, and then the digit four, 1.4, one and four-tenths.

So what have we learned in this video? We’ve learned how to represent tenths using models, fractions, words, and decimals.

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