Question Video: Using Fraction Models to Understand Tenths Mathematics • 4th Grade

Each square is one whole. James has colored 1 whole and four-tenths orange. (a) Write this as a mixed number. (b) Write the decimal shown by the model. Hint: Use a place value table to help you.

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Video Transcript

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.

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