What decimal represents the shaded portion of the shown figure?
In this question, we’re given a rectangle. And the rectangle seems to have been split into equal parts. And some of them have been shaded. And we’re asked to find a decimal that represents the value of the shaded part. So how are we gonna do this? Why do we write the shaded part as a fraction first, and then try to convert it and write it as a decimal? We can see that the rectangle has been split into eight equal parts. So we know that the shaded area is a number of eighths. How many of the parts are shaded? Well, only the two parts on the end aren’t shaded. So we know that six out of eight parts are. The fraction that represents the shaded portion is six-eighths.
Now, we need to think about how to write this as a decimal. If the rectangle had been split into tenths or even one hundredths, then it will be a lot easier to convert into a decimal. We know how to use place value to convert tenths and hundredths into decimals. But the shape is split into eighths. You might know what one-eighth is worth as a decimal. We’ll go over that at the end. But what if you don’t? Is there an equivalent fraction that we can change six-eighths to, to help us to write it as a decimal? What if we convert it into quarters? We know how to write different numbers of quarters as decimals. Perhaps this would help.
To convert eighths into quarters, we divide the denominator by two. This is the same as saying, instead of the rectangle having eight equal parts, what we wanted to have is four equal parts. And if we do this, how many parts, or how many quarters, are shaded? We can see on the diagram that three out of four parts are now shaded. Because we’ve divided the denominator by two, we also need to divide the numerator by two. That’s the number of shaded parts. And so, six-eighths is the same as three-quarters. And we know how to write three-quarters as a decimal; it’s 0.75.
When we looked at the shaded area, we said that it was worth six-eighths. Now, one-eighth is actually worth 0.125. And if we knew that fact, then we could’ve just multiplied this by six to find the answer. But if we don’t know what one-eighth is as a decimal, then there’s another way that we use to find the answer. We converted six-eighths into quarters. Six-eighths is the same as three-quarters. And we know how to write three-quarters as a decimal. The decimal that represents the shaded portion of the figure is 0.75.