Question Video: Identifying Fractions of a Whole Using Visual Fraction Models | Nagwa Question Video: Identifying Fractions of a Whole Using Visual Fraction Models | Nagwa

Question Video: Identifying Fractions of a Whole Using Visual Fraction Models

What fraction is shaded?

03:15

Video Transcript

What fraction is shaded?

This shape is a hexagon. It’s got six sides. And it’s also being split into equal parts. They’re all triangles. Now, some of those equal parts have been shaded. And we’re asked in this question, what fraction of the shape is shaded. A fraction, as we know, is made up of two numbers separated by a line. The bottom number is the denominator. The job of the denominator is to show us the total number of equal parts in the whole shape. So let’s start by counting them. How many equal parts has this shape been split into? There are five triangles on the top row and five more triangles on the bottom row. That’s 10 altogether. And so we can say that our hexagon has been split into tenths. The denominator is 10.

The top number in a fraction is the numerator. This number represents the number of equal parts that we’re talking about, the numbers that are selected. And in this particular question, we’re talking about the number of those equal parts that are shaded. And we can see that there are two triangles that have been shaded. So that’s two triangles out of a possible 10 triangles. Our numerator is two. Our denominator is 10. And the fraction that is shaded is two-tenths.

Now, if we wrote two-tenths as answer to this question, it would be a correct answer. But there’s a simpler way to express this fraction. And it’s always a good idea to simplify a fraction where we can. Simplifying a fraction involves finding another fraction that’s worth the same, that’s equivalent. And we can do this by dividing the numerator and the denominator by the same number. What can we divide two and 10 by? We could divide them by one. But then, they’d stay the same. But another factor of both two and 10 is the number two itself. Let’s see what happens when we divide them by two. Two divided by two equals one. And 10 divided by two equals five. Two-tenths is the same as one-fifth. And so we can say that one-fifth of our shape is shaded.

Here’s a diagram to show why this works. At the moment, here’s our shape split into tenths. And here are our two shaded triangles showing two-tenths. Now imagine we move one of those triangles. It won’t change the fraction. But if we just move it next to the other one, so we’ll move the top one. We can still see that two-tenths is shaded. But we can see by putting the two parts together, they make a parallelogram shape. How many of these parallelogram shapes can we see? There are five of them. And one out of those five is shaded, two-tenths, one-fifth.

The fraction of this shape that’s shaded is two-tenths. And we can simplify this and write it as one-fifth.

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