What fraction is shaded?
Here, we have a shape. This is a regular hexagon. It has been divided into equal parts. And we know that a fraction is made up of a numerator, which is our top number, and the denominator, which is the bottom number. If we think about the denominator to begin with, the denominator shows us how many equal parts our whole amount has been split into. Let’s count the number of equal parts that this hexagon has been split into: one, two, three, four, five, six equal parts. And so, the denominator in our fraction is six. We can describe the shaded amount as a number of sixths. But how many sixths?
The numerator or the top number in our fraction shows us the number of parts that we’re talking about. And in this instant, we’re talking about the shaded parts. And there are one, two, three shaded parts, three out of six. And so, our numerator is going to be the number three. Three-sixths of the shape is shaded. Now, if we gave the answer three-sixths, this would be correct. But we can actually simplify this fraction. We can look for an equivalent fraction that has the same value as three-sixths, but it’s simpler.
To find our equivalent fraction to simplify three-sixths, we need to think of a number that we can divide both three and six by. Which number is that? Well, apart from the number one, there’s only one of the number that the numbers three and six both have in common. They both have three as a factor. We can divide both numbers by three. So let’s do that. Three divided by three equals one and six divided by three equals two. Three-sixths is equivalent to one-half. And so, we can say one-half of the shape is shaded. Just to prove that the two fractions are equivalent, here is one-half and here is three-sixths. The shaded part is the same size.
To find the answer, we first counted the number of parts and then the number of those parts that were shaded to give a fraction three-sixths. We then simplified the fraction by dividing both the numerator and the denominator by a factor that they had in common. And by doing this, we found an equivalent fraction. The fraction of our hexagon that’s shaded is one-half.