What fraction of figure a is shaded? What fraction of figure b is shaded? Which figure has a greater fraction shaded?
We’re given two images that accompany this question, and they’re labeled a and b. Now, both figure a and figure b are squares. How do we know this? Well, both shapes are split into smaller squares. And this helps us to see how large they are. Both shapes are five squares tall and both shapes are five squares wide. Because the shapes are as tall as they are wide, we know that they must be squares. Now, we can use these measurements to help us answer the question. We’ll see how in a second.
There are three parts to our problem and the first part asks us what fraction of figure a is shaded. And we know a fraction is made up of two numbers with a small line in between. The bottom number, the denominator, shows the total number of equal parts that the whole shape has been split into. Let’s complete the denominator first.
How many parts has our large square in figure a being split into? This is where our measurements come in handy. We said that our shape was five squares tall and five squares wide. In other words, it has five rows, and each row contains five squares. And we know that five lots of five equals 25. The total number of equal parts that our large square has been split into is 25.
To complete our fraction, we need to write the numerator or the top number. And the numerator always shows the number of parts that we’re talking about. In this case, we’re talking about the number of shaded parts. In other words, how many parts out of 25 parts are shaded? So, to find our numerator, let’s count the number of shaded parts. One, two, three, four, five, six, seven, eight, nine, 10, 11, 12. 12 parts out of a possible 25 parts are shaded. And we’d read this fraction as twelve twenty-fifths or 12 out of 25.
The second part of our problem also asked us which fraction is shaded. But this time we’re talking about figure b. Because the square in figure b is the same size as the square in figure a, part of our work has already been done for us. We know that the denominator for the fraction is going to be 25 again. Five lots of five small squares. But how many squares out of our 25 squares are shaded this time? What’s the numerator going to be?
This time, the way the squares have been shaded, they’re in blocks, so they’re a little bit easier to count. We can see a block of three here and then another block of three going downwards. So, that’s six altogether. And then, we have a block of five going down the side, and six and five makes 11. The fraction of figure b that’s shaded is eleven twenty-fifths or 11 out of 25.
The final part of our problem asks us which figure has a greater fraction shaded. In other words, which is larger, twelve twenty-fifths or eleven twenty-fifths? It might be tricky to look at both diagrams and try to see which one has a greater fraction shaded because the squares that are colored in are different squares in both cases. It’s quite difficult to compare them. But we can compare the fractions. Both fractions have a denominator of 25.
In other words, the square, the large square around the outside, has been split in both cases into 25 smaller squares. This means that the parts of the large squares being split into are all the same size. So, we can just compare the numerators to find the answer. 12 is one more than 11. So, twelve twenty-fifths is a greater fraction than eleven twenty-fifths. One more square has been shaded, hasn’t it?
And so, we can say the figure that has the greater fraction shaded is figure a. The fraction of figure a that’s been shaded is twelve twenty-fifths. The fraction of figure b that’s been shaded is eleven twenty-fifths. And so, we know the figure that has the greater fraction shaded is figure a. Twelve twenty-fifths is greater than eleven twenty-fifths.