Express the percentage that represents the colored parts of the given figure.
We can answer this question in a few different ways. Let’s start by finding the fraction of the shape that’s colored and then work out that as a percentage. Here we have that the fraction that’s colored is six over eight, because there’s six colored-in sections and there’s eight sections in total.
We can then simplify this fraction by dividing the numerator and the denominator by the same number. And since two goes into six and two also goes into eight, we can divide by two, giving us the fraction three-quarters or three over four.
So now we know that three-quarters of the shape is colored. We need to work out three-quarters as a percentage. And to find a fraction as a percentage, we multiply it by 100. And since three times 100 is 300, this will give us 300 over four. Since 300 over four is the same as 300 divided by four, then we calculate that using a short division method, which gives us the answer 75. And so the percentage here is 75 percent.
In our second method, we’re going to take a look at finding the percentage of one section. We know that since there’s eight pieces in total, then each piece is the same as one out of eight or one-eighth as a fraction. So to change one-eighth to a percentage, we’re going to use a similar method to the one we did in the first method. And we’re going to multiply one-eighth by 100, giving us 100 over eight.
So we’re going to calculate 100 divided by eight using a short division method. Let’s have a look at the calculation in this case. So here we have one divided by eight, which we can’t do. So let’s try 10 divided by eight, which will give us one and a remainder of two. Then we have 20 divided by eight, which gives us two and a remainder of four. But we can’t let this four by itself. So we put a decimal point and a zero. And now we have 40 divided by eight, which gives us five. And so we carry the decimal point up above as well. So 100 divided by eight is 12.5.
So now we know that each piece of our diagram is equal to 12.5 percent. We now need to multiply 12.5 by six since there are six colored pieces. To calculate 12.5 times six, we remove the decimal point from 12.5 and we multiply 125 by six, which will give us 750. And then since there’s one decimal place value in our values, 12.5, this means that there’ll be one decimal place value in our answer, giving us 75.0, which is 75. And so either of our methods will give us the answer 75 percent for the percentage that’s colored.