Which of the following addition sentences describes the figure shown? One-sixth plus two-thirds equals five-sevenths, one-seventh plus one-half equals five-sixths, one-sixth plus two-thirds equals five-sixths, one-sixth plus two-thirds equals one-third, or two-sevenths plus three-quarters equals six-sevenths?
This figure, or diagram, is a really interesting way of showing an addition of two fractions. But what are the two fractions? And what’s the answer? We’re given five possible addition sentences. One of them describes the figure. Let’s look at the diagram carefully, understand what’s going on, and then look for the addition sentence that describes it.
The first strip in our figure represents the first number in the calculation. This is the fraction that we’re starting with. How many equal parts has the strip been divided into? One, two, three, four, five, six. So, the first shaded fraction shows a number of sixths. How many parts have been shaded? Only one out of six have been shaded. And so, our first fraction in the addition is one-sixth, one out of six.
We can look across at our possible answers now. Which answers show one-sixth as the first number? We can see that the correct answer must be this one, this one, or this one. All three addition sentences begin with the fraction one-sixth.
Now let’s look at our second strip. We can see that it’s shifted slightly along to the right to show that it’s been added to one-sixth. But what fraction does the strip show? First of all, how many equal parts has the strip been divided into? One, two, three. Our second fraction shows a number of thirds. The strip has been split into three equal parts. And we can see that two out of these three equal parts are shaded. So, the fraction that it shows is two-thirds.
By putting these two strips next to each other, we’ve added one-sixth and two-thirds. Let’s look across at our possible answers. Can we get rid of any? No, all three say one-sixth plus two-thirds. The difference is in their answers. We need to identify what the answer is to the addition, and then we’ll be able to find the correct addition sentence.
We can see that by adding the fraction in the first strip and the second strip together, we get the fraction in the final strip. But how many equal parts has it been split into? If we compare it to the top strip, we can see that it’s been split into the same number of parts.
There are six equal parts, which means the answer is going to be a number of sixths. But how many sixths have been shaded? We can see that only one part has not been shaded. That this must mean that five out of six equal parts have been shaded, or five-sixths.
The answer to our addition is five-sixths. And so, we’ve identified the correct addition sentence. This figure is a really interesting way of showing how to add two fractions together. And the addition that it shows is one-sixth plus two-thirds equals five-sixths.