Video: Identifying the Model That Represents the Result of Adding Two Fractions

While walking her dog, Olivia walked 1/3 of a mile to the park and then 1/9 of a mile inside it. Given that each of the strips below represents 1 mile, which of the strips shows the total number of miles Olivia walked?

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Video Transcript

While walking her dog, Olivia walked one-third of a mile to the park and then one-ninth of a mile inside it. Given that each of the strips below represents one mile, which of the strips shows the total number of miles Olivia walked?

In this problem, we’re told two distances that Olivia walked whilst walking her dog. The first distance we’re given is one-third of a mile. That’s the distance she walked to the park. And then, we’re also told that she walked one-ninth of a mile inside it. So, to calculate the total number of miles that Olivia walked, we need to add one-third and one-ninth together.

Now, we’re also told that each of the strips represents one mile. But most of the strips only have a fraction coloured in. To begin with, it might be helpful if we write down which fraction has been coloured in. This will help us identify the answer at the end. The first strip contains nine equal parts, and we can see that they’ve all been coloured in. So, we know this represents one whole, or one mile.

Our second strip has also been divided into ninths, but this time only four of them are shaded. This strip represents four-ninths of a mile. Another strip that shows ninths is the third strip. This time only three of them are shaded. This one represents three-ninths of a mile. Our next strip has been divided into six equal parts. Each part is worth one-sixth of a mile. But only one of them has been coloured in. So, the whole strip represents one-sixth of a mile.

Our final strip contains three shaded parts out of a possible eight. And three out of eight equals three-eighths of a mile. So, now, we’ve worked out what the shaded part on each strip shows, let’s calculate the answer to our addition. Hopefully, it will equal one of the strips. Now, at the moment, it’s going to be tricky to add our two fractions together. Can you see why?

They have different denominators; we’re dealing with thirds and ninths. And if we want to add or subtract fractions together, we really want them to have the same denominator. So, why don’t we take one-third and convert it so that we find an equivalent fraction in ninths. Then, both fractions will be in ninths, so we can add them together. So, what happens to the denominator if we want to convert it from thirds into ninths?

Well, three times three equals nine. So, we multiply the denominator by three. And if we want to keep the fraction having the same value, and to be equivalent, we need to also multiply the numerator by three too. One times three equals three. So, one-third is actually the same as three-ninths. Let’s write out our addition again, one-third, which we’re now going to write as three-ninths, plus one-ninth. Now, it’s much easier to find out the total number of miles that Olivia walked.

Three-ninths plus one-ninth equal four-ninths. And because we spent time at the start working out the value of each strip, we can see straightaway which strip represents four-ninths of a mile. To find the answer, we knew we needed to add one-third and one-ninth of a mile together. But we knew we could only do this if we converted one-third into ninths so that both fractions were written in ninths. We could then add them together easily.

We worked out that one-third is equal to three-ninths. Then, we just added three-ninths and one-ninth together to get the answer four-ninths. The strip that shows the total number of miles that Olivia walked is the one that is split into nine equal parts where four of those nine parts, or four-ninths, are shaded.

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