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
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
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.