Video Transcript
Work out three and one-third
divided by two and one-half.
We have two methods for dividing
fractions. But before we perform either of
these, we need to spot that we’ve been given a problem involving mixed numbers. And so before we can perform the
division, we need to convert the mixed numbers into improper fractions. Let’s begin with three and
one-third. We multiply the integer part by the
denominator of the fraction. Three times three is nine. We then add this value to the
numerator of the fraction. So nine plus one is 10. This forms the numerator part of
our improper fraction, and the denominator remains unchanged. So three and one-thirds is equal to
ten-thirds.
We’ll repeat this process for two
and a half. This time, the integer part
multiplied by the denominator is two times two, which is four. And adding this to our numerator
gives us five. So two and a half is equal to five
over two. We’ll now consider one method we
have for dividing fractions. And that is to find a common
denominator. Once we’ve created equivalent
fractions with that denominator, we simply divide the numerator. So what’s the least common
denominator for our two fractions? Well, the least common multiple of
three and two is six. So we create equivalent fractions
by making a denominator of six.
With our first fraction to achieve
this, we multiply by two. So we do the same to our
numerator. This means our first fraction,
ten-thirds, becomes 20 over six. With our second fraction, we need
to multiply the numerator and denominator by three. And so five over two is equivalent
to 15 over six. Now that our denominators are
equal, to divide, we simply divide the numerators. 20 divided by 15 we can write as 20
over 15. We’ll simplify this fraction by
dividing through by a common factor of five to give us four-thirds.
Now, of course, since the question
was given to us as a pair of mixed numbers, we should convert this back. Four divided by three is one
remainder one. The denominator remains
unchanged. So we see that three and one-third
divided by two and a half is one and one-third. Let’s now consider the alternative
method. To divide by a fraction, we
multiply by the reciprocal of that fraction. Informally, this has the name keep,
change, flip, though this name can be quite unpopular. To divide by five over two, we
multiply by the reciprocal of five over two. The reciprocal of a fraction
involves inverting the two numbers by switching the numerator with the
denominator.
So we’re going to multiply by two
over five. We keep the first fraction the
same, we change the divides to a multiply, and we flip the second fraction. That’s a nice way of saying, “find
the reciprocal.” Then what we could do is multiply
the two numerators and multiply the two denominators, 10 times two over three times
five. Alternatively, we can perform a
little time-saver. And notice that we have a common
factor of five diagonally across our sum. And so let’s divide through by this
factor. And we get two-thirds multiplied by
two over one. Now, when we multiply the
numerators and then the denominators, we get two times two over three times one
which, once again, gives us four-thirds. Three and one-third divided by two
and a half is one and one-third.
