Video Transcript
Calculate fourteen fifteenths plus
ten-fifths divided by one and two-fifths, giving your answer in its simplest
form.
Remember, when we’re performing
calculations involving mixed numbers, we always begin by turning those mixed numbers
into improper fractions. Here we have one and
two-fifths. And we know that to convert a mixed
number into an improper fraction, we begin by multiplying the integer part by the
denominator. Here that’s one times five, which
is five. We then take that number and we add
it to the numerator of the proper-fraction part. That gives us five plus two, which
is equal to seven. This number forms the numerator
part of our improper fraction. And the denominator is the same as
the denominator in the proper fraction. So one and two-fifths is equal to
seven-fifths.
Now, we’re also going to apply the
order of operations. And we’re going to begin by
performing the calculation inside the pair of parentheses. That’s fourteen fifteenths plus
ten-fifths. Now we might also even notice that
ten-fifths or 10 divided by five is equal to two. And then we might look to create a
mixed number by adding two and fourteen fifteenths. But of course then we will need to
convert that back into an improper fraction.
So let’s recall how we actually add
fractions. We create a common denominator. So what we’re going to do is
multiply both the numerator and denominator of our second fraction by three to give
us a denominator of 15. When we do, we find that ten-fifths
is equivalent to thirty fifteenths. And so we get fourteen fifteenths
plus thirty fifteenths. And of course now we have that
common denominator; we just add the numerators. And we get forty-four
fifteenths. And so our calculation now becomes
forty-four fifteenths divided by seven-fifths.
And we know that there are a couple
of ways that we can divide fractions. Let’s look at the first method. That involves creating a common
denominator. Once again, that denominator is
actually going to be 15. And so we’re going to multiply the
numerator and denominator of our second fraction by three. And so we get forty-four fifteenths
divided by twenty-one fifteenths.
Now that the denominators are
equal, we simply divide the numerators. We can write 44 divided by 21 as 44
over 21. And since we’re asked to give our
answer in its simplest form, we’re going to finally turn this back into a mixed
number. 44 divided by 21 is two with a
remainder of two. So two forms the integer part, and
then another two forms the numerator of the proper-fraction part. The denominator remains unchanged,
so 44 over 21 is two and two twenty-oneths.
Now, of course, we do have one
second method, so we’ll briefly consider that. In the second method, we simply
multiply by the reciprocal of the second fraction, by the divisor. So forty-four fifteenths divided by
seven-fifths is equal to forty-four fifteenths times five-sevenths. Then we could multiply the
numerators and separately multiply the denominators. But we might notice that we can
divide both five and 15 by five. And so now we do 44 times one to
get 44 and three times seven to get 21. And once again we find that
forty-four fifteenths divided by seven-fifths is 44 over 21, which we’ve seen is
equal to two and two over 21.
