Video Transcript
Calculate four-fifths divided by
three-quarters.
One method we have to divide
fractions is to create equivalent fractions with a common denominator and then
simply divide the numerators. Now, whilst we don’t need to find
the least common denominator, it does ensure that there’ll be minimal simplifying at
the other end. So what is the common denominator
of our two fractions? Well, the least common multiple of
five and four is 20. So that’s the denominator we’re
going to use. So how do we convert from fifths
into twentieths? Well, to get from five to 20, we
multiply by four. To create an equivalent fraction,
we must do the same to the numerator. So four times four is 16, meaning
four-fifths is equivalent to sixteen twentieths.
We repeat this process for
three-quarters. To turn quarters into twentieths,
we multiply by five. And so we have to do the same to
our numerator. We’re going to multiply three by
five, which is 15, meaning three-quarters is equivalent. It’s the same as fifteen
twentieths. So we’re dividing sixteen
twentieths by fifteen twentieths. Once their denominators are the
same, we’re able simply to divide the numerators. So we’re going to divide 16 by
15. Of course, the fraction line
actually means divide. So 16 divided by 15 can be written
as 16 over 15.
And since this is an improper
fraction — in other words, the numerator is greater than the denominator — we’re
going to convert it into a mixed number. We ask ourselves how many 15s make
16? Well, it’s one remainder one. This means the integer part is one
and the numerator of our fraction is also one. The denominator remains unchanged,
so 16 over 15 is equivalent to one and one fifteenth. And so four-fifths divided by
three-quarters is one and one fifteenth. But this isn’t the only method we
have to divide fractions.
To divide by a fraction, we can
multiply by the reciprocal of that fraction. So the first fraction remains
unchanged. And instead of dividing, we’re
timesing. Reciprocal means one over. But if we already have it in
fraction form, we simply invert it. We switch the numerators and
denominators. So the reciprocal of three-quarters
is four-thirds. And the sum becomes four-fifths
times four-thirds.
But why does this work? Well, what we’re doing is dividing
by the numerator of our second fraction to get a unit fraction and then multiplying
by the denominator to get the whole. And the beauty of this method is we
already know how to multiply fractions. We simply multiply their numerators
and then separately multiply their denominators. So this becomes four times four
over five times three, which is sixteen fifteenths. Once again, we know that this
becomes one and one fifteenth. So we have our alternative method
for dividing four-fifths by three-quarters. Now, both of these methods are
equally valid.
