Work out one and one-quarter
multiplied by one and two-thirds.
Here, we have a pair of mixed
numbers. Now, we know that, to multiply
proper fractions, in other words, fractions between zero and one, we multiply the
numerators together and then separately multiply the denominators. Now, in fact, this holds for
improper fractions. And so to be able to find the
product of a mixed number and any other fraction, we first begin by converting that
mixed number into an improper fraction. So let’s begin by converting one
and one-quarter into an improper fraction.
We begin by multiplying the integer
part, that’s the whole number, by the denominator of the fraction. One times four is four. We then add this number to the
numerator of our fraction. Four plus one is equal to five. This forms the numerator of the
fraction; the denominator remains unchanged. So one and one-quarter is the same
as five-quarters. Let’s do this again with one and
two-thirds. Once again, we multiply the integer
part by the denominator of the fraction; one times three is three. And then we take this number and we
add it to the numerator of our fraction; three plus two is five.
Again, five forms the numerator of
our improper fraction, and the denominator remains unchanged. So one and two-thirds is
five-thirds. And so to multiply one and a
quarter by one and two-thirds, we’re going to multiply five-quarters by
five-thirds. We know, of course, that to
multiply fractions, we simply multiply their numerators together and then multiply
their denominators together. So here, that’s five times five
over four times three, which gives us 25 over 12. Now, of course, we were given a
question in mixed numbers, so we’re not quite finished.
We’re going to need to convert
twenty-five twelfths back into a mixed number. And to do so, we essentially
perform a reverse process to changing a number from a mixed number into an improper
fraction. We divide our numerator by our
denominator. We ask ourselves how many 12s make
25? And this is one of the very few
times we use remainders. We say that 25 divided by 12 is two
remainder one. Two forms the integer part of our
answer; it’s the whole number. And one is the numerator of the
fraction. The denominator remains unchanged,
so it’s 12. And so we see that one and a
quarter times one and two-thirds is two and one twelfth.