Video Transcript
Find the multiplicative inverse of
negative four and one-fourth.
What do we know about
multiplicative inverse? Multiplicative inverse is another
word for reciprocal. And for the fraction π over π,
its reciprocal is π over π because π over π times π over π equals one. But negative four and one-fourth is
not in the form π over π. Negative four and one-fourth is a
mixed number. Before we can find the
multiplicative inverse, we need to take this mixed number and write it as an
improper fraction.
The first thing we need to do is
bring down this negative as this whole mixed number is negative. After that, we multiply the integer
piece, the whole number piece, four, by the denominator four. And then, we add whatβs in the
numerator. Again, we need to be really careful
here to notice that the negative applies to the entire numerator. And the denominator will be
whatever the denominator of the mixed number was. Four times four is 16. 16 plus one is 17. So we have negative 17 over
four. The mixed number negative four and
one-fourth can be rewritten as the improper fraction negative 17 over four.
To find its multiplicative inverse,
we flip the numerator and the denominator so that we have four over negative 17. If we multiply negative 17 times
four, we get negative 68. And if we multiply four times
negative 17, we get negative 68. And negative 68 over negative 68 is
the same thing as one, which means the multiplicative inverse of negative four and
one-fourth is equal to four over negative 17. We know a negative times a negative
equals a positive. What we see here is that negative
numbers have negative reciprocals. We usually keep the negative symbol
in the numerator. So our final answer for the
multiplicative inverse of negative four and one-fourth can be written as negative
four over 17.