Question Video: Finding the Multiplicative Inverse of a Mixed Number Mathematics • 6th Grade

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 𝑎 over 𝑏, its reciprocal is 𝑏 over 𝑎 because 𝑎 over 𝑏 times 𝑏 over 𝑎 equals one. But negative four and one-fourth is not in the form 𝑎 over 𝑏. 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 what’s 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.