Video Transcript
Evaluate negative five-halves divided by negative two-thirds.
We recall that when we are dividing two fractions, this is the same as multiplying the first fraction by the reciprocal of the second fraction. This is often remembered as KCF: keep it, change it, flip it. We keep the first fraction the same, we change the division to a multiplication, and we flip the second fraction. This means that, in our question, we need to multiply negative five-halves by negative three-halves. The reciprocal of two-thirds is three-halves. When multiplying two fractions, we simply multiply the numerators and then multiply the denominators separately.
We also recall that multiplying a negative number by a negative number gives a positive answer. As we are multiplying two negative fractions, our answer will be positive. Five multiplied by three is equal to 15, and two multiplied by two is equal to four. Negative five-halves multiplied by negative three-halves is therefore equal to fifteen-quarters or 15 over four. This means that the answer to our initial calculation negative five-halves divided by negative two-thirds is also fifteen-quarters.
We could also write our answer as a mixed number. Fifteen-quarters is equal to three and three-quarters. This is because 15 divided by four is equal to three remainder three.
