Evaluate negative six divided by three-eighths giving the answer in its simplest form.
We begin by recalling that any integer or whole number can be written as this number over one. Therefore, negative six is equal to negative six over one. When dividing two fractions, we multiply the first fraction by the reciprocal of the second. This is often referred to as KCF. We keep the first fraction the same, we change the division sign to a multiplication, and we flip the second fraction. This means that we need to multiply negative six over one by eight over three or eight-thirds.
When multiplying two fractions, we simply multiply the numerators and then separately multiply the denominators. We also recall that when multiplying a negative number by a positive number, we get a negative answer. In this question, we are multiplying a negative fraction by a positive one, so our answer will be negative. Six multiplied by eight is 48, and one multiplied by three is three. This means that negative six over one multiplied by eight over three is negative 48 over three.
48 is divisible exactly by three. This is equal to 16 as four divided by three is one remainder one and 18 divided by three is six. Negative 48 over three is, therefore, equal to negative 16.
We could have calculated this a different way by cross simplifying or cross canceling in our line above. Both six and three are divisible by three. So, this would leave us with negative two over one multiplied by eight over one. As two multiplied by eight is 16 and one multiplied by one is one, we would also get the answer of negative 16.
In its simplest form, negative six divided by three-eighths is negative 16.