To get -3.2 into a fraction, we will multiply the number by [tex]\frac{10}{10}[/tex] to get:
[tex]-3.2 \cdot \dfrac{10}{10}[/tex]
[tex]- \dfrac{32}{10} = - \dfrac{17}{5}[/tex]
-3.2 = -17/5
To get -1 7/8 into the fraction form of [tex]\frac{a}{b}[/tex], we will multiply the 1 by the denominator 8 to get 8, which we will add to the numerator of 7 to get a final fraction of -15/8. This is represented as:
[tex]-1 \dfrac{7}{8} = - \dfrac{(1 \cdot 8) + 7}{8} = -\dfrac{15}{8}[/tex]
-5/6 is already in the form a/b.
To get 3 4/5 into the fraction form a/b, we will do the same process as the first mixed fraction. First, multiply the whole number by the denominator to get 15, which we will then add to the numerator of 4 to get the fraction 19/5. This is represented as:
[tex]3 \dfrac{4}{5} = \dfrac{(3 \cdot 5) + 4}{5} = \dfrac{19}{5}[/tex]
To summarize, our four numbers are now -17/5, -15/8, -5/6, and 19/5. -17/5 is the smallest, because its numerator is over 3 times the value of the denominator, but it is negative. -15/8 is the next smallest, because its numerator is around 2 times the size of the denominator, but it is negative. -5/6 is the next smallest, because it is negative and its numerator is less than its denominator. 19/5 is the biggest because its numerator is almost 4 times the value of the denominator.
Thus, the order (greatest to least) would be 19/5, -5/6, -15/8, -17/5, or 3 4/5, -5/6, -1 7/8, -3.2.
