Question

Write the numbers -3.2,-1 7\8,- 5/6 and 3 4/5 in the form a/b, from greatest to least.

Answer 1

To get -3.2 into a fraction, we will multiply the number by
`(10)/(10)` to get:

`-3.2 \cdot (10)/(10)`

`- (32)/(10) = - (17)/(5)`

-3.2 = -17/5

To get -1 7/8 into the fraction form of
`(a)/(b)`, 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:

`-1 (7)/(8) = - ((1 \cdot 8) + 7)/(8) = -(15)/(8)`

-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:

`3 (4)/(5) = ((3 \cdot 5) + 4)/(5) = (19)/(5)`

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.