Rearrange the fractions in order from least to greatest. Show your work

A) 2/3, -3/4, 1/2, -1/3

Start by making all of them have the same denominator. They all multiply to 12 easily, so I will use that. Remember that whatever you do to the top you have to do to the bottom, and vice versa.

Multiply 2/3 by 4/4 to get 8/12

Multiply -3/4 by 3/3 to get -9/12

Multiply 1/2 by 6/6 to get 6/12

Multiply -1/3 by 4/4 to get -4/12

Least to greatest (new): -9/12, -4/12, 6/12, 8/12

Least to greatest (old): -3/4, -1/3, 1/2, 2/3 < this is your answer

C) -9/10, -8/9, -4/5, -41/45

Make them have the same denominator. They all multiply to 90, so I'll use that.

Multiply -9/10 by 9/9 to get -81/90

Multiply -8/9 by 10/10 to get -80/90

Multiply -4/5 by 18/18 to get -72/90

Multiply -41/45 by 2/2 to get -82/90

Least to greatest (new): -82/90, -81/90, -80/90, -72/90

Least to greatest (old): -41/45, -9/10, -8/9, -4/5 < this is your answer

E) -3, -2 2/3, -3 1/6, 2 3/4

Make the mixed numbers into improper fractions by multiplying the whole number with the denominator, and then adding the numerator:

-3 ---> -3/1 (this one's easy)

-2 2/3 ---> -8/3

-3 1/6 ---> -19/6

2 3/4 ---> 11/4 (this one is the only positive one, so it will be the greatest)

Same denominator. I'm using 12.

Multiply -3/1 by 12/12 to get -36/12

Multiply -8/3 by 4/4 to get -32/12

Multiply -19/6 by 2/2 to get -38/12

Multiply 11/4 by 3/3 to get 33/12

Least to greatest (new): -38/12, -36/12, -32/12, 33/12

Least to greatest (old): -3 1/6, -3, -2 2/3, 2 3/4 < this is your answer