Divide: 16/5 / - 2 2/5

(-4) / 3

Step-by-step explanation:

Simplify the following:

16 / (5 ( - (2 + 2/5)))

Put 2 + 2/5 over the common denominator 5. 2 + 2/5 = (5*2) / 5 + 2/5:

16 / (5 ( - (5*2) / 5 + 2/5))

5*2 = 10:

16 / (5 ( - (10/5 + 2/5)))

10/5 + 2/5 = (10 + 2) / 5:

16 / (5 ( - (10 + 2) / 5))

10 + 2 = 12:

(16/5) / (-12/5)

(16/5) / ((12 (-1)) / 5) = 16 / (-12/5*5):

16 / (-12/5*5)

-12*5 = - 60:

16 / ((-60) / 5)

Multiply the numerator of 16 / ((-60) / 5) by the reciprocal of the denominator. 16 / ((-60) / 5) = (16*5) / (-60):

(16*5) / (-60)

5 / (-60) = 5 / (5 (-12)) = 1 / (-12):

16 / (-12)

The gcd of 16 and - 12 is 4, so 16 / (-12) = (4*4) / (4 (-3)) = 4/4*4 / (-3) = 4 / (-3):

4 / (-3)

Multiply numerator and denominator of 4 / (-3) by - 1:

Answer: (-4) / 3

The answer is - 4/3

Step-by-step explanation:

Let's divide 16/5 : 2 2/5, this way:

16/5 : - 2 2/5

16/5 : - 12/5

16/5 * - 5/12

-80/60

Simplifying:

-4/3 (Dividing by 20 in the numerator and in the denominator)

The answer is - 4/3