To find the quotient when you divide -2 3/5 by 4/5, you can follow these steps:
Step 1: Convert the mixed number -2 3/5 into an improper fraction.
To do this, multiply the whole number (-2) by the denominator of the fraction (5), and then add the numerator (3). This gives you (-2 × 5) + 3 = -10 + 3 = -7.
So, the improper fraction is -7/5.
Step 2: Divide the numerator of the dividend (-7/5) by the numerator of the divisor (4/5) and then multiply it by the reciprocal of the divisor.
The reciprocal of 4/5 is 5/4. Therefore, you need to multiply -7/5 by 5/4.
Step 3: Multiply the numerators together and the denominators together.
(-7/5) * (5/4) = ((-7*5) / (5*4)) = -35/20.
Step 4: Simplify the fraction, if possible.
The fraction -35/20 can be simplified by finding the greatest common divisor (GCD) of the numerator (-35) and the denominator (20), which is 5.
Dividing both the numerator and the denominator by 5, we get:
-35/20 = (-35 ÷ 5) / (20 ÷ 5) = -7/4.
Therefore, the quotient when you divide -2 3/5 by 4/5 is -7/4.