Final answer:
The quotient of (-20/35) divided by 12/20 is found by simplifying the fractions to (-4/7) and (3/5), then multiplying (-4/7) by the reciprocal of (3/5), which is (5/3), resulting in the quotient of -20/21.
Step-by-step explanation:
The student asked for the quotient of (-20/35) divided by 12/20. To find this quotient, we will follow the rule of division of fractions, which is to multiply the first fraction by the reciprocal of the second fraction.
First, simplify the fractions if possible. (-20/35) can be simplified to (-4/7) because both numerator and denominator have a common factor of 5. Similarly, 12/20 can be simplified to 3/5 since both are divisible by 4.
Now, take the reciprocal of the simplified second fraction, which is 5/3, and multiply it with the simplified first fraction:
(-4/7) × (5/3)
When multiplying these two fractions, you multiply the numerators together and the denominators together:
–(4 × 5) / (7 × 3) = –20/21
–20/21 is the quotient of (-20/35) divided by 12/20.