Final answer:
To find −3 1/5÷1 3/4 and express it as a mixed number, first convert to improper fractions, then multiply by the reciprocal, simplify, and convert back to a mixed number, resulting in −1 29/35 in its simplest form.
Step-by-step explanation:
To find −3 1/5÷1 3/4 and write the answer as a mixed number in simplest form, we first convert the mixed numbers to improper fractions. The fraction for −3 1/5 is −16/5 because -3×5 = -15 and -15+1 = -16. The fraction for 1 3/4 is 7/4 because 1×4 = 4 and 4+3 = 7. Next, we divide the two fractions, which is the same as multiplying the first fraction by the reciprocal of the second fraction. Therefore, −16/5÷7/4 turns into −16/5×4/7.
When we multiply the numerators and the denominators separately, we get −64/35. To simplify the fraction, we find the greatest common divisor that both 64 and 35 have in common is 1, so the fraction is already in its simplest form. Finally, to convert −64/35 back into a mixed number, we divide 64 by 35, which is 1 with a remainder of 29. Therefore, the mixed number is −1 29/35.