Final answer:
The quotient of 3 3/4 divided by 2 is 1 7/8, which is found by converting the mixed number to an improper fraction, multiplying by the reciprocal of 2, and then simplifying the result.
Step-by-step explanation:
To find the quotient of 3 3/4 ÷ 2, you first need to express the mixed number 3 3/4 as an improper fraction. Since there are 4 fourths in a whole, you have 3 × 4 (12) fourths from the whole numbers plus the 3 fourths from the fractional part, totaling 15 fourths (15/4). To divide by 2, you can multiply by the reciprocal of 2, which is 1/2. So, 15/4 ÷ 2 is the same as 15/4 × 1/2.
Multiplying these together, you have (15 × 1) / (4 × 2) which equals 15/8. Since 15/8 is an improper fraction, you can convert it back to a mixed number. There are 8 eighths in a whole, and 15 eighths is 1 whole plus 7 eighths left over. Therefore, the final quotient is 1 7/8.