Final answer:
To find the quotient of 3 1/2 ÷ 2 3/4, convert each mixed number to an improper fraction, flip the second and change the division to multiplication, then multiply and simplify. The final answer is 14/11 or 1 3/11.
Step-by-step explanation:
To find the quotient of 3 1/2 ÷ 2 3/4, first, convert each mixed number to an improper fraction. For 3 1/2, we multiply the whole number 3 by the denominator 2 and add the numerator 1 to get 7/2. For 2 3/4, we multiply the whole number 2 by the denominator 4 and add the numerator 3 to get 11/4.
Next, flip the second fraction (the divisor) and change the division operation to multiplication (the reciprocal).
3 1/2 ÷ 2 3/4 becomes 7/2 × 4/11
Now, multiply the numerators and the denominators separately:
(7 × 4)/(2 × 11) = 28/22
Simplify the resulting fraction, if possible. In this case, 28/22 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2. The simplified answer is 14/11 or 1 3/11.