Final answer:
The quotient of 3 1/2 ÷ 2 1/4 is 14/9.
Step-by-step explanation:
To divide mixed numbers, we need to convert them into improper fractions.
First, we convert 3 1/2 to an improper fraction: 3 1/2 = 7/2.
Next, we convert 2 1/4 to an improper fraction: 2 1/4 = 9/4.
Now, we can divide the fractions:
7/2 ÷ 9/4
= 7/2 × 4/9
= (7 × 4) / (2 × 9)
= 28/18.
However, we can simplify this fraction by finding the greatest common factor (GCF) of the numerator and denominator, which is 2.
Dividing both the numerator and denominator by 2 gives us: 28/18 = 14/9.
So, the quotient of 3 1/2 ÷ 2 1/4 is 14/9.