Final answer:
To find the quotient in simplest form, convert the mixed numbers to improper fractions, divide the fractions, and simplify the result. The quotient in simplest form is 2.
Step-by-step explanation:
To find the quotient in simplest form: 7 1/2 ÷ 3 3/4, we need to convert the mixed numbers to improper fractions and then divide.
Step 1: Convert 7 1/2 to an improper fraction. Multiply the whole number (7) by the denominator (2) and add the numerator (1): 7 * 2 + 1 = 15. The result is 15/2.
Step 2: Convert 3 3/4 to an improper fraction. Multiply the whole number (3) by the denominator (4) and add the numerator (3): 3 * 4 + 3 = 15. The result is 15/4.
Step 3: Divide the two fractions. Invert the second fraction (15/4) to find its reciprocal: 4/15. Multiply the first fraction (15/2) by the reciprocal (4/15): (15/2) * (4/15) = 60/30.
Step 4: Simplify the fraction. Both the numerator (60) and denominator (30) have a common factor of 30. Divide both by 30 to get the simplified fraction: 60/30 ÷ 30/30 = 2/1.
The quotient in simplest form is 2.