To find the quotient of 35 ÷ 3 4/7 in simplest form, you can follow these steps:
Step 1: Convert the mixed number 3 4/7 to an improper fraction.
3 4/7 = (7 * 3 + 4) / 7 = (21 + 4) / 7 = 25/7
Step 2: Now, you have the division problem 35 ÷ (25/7). To divide by a fraction, you can multiply by its reciprocal.
35 ÷ (25/7) = 35 * (7/25)
Step 3: Multiply the whole number 35 by the fraction (7/25).
35 * (7/25) = (35 * 7) / 25 = 245/25
Step 4: Simplify the fraction by finding a common factor for the numerator and denominator. In this case, both 245 and 25 can be divided by 5.
245/25 = (245 ÷ 5) / (25 ÷ 5) = 49/5
So, the quotient of 35 ÷ 3 4/7 in simplest form is 49/5.