Final answer:
To divide 3 3/8 by 9, first convert the mixed number to an improper fraction (27/8), then multiply by the reciprocal of 9 (1/9) to get 27/72, and finally simplify to 3/8, which is the quotient in lowest terms.
Step-by-step explanation:
To divide the mixed number 3 3/8 by 9 and write the quotient in lowest terms, we need to follow a few steps. First, convert the mixed number into an improper fraction. Since there are 8 eighths in a whole, and we have 3 whole numbers each consisting of 8 eighths plus the additional 3 eighths, our improper fraction will be (3×8)+3 over 8, which is 27/8.
Next, dividing by 9 is equivalent to multiplying by its reciprocal, which is 1/9. Now you are multiplying fractions, so multiply the numerators and denominators across.
So the equation becomes (27/8) × (1/9). Multiplying the numerators, 27 and 1, gives us 27, and multiplying the denominators, 8 and 9, gives us 72.
Thus, we have a new fraction: 27/72. To simplify it to lowest terms, we can divide both the numerator and the denominator by their greatest common divisor, which in this case is 9. This simplification gives us 27÷9 over 72÷9, which is 3/8. The quotient in lowest terms is 3/8.