Final answer:
To perform the operation 8/9 ÷3/7, we change the division to multiplication by the reciprocal of 3/7, resulting in the expression 8/9 × 7/3, which simplifies to 56/27. This fraction does not have any common factors and is thus already in its simplest form.
Step-by-step explanation:
To perform the operation and reduce the answer fully for the expression 8/9 ÷3/7, we use the concept that dividing by a fraction is the same as multiplying by its reciprocal. Thus, the given expression becomes 8/9 × 7/3 when we find the reciprocal of 3/7. The next step is to multiply the numerators (top numbers) together and the denominators (bottom numbers) together. So we have:
Numerator: 8 × 7 = 56
Denominator: 9 × 3 = 27
Therefore, the result is 56/27. To reduce the answer, we look for any common factors between the numerator and the denominator. In this case, there are none, so the fraction 56/27 is already in its simplest form.
We always want to eliminate terms wherever possible to simplify the algebra and check the answer to see if it is reasonable. Since 56 and 27 do not have common factors besides 1, we can confidently say our answer is reduced fully.