Final answer:
To solve the expression 6/7-:2(2)/5, we convert the division into a multiplication by the reciprocal, multiply numerators, multiply denominators, and simplify the result to get 15/7.
Step-by-step explanation:
The expression given in the question is 6/7 divided by 2/5. To solve this, we first convert the division into a multiplication by the reciprocal of 2/5, which is 5/2. Therefore, the new expression becomes 6/7 multiplied by 5/2. Now, we multiply the numerators together and multiply the denominators together. This gives us (6×5)/(7×2), which equals 30/14. This fraction can be simplified by dividing both the numerator and the denominator by the greatest common factor, which is 2. After simplifying, we are left with 15/7 as the final answer in its simplest form.
The process involves understanding that the division of fractions can be converted to multiplication by the reciprocal, and that when multiplying fractions, we multiply numerators with numerators and denominators with denominators. We must always strive to simplify the resulting fraction to its simplest form to find the most accurate and simplified solution. Common denominators are not needed in this scenario since we are dealing with multiplication, not addition or subtraction of fractions.
Finally, after simplifying the fraction, it is important to eliminate terms wherever possible to simplify the algebra and check the answer for reasonableness.