Final answer:
To solve the equation 9/14 ÷ 2/3 + 4/7, first find the reciprocal of 2/3 to perform the division, then add the result to 4/7 to get the final answer of 43/28 or 1 15/28 as a mixed number.
Step-by-step explanation:
To solve the equation 9/14 ÷ 2/3 + 4/7, we need to follow the order of operations, which guides us to perform division before addition. We start by dealing with the division part, which can be done by multiplying the first fraction by the reciprocal of the second fraction. Hence:
× (3/2) = (9/14) × (3/2) = (9 × 3) / (14 × 2) = 27/28.
Now, we proceed with the addition part:
27/28 + 4/7 = 27/28 + (4 × 4) / (7 × 4) = 27/28 + 16/28 = (27 + 16) / 28 = 43/28.
The solution to the original equation is:
43/28, which can also be written as 1 15/28 when expressed as a mixed number.