Answer: 7/6
Explanation:
To simplify the expression (7/9) + (1/6) ÷ (3/7), we need to follow the order of operations and perform the operations from left to right.
1. Division: We start by dividing (1/6) by (3/7). To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
(1/6) ÷ (3/7) = (1/6) * (7/3)
When we multiply the numerators and denominators, we get:
1 * 7 / 6 * 3 = 7/18
2. Addition: Now, we add (7/9) to (7/18). To add fractions, we need to have a common denominator. In this case, the common denominator is 18.
(7/9) + (7/18) = (14/18) + (7/18)
Since the denominators are the same, we can add the numerators directly:
14/18 + 7/18 = 21/18
3. Simplification: To simplify the resulting fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 21 and 18 is 3.
Dividing both the numerator and denominator by 3, we get:
21/18 ÷ 3/3 = 7/6
Therefore, the simplified form of the expression (7/9) + (1/6) ÷ (3/7) is 7/6.