Answer:
7/12 sq yd
Explanation:
The area of a rectangle (which includes a rug) is given by the formula:
Area = Length x Width
We are given that the rug is 1/2 yard wide and 7/6 yards long. So, we can substitute these values into the formula:
Area = (7/6) x (1/2)
To multiply these fractions, we need to find a common denominator. The least common multiple of 6 and 2 is 6, so we can convert both fractions to have a denominator of 6:
Area = (7/6) x (1/2) = (7/6) x (3/3) x (1/2) = 21/36
We can simplify this fraction by dividing the numerator and denominator by their greatest common factor, which is 3:
Area = 21/36 = (21 ÷ 3) / (36 ÷ 3) = 7/12
Therefore, the area of the rug is 7/12 square yards.