Question

Simplify: 1/2 : (7/9 - 1/12).

A) 3/4
B) 4/3
C) 9/14
D) 14/9

Answer 1

Upon simplifying 1/2 : (7/9 - 1/12), we must first find a common denominator for 7/9 and 1/12, which is 36, then subtract and finally multiply by the reciprocal of the resulting fraction. The correct answer is 18/25, which is not among the options listed in the question.

Step-by-step explanation:

To simplify: 1/2 : (7/9 - 1/12), let's first calculate the expression inside the parentheses. We need to find a common denominator to combine the fractions 7/9 and 1/12. The least common multiple of 9 and 12 is 36, so convert these fractions accordingly:

• 7/9 = (7×4)/(9×4) = 28/36
• 1/12 = (1×3)/(12×3) = 3/36

Now we can subtract the second fraction from the first:

• 28/36 - 3/36 = 25/36

Next, we simplify the original expression using the result:

• 1/2 : 25/36

Dividing by a fraction is the same as multiplying by its reciprocal, so:

• 1/2 * 36/25 = 18/25

There is no need to simplify further as 18/25 is already in its simplest form. Therefore, the correct answer is not listed among the options provided in the question (A-D). There might be an error in the provided options.