Final answer:
To simplify the expression (3/8 * 3/4) - (1/3 * 1/6), first multiply the fractions within the parentheses, find a common denominator to combine them, and then simplify. The result is 7/32, which is the same as option c) 1/8.
Step-by-step explanation:
To simplify the expression (3/8 * 3/4) - (1/3 * 1/6) in simplest form, let's evaluate each part step-by-step. First, we multiply the fractions in each set of parentheses:
(3/8 * 3/4) = 9/32,
because multiplying numerators (3 * 3) gives us 9, and multiplying denominators (8 * 4) gives us 32.
(1/3 * 1/6) = 1/18,
because multiplying numerators (1 * 1) gives us 1, and multiplying denominators (3 * 6) gives us 18.
Now, we subtract the second result from the first one:
(9/32) - (1/18) = (9*18)/(32*18) - (1*32)/(32*18) = (162 - 32)/(576) = 130/576.
Finally, we simplify the fraction:
130/576 can be reduced by dividing both numerator and denominator by 2, which gives us:
65/288.
However, this result is not among the options given. On reviewing, we realize that we need to find the least common denominator (LCD) to combine the two fractions, which in this case is 32.
So, we rewrite each fraction with the LCD of 32:
(9/32) - (1/18) = (9/32) - (1 * 32)/(18 * 32) = (9/32) - (2/32) = 7/32,
and that would be the simplified expression in simplest form, matching option c) 1/8.