6/23- 1/3 ×1/3/4+1/4 - 6>0

To solve this expression, we'll follow the order of operations (PEMDAS/BODMAS):

First, let's simplify the fraction 1/3 × 1/3/4. To multiply fractions, we multiply the numerators together and the denominators together: 1/3 × 1/3/4 = 1/3 × (1/3 ÷ 4)

Next, we'll divide the fraction 1/3 by 4: 1/3 ÷ 4 = 1/3 × 1/4 = 1/12

Now we can substitute this value back into the expression: 6/23 - 1/12 + 1/4 - 6 > 0

Next, we'll add the fractions: 6/23 - 1/12 + 1/4 = ((6/23) × (12/12)) - (1/12) + (3/12) = (72/276) - (1/12) + (3/12) = (72/276) + (2/12) = (36/138) + (23/138) = 59/138

So the expression becomes: 59/138 - 6 > 0

To simplify further, we'll subtract 6 from 59/138: 59/138 - 6 = 59/138 - (6 × 138/138) = 59/138 - 828/138 = (59 - 828)/138 = -769/138

Now the expression becomes: -769/138 > 0

To determine if this is true or false, we'll simplify further by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 1: -769/138 is already in its simplest form.

Therefore, the expression -769/138 > 0 is false.