6/23- 1/3 ×1/3/4+1/4 - 6>0

To solve this expression, we need to follow the order of operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

Let's break down the expression step by step:

Step 1: Simplify the division of fractions. 1/3 × 1/3 = (1 × 1) / (3 × 3) = 1/9

Step 2: Divide numerator by denominator and simplify. 6/23 - (1/9 / 4) + 1/4 - 6 > 0

Step 3: Simplify the division in parentheses. (1/9 / 4) = (1/9) × (1/4) = 1/36

Step 4: Combine like terms. 6/23 - 1/36 + 1/4 - 6 > 0

Step 5: Find the common denominator for fractions. The common denominator is 36. We need to convert all fractions to have a denominator of 36.

Multiplying 6/23 by 36/36: (6/23) × (36/36) = 216/828

Multiplying 1/36 by 9/9: (1/36) × (9/9) = 9/324

Multiplying 1/4 by 9/9: (1/4) × (9/9) = 9/36

Now the expression becomes: 216/828 - 9/324 + 9/36 - 6 > 0

Step 6: Perform the calculation. 216/828 - 9/324 + 9/36 - 6 ≈ 0.261 - 0.028 + 0.25 - 6 ≈ -5.517

Step 7: Compare with zero. -5.517 > 0

Therefore, the statement 6/23 - 1/3 × 1/3/4 + 1/4 - 6 > 0 is FALSE.