Let's break down the expression step by step:

Given expression:
\[
\frac{1}{3} \left( \frac{1}{3} - \frac{1}{4} \times \frac{3}{4} \right)
\]

### Step 1: Simplify the multiplication inside the parentheses
\[
\frac{1}{4} \times \frac{3}{4} = \frac{3}{16}
\]

Now the expression becomes:
\[
\frac{1}{3} \left( \frac{1}{3} - \frac{3}{16} \right)
\]

### Step 2: Simplify the subtraction inside the parentheses
We need a common denominator to subtract \(\frac{1}{3}\) and \(\frac{3}{16}\). The least common denominator between 3 and 16 is 48.

\[
\frac{1}{3} = \frac{16}{48}, \quad \frac{3}{16} = \frac{9}{48}
\]

So:
\[
\frac{1}{3} - \frac{3}{16} = \frac{16}{48} - \frac{9}{48} = \frac{7}{48}
\]

Now the expression is:
\[
\frac{1}{3} \times \frac{7}{48}
\]

### Step 3: Multiply the fractions
\[
\frac{1}{3} \times \frac{7}{48} = \frac{7}{144}
\]

### Final Answer:
\[
\frac{7}{144}
\]

Would you like a more detailed breakdown, or do you have any questions?

### Related questions:
1. How do you find the least common denominator?
2. Can you explain multiplying fractions in more detail?
3. What is the process for simplifying fractions after subtraction?
4. How do you convert improper fractions to mixed numbers?
5. How do you simplify complex fraction expressions?

**Tip:** Always simplify each part of an expression step by step to avoid errors when working with fractions.

Learn how to solve the fraction expression 1/3(1/3 - 1/4 * 3/4) with a detailed step-by-step breakdown. This solution covers essential fraction concepts, including multiplication, subtraction, and simplification. Suitable for students in Grades 5-7.

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