Let's solve the expression \( \frac{1}{4} + 3 \times \frac{7}{9} - \frac{5}{6} \) step by step:

### Step 1: Multiply \(3 \times \frac{7}{9}\)
\[
3 \times \frac{7}{9} = \frac{3}{1} \times \frac{7}{9} = \frac{21}{9}
\]

### Step 2: Simplify \(\frac{21}{9}\)
\[
\frac{21}{9} = \frac{7}{3}
\]

### Step 3: Rewrite the expression
The expression now becomes:
\[
\frac{1}{4} + \frac{7}{3} - \frac{5}{6}
\]

### Step 4: Find a common denominator
The least common denominator (LCD) of 4, 3, and 6 is 12. Now, rewrite each fraction with denominator 12:

\[
\frac{1}{4} = \frac{3}{12}, \quad \frac{7}{3} = \frac{28}{12}, \quad \frac{5}{6} = \frac{10}{12}
\]

### Step 5: Add and subtract the fractions
Now, add and subtract the fractions:
\[
\frac{3}{12} + \frac{28}{12} - \frac{10}{12} = \frac{3 + 28 - 10}{12} = \frac{21}{12}
\]

### Step 6: Simplify \(\frac{21}{12}\)
\[
\frac{21}{12} = \frac{7}{4}
\]

So, the final result is:
\[
\boxed{\frac{7}{4}} \text{ or } 1.75
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the least common denominator of fractions?
2. What are the rules for adding and subtracting fractions?
3. How can improper fractions be converted to mixed numbers?
4. How do you multiply and divide fractions?
5. What is the process for simplifying fractions?

**Tip:** When working with multiple fractions, always find the least common denominator for easier calculation.

Learn how to solve the expression 1/4 + 3 x 7/9 - 5/6 with this detailed step-by-step guide. This problem covers key arithmetic concepts such as multiplication and addition of fractions, and finding the least common denominator. Suitable for students in Grades 6-8.

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