Ricco plans to dig a trench that is $$ 1 \frac{5}{6} $$ of a yard long. He measures his work and realizes he still has $$ \frac{1}{3} $$ yard to go. How much of the trench has he dug so far? Date omaneuvering the Midale ucc, 2015

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To determine how much of the trench Ricco has dug so far, follow these steps:

1. **Understand the Problem:**
   - **Total planned length of the trench:** $$ 1 \frac{5}{6} $$ yards
   - **Remaining length to dig:** $$ \frac{1}{3} $$ yard
   - **Objective:** Find the length already dug.

2. **Convert Mixed Numbers to Improper Fractions:**
   
   It's easier to perform subtraction with improper fractions.
   
   - $$ 1 \frac{5}{6} $$ yards can be converted to an improper fraction:
     $$
     1 \frac{5}{6} = \frac{6 \times 1 + 5}{6} = \frac{11}{6} \text{ yards}
     $$
   - $$ \frac{1}{3} $$ yard is already an improper fraction.

3. **Subtract the Remaining Length from the Total Length:**
   
   $$
   \text{Length dug} = \text{Total length} - \text{Remaining length}
   $$
   
   $$
   \text{Length dug} = \frac{11}{6} - \frac{1}{3}
   $$
   
4. **Find a Common Denominator:**
   
   The common denominator for 6 and 3 is 6.
   
   - Convert $$ \frac{1}{3} $$ to sixths:
     $$
     \frac{1}{3} = \frac{2}{6}
     $$
   
   - Now, subtract:
     $$
     \frac{11}{6} - \frac{2}{6} = \frac{9}{6}
     $$
   
5. **Simplify the Fraction:**
   
   $$
   \frac{9}{6} = \frac{3 \times 3}{3 \times 2} = \frac{3}{2} = 1 \frac{1}{2}
   $$
   
6. **Conclusion:**
   
   Ricco has dug **$$ 1 \frac{1}{2} $$ yards** of the trench so far.
Ricco has dug $$ 1 \frac{1}{2} $$ yards of the trench so far.

Ricco plans to dig a trench that is of a yard long. He measures his work and realizes he still has
yard to go. How much of the trench has he dug so far?
Date omaneuvering the Midale ucc, 2015

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Ricco plans to dig a trench that is of a yard long. He measures his work and realizes he still has yard to go. How much of the trench has he dug so far? Date omaneuvering the Midale ucc, 2015