Number Sense Mary has three lengths of cable, $$ \frac{3}{6} $$ yard long, $$ \frac{1}{4} $$ yard long, and $$ \frac{1}{3} $$ yard long. Which two pieces together make a length of $$ \frac{20}{24} $$ yard?

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To determine which two cable lengths add up to $$ \frac{20}{24} $$ yard, let's analyze each pair of lengths step by step.

### Given Cable Lengths:
1. $$ \frac{3}{6} $$ yard
2. $$ \frac{1}{4} $$ yard
3. $$ \frac{1}{3} $$ yard

### Goal:
Find two lengths whose sum equals $$ \frac{20}{24} $$ yard.

### Step 1: Simplify the Target Length
First, simplify $$ \frac{20}{24} $$:

$$
\frac{20}{24} = \frac{5}{6} \quad (\text{divided numerator and denominator by 4})
$$

So, we need to find two lengths that add up to $$ \frac{5}{6} $$ yard.

### Step 2: Simplify Given Lengths
Simplify each cable length to make calculations easier:

1. $$ \frac{3}{6} = \frac{1}{2} $$ yard
2. $$ \frac{1}{4} $$ yard (already simplified)
3. $$ \frac{1}{3} $$ yard (already simplified)

### Step 3: Calculate Pairwise Sums
Now, calculate the sum of each possible pair:

1. **First and Second Lengths:**
   $$
   \frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4} = \frac{18}{24}
   $$
   
2. **First and Third Lengths:**
   $$
   \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6} = \frac{20}{24}
   $$
   
3. **Second and Third Lengths:**
   $$
   \frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12} = \frac{14}{24}
   $$

### Step 4: Identify the Correct Pair
From the calculations:

- **First and Third lengths** add up to $$ \frac{5}{6} $$ yard, which is equivalent to $$ \frac{20}{24} $$ yard.

### **Conclusion:**
Mary should use the $$ \frac{3}{6} $$ yard (which simplifies to $$ \frac{1}{2} $$ yard) and the $$ \frac{1}{3} $$ yard cables together. Their combined length is $$ \frac{20}{24} $$ yard.
Mary should use the $$ \frac{1}{2} $$ yard and $$ \frac{1}{3} $$ yard cables together, which add up to $$ \frac{20}{24} $$ yard.

Number Sense Mary has three lengths of cable, \( \frac{3}{6} \) yard long, \( \frac{1}{4} \) yard long, and \( \frac{1}{3} \) yard long. Which two pieces together make a length of \( \frac{20}{24} \) yard?

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