**Adding Mixed Numbers: 7 2/3 plus 10 3/5 as a Fraction**

When dealing with mixed numbers, adding them can be a bit tricky. But don't worry, we're here to break it down step by step. In this article, we'll explore how to add 7 2/3 and 10 3/5 as a fraction.

**Step 1: Convert Mixed Numbers to Improper Fractions**

To add mixed numbers, we need to convert them to improper fractions first. Here's how we do it:

### 7 2/3

To convert 7 2/3 to an improper fraction, we multiply the whole number part (7) by the denominator (3) and then add the numerator (2):

7 × 3 = 21 21 + 2 = 23

So, 7 2/3 is equal to **23/3**.

### 10 3/5

Now, let's convert 10 3/5 to an improper fraction:

10 × 5 = 50 50 + 3 = 53

So, 10 3/5 is equal to **53/5**.

**Step 2: Find the Least Common Multiple (LCM)**

To add these two improper fractions, we need to find the least common multiple (LCM) of their denominators, which are 3 and 5. The LCM of 3 and 5 is **15**.

**Step 3: Convert Fractions to Equivalent Fractions with the LCM**

Now, we'll convert both fractions to have a denominator of 15:

### 23/3

To convert 23/3 to have a denominator of 15, we'll multiply both the numerator and denominator by 5:

23 × 5 = 115 3 × 5 = 15

So, **23/3 = 115/15**.

### 53/5

To convert 53/5 to have a denominator of 15, we'll multiply both the numerator and denominator by 3:

53 × 3 = 159 5 × 3 = 15

So, **53/5 = 159/15**.

**Step 4: Add the Fractions**

Now that we have equivalent fractions with the same denominator, we can add them:

**115/15 + 159/15 = 274/15**

**The Result**

So, 7 2/3 plus 10 3/5 as a fraction is equal to **274/15**.