15. $$ 2 \frac{3}{4}+7 \frac{3}{5} $$

Question

UpStudy AI · Accepted Answer

To solve the addition of the mixed numbers $$ 2 \frac{3}{4} + 7 \frac{3}{5} $$, follow these steps:

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

**For $$ 2 \frac{3}{4} $$:**
$$
2 \frac{3}{4} = \frac{(2 \times 4) + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}
$$

**For $$ 7 \frac{3}{5} $$:**
$$
7 \frac{3}{5} = \frac{(7 \times 5) + 3}{5} = \frac{35 + 3}{5} = \frac{38}{5}
$$

### Step 2: Find a Common Denominator

The denominators are 4 and 5. The least common denominator (LCD) is 20.

**Convert $$ \frac{11}{4} $$ to 20th denominator:**
$$
\frac{11}{4} = \frac{11 \times 5}{4 \times 5} = \frac{55}{20}
$$

**Convert $$ \frac{38}{5} $$ to 20th denominator:**
$$
\frac{38}{5} = \frac{38 \times 4}{5 \times 4} = \frac{152}{20}
$$

### Step 3: Add the Fractions

$$
\frac{55}{20} + \frac{152}{20} = \frac{55 + 152}{20} = \frac{207}{20}
$$

### Step 4: Convert the Improper Fraction Back to a Mixed Number

$$
\frac{207}{20} = 10 \frac{7}{20}
$$

**Final Answer:**
$$
2 \frac{3}{4} + 7 \frac{3}{5} = 10 \frac{7}{20}
$$
$$ 2 \frac{3}{4} + 7 \frac{3}{5} = 10 \frac{7}{20} $$

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