4. $$ 2 \frac{3}{5}-1 \frac{3}{8} $$

Question

UpStudy AI · Accepted Answer

To solve the subtraction $$ 2 \frac{3}{5} - 1 \frac{3}{8} $$, follow these steps:

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

First, convert each mixed number to an improper fraction.

1. **For $$ 2 \frac{3}{5} $$:**
   $$
   2 \frac{3}{5} = \left(2 \times 5\right) + 3 = 10 + 3 = \frac{13}{5}
   $$

2. **For $$ 1 \frac{3}{8} $$:**
   $$
   1 \frac{3}{8} = \left(1 \times 8\right) + 3 = 8 + 3 = \frac{11}{8}
   $$

### Step 2: Find a Common Denominator

To subtract the fractions, they must have the same denominator. The least common denominator (LCD) of 5 and 8 is 40.

1. **Convert $$ \frac{13}{5} $$ to a denominator of 40:**
   $$
   \frac{13}{5} = \frac{13 \times 8}{5 \times 8} = \frac{104}{40}
   $$

2. **Convert $$ \frac{11}{8} $$ to a denominator of 40:**
   $$
   \frac{11}{8} = \frac{11 \times 5}{8 \times 5} = \frac{55}{40}
   $$

### Step 3: Subtract the Fractions

Now, subtract the two fractions:
$$
\frac{104}{40} - \frac{55}{40} = \frac{104 - 55}{40} = \frac{49}{40}
$$

### Step 4: Convert Back to a Mixed Number

Finally, convert the improper fraction $$ \frac{49}{40} $$ back to a mixed number:
$$
\frac{49}{40} = 1 \frac{9}{40}
$$

### Final Answer

$$
2 \frac{3}{5} - 1 \frac{3}{8} = 1 \frac{9}{40}
$$
$$ 1 \frac{9}{40} $$

4. \( 2 \frac{3}{5}-1 \frac{3}{8} \)