8. $$ 2 \frac{2}{5}-1 \frac{1}{2}= $$

Question

UpStudy AI · Accepted Answer

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

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

1. **Convert $$ 2 \frac{2}{5} $$ to an improper fraction:**
   $$
   2 \frac{2}{5} = \frac{2 \times 5 + 2}{5} = \frac{10 + 2}{5} = \frac{12}{5}
   $$

2. **Convert $$ 1 \frac{1}{2} $$ to an improper fraction:**
   $$
   1 \frac{1}{2} = \frac{1 \times 2 + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}
   $$

### Step 2: Subtract the Fractions

Now, subtract $$ \frac{3}{2} $$ from $$ \frac{12}{5} $$:

$$
\frac{12}{5} - \frac{3}{2}
$$

To subtract these fractions, find a common denominator. The least common denominator (LCD) of 5 and 2 is 10.

1. **Convert $$ \frac{12}{5} $$ to a fraction with denominator 10:**
   $$
   \frac{12}{5} = \frac{12 \times 2}{5 \times 2} = \frac{24}{10}
   $$

2. **Convert $$ \frac{3}{2} $$ to a fraction with denominator 10:**
   $$
   \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10}
   $$

3. **Perform the subtraction:**
   $$
   \frac{24}{10} - \frac{15}{10} = \frac{24 - 15}{10} = \frac{9}{10}
   $$

### Final Answer

$$
2 \frac{2}{5} - 1 \frac{1}{2} = \frac{9}{10}
$$
$$ \frac{9}{10} $$

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