11. $$ \frac{31}{10}-\frac{13}{5} $$

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UpStudy AI · Accepted Answer

To solve the expression:

$$
\frac{31}{10} - \frac{13}{5}
$$

follow these steps:

### Step 1: Find a Common Denominator

The denominators of the two fractions are 10 and 5. To subtract the fractions, they need to have the same denominator. The least common denominator (LCD) of 10 and 5 is **10**.

### Step 2: Convert $$\frac{13}{5}$$ to a Fraction with Denominator 10

Multiply both the numerator and the denominator of $$\frac{13}{5}$$ by 2 to get a denominator of 10:

$$
\frac{13}{5} = \frac{13 \times 2}{5 \times 2} = \frac{26}{10}
$$

### Step 3: Subtract the Fractions

Now that both fractions have the same denominator, subtract the numerators:

$$
\frac{31}{10} - \frac{26}{10} = \frac{31 - 26}{10} = \frac{5}{10}
$$

### Step 4: Simplify the Resulting Fraction

Simplify $$\frac{5}{10}$$ by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

$$
\frac{5}{10} = \frac{5 \div 5}{10 \div 5} = \frac{1}{2}
$$

### Final Answer

$$
\frac{31}{10} - \frac{13}{5} = \frac{1}{2}
$$
$$ \frac{1}{2} $$

11. \( \frac{31}{10}-\frac{13}{5} \)

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