9. $$ 9 \frac{3}{16}-7 \frac{5}{8} $$

Question

UpStudy AI · Accepted Answer

To subtract the mixed numbers $$ 9 \frac{3}{16} - 7 \frac{5}{8} $$, follow these steps:

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

**For $$ 9 \frac{3}{16} $$:**
$$
9 \frac{3}{16} = \left(9 \times 16\right) + 3 = 144 + 3 = \frac{147}{16}
$$

**For $$ 7 \frac{5}{8} $$:**
$$
7 \frac{5}{8} = \left(7 \times 8\right) + 5 = 56 + 5 = \frac{61}{8}
$$

### Step 2: Find a Common Denominator

The denominators are 16 and 8. The least common denominator (LCD) is **16**.

Convert $$ \frac{61}{8} $$ to have a denominator of 16:
$$
\frac{61}{8} = \frac{61 \times 2}{8 \times 2} = \frac{122}{16}
$$

### Step 3: Subtract the Fractions

Now, subtract the two improper fractions:
$$
\frac{147}{16} - \frac{122}{16} = \frac{147 - 122}{16} = \frac{25}{16}
$$

### Step 4: Simplify the Result

Convert $$ \frac{25}{16} $$ back to a mixed number:
$$
\frac{25}{16} = 1 \frac{9}{16}
$$
(since $$ 16 \times 1 = 16 $$ and $$ 25 - 16 = 9 $$)

### Final Answer

$$
9 \frac{3}{16} - 7 \frac{5}{8} = 1 \frac{9}{16}
$$
$$ 1 \frac{9}{16} $$

9. \( 9 \frac{3}{16}-7 \frac{5}{8} \)