10. \( 3 \frac{1}{4} - 1 \frac{7}{8} \)

To solve the subtraction of mixed numbers \( 3 \frac{1}{4} - 1 \frac{7}{8} \), follow these steps: ### Step 1: Convert Mixed Numbers to Improper Fractions 1. **Convert \( 3 \frac{1}{4} \) to an Improper Fraction:** \[ 3 \frac{1}{4} = \left(3 \times 4\right) + 1 = 12 + 1 = \frac{13}{4} \] 2. **Convert \( 1 \frac{7}{8} \) to an Improper Fraction:** \[ 1 \frac{7}{8} = \left(1 \times 8\right) + 7 = 8 + 7 = \frac{15}{8} \] ### Step 2: Find a Common Denominator To subtract the fractions, they need to have the same denominator. The least common denominator (LCD) of 4 and 8 is 8. 1. **Convert \( \frac{13}{4} \) to have a denominator of 8:** \[ \frac{13}{4} = \frac{13 \times 2}{4 \times 2} = \frac{26}{8} \] 2. **\( \frac{15}{8} \) already has the denominator of 8.** ### Step 3: Subtract the Fractions \[ \frac{26}{8} - \frac{15}{8} = \frac{26 - 15}{8} = \frac{11}{8} \] ### Step 4: Convert Back to a Mixed Number (If Desired) \[ \frac{11}{8} = 1 \frac{3}{8} \] ### Final Answer \[ 3 \frac{1}{4} - 1 \frac{7}{8} = 1 \frac{3}{8} \]