\#1: \( 5 \frac{1}{3}+3 \frac{1}{4}= \)

To solve the addition of the mixed numbers \( 5 \frac{1}{3} + 3 \frac{1}{4} \), follow these steps: ### Step 1: Convert Mixed Numbers to Improper Fractions A mixed number consists of an integer and a proper fraction. To add mixed numbers, it's easier to first convert them into improper fractions. - For \( 5 \frac{1}{3} \): \[ 5 \frac{1}{3} = \left(5 \times 3\right) + 1 = 15 + 1 = \frac{16}{3} \] - For \( 3 \frac{1}{4} \): \[ 3 \frac{1}{4} = \left(3 \times 4\right) + 1 = 12 + 1 = \frac{13}{4} \] ### Step 2: Find a Common Denominator To add the fractions \(\frac{16}{3}\) and \(\frac{13}{4}\), they need to have the same denominator. The least common denominator (LCD) of 3 and 4 is 12. - Convert \(\frac{16}{3}\) to a denominator of 12: \[ \frac{16}{3} = \frac{16 \times 4}{3 \times 4} = \frac{64}{12} \] - Convert \(\frac{13}{4}\) to a denominator of 12: \[ \frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12} \] ### Step 3: Add the Fractions Now that both fractions have the same denominator, add them together: \[ \frac{64}{12} + \frac{39}{12} = \frac{64 + 39}{12} = \frac{103}{12} \] ### Step 4: Convert Back to a Mixed Number (Optional) If you prefer the answer as a mixed number: \[ \frac{103}{12} = 8 \frac{7}{12} \] *(Because 12 goes into 103 eight times with a remainder of 7.)* ### Final Answer \[ 5 \frac{1}{3} + 3 \frac{1}{4} = 8 \frac{7}{12} \]