Laney uses \( 3 \frac{1}{4} \) bags of red beads and \( 2 \frac{5}{6} \) bags of yellow beads for a craft at summer camp. How many bags of red and yellow beads does Laney use? A \( 5 \frac{11}{12} \) bags B \( 6 \frac{1}{4} \) bags \( 5 \frac{3}{5} \) bags \( 6 \frac{1}{10} \) bags

To find the total number of bags of red and yellow beads that Laney uses, we need to add the two mixed numbers together: \( 3 \frac{1}{4} \) and \( 2 \frac{5}{6} \). ### Step 1: Convert mixed numbers to improper fractions 1. For \( 3 \frac{1}{4} \): \[ 3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} \] 2. For \( 2 \frac{5}{6} \): \[ 2 \frac{5}{6} = \frac{2 \times 6 + 5}{6} = \frac{12 + 5}{6} = \frac{17}{6} \] ### Step 2: Find a common denominator The denominators are 4 and 6. The least common multiple (LCM) of 4 and 6 is 12. ### Step 3: Convert the fractions to have the same denominator 1. Convert \( \frac{13}{4} \) to a denominator of 12: \[ \frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12} \] 2. Convert \( \frac{17}{6} \) to a denominator of 12: \[ \frac{17}{6} = \frac{17 \times 2}{6 \times 2} = \frac{34}{12} \] ### Step 4: Add the fractions Now we can add the two fractions: \[ \frac{39}{12} + \frac{34}{12} = \frac{39 + 34}{12} = \frac{73}{12} \] ### Step 5: Convert back to a mixed number To convert \( \frac{73}{12} \) back to a mixed number: - Divide 73 by 12, which gives 6 with a remainder of 1. - Thus, \( \frac{73}{12} = 6 \frac{1}{12} \). ### Conclusion Laney uses \( 6 \frac{1}{12} \) bags of beads. Now, let's check the options provided: - A \( 5 \frac{11}{12} \) bags - B \( 6 \frac{1}{4} \) bags - \( 5 \frac{3}{5} \) bags - \( 6 \frac{1}{10} \) bags None of the options match \( 6 \frac{1}{12} \). It seems there might be an error in the options provided. The correct answer is \( 6 \frac{1}{12} \).