5. Reilly used \( 1 \frac{7}{10} \) tubes of paint to paint a model. He used \( 2 \frac{3}{8} \) tubes finish an art project. How many tubes did he use in total?

To find the total number of tubes of paint Reilly used, we need to add the two mixed numbers together: \( 1 \frac{7}{10} \) and \( 2 \frac{3}{8} \). ### Step 1: Convert mixed numbers to improper fractions 1. For \( 1 \frac{7}{10} \): \[ 1 \frac{7}{10} = \frac{1 \times 10 + 7}{10} = \frac{10 + 7}{10} = \frac{17}{10} \] 2. For \( 2 \frac{3}{8} \): \[ 2 \frac{3}{8} = \frac{2 \times 8 + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8} \] ### Step 2: Find a common denominator The denominators are 10 and 8. The least common multiple (LCM) of 10 and 8 is 40. ### Step 3: Convert the fractions to have the same denominator 1. Convert \( \frac{17}{10} \) to a denominator of 40: \[ \frac{17}{10} = \frac{17 \times 4}{10 \times 4} = \frac{68}{40} \] 2. Convert \( \frac{19}{8} \) to a denominator of 40: \[ \frac{19}{8} = \frac{19 \times 5}{8 \times 5} = \frac{95}{40} \] ### Step 4: Add the fractions Now we can add the two fractions: \[ \frac{68}{40} + \frac{95}{40} = \frac{68 + 95}{40} = \frac{163}{40} \] ### Step 5: Convert back to a mixed number To convert \( \frac{163}{40} \) back to a mixed number: 1. Divide 163 by 40: - \( 163 \div 40 = 4 \) (whole number part) - Remainder: \( 163 - (40 \times 4) = 3 \) Thus, we have: \[ \frac{163}{40} = 4 \frac{3}{40} \] ### Final Answer Reilly used a total of \( 4 \frac{3}{40} \) tubes of paint.