1. Find the answers. Show all your a. \( 2 \frac{2}{3}+1 \frac{1}{2}+3 \frac{3}{4}= \)
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To solve \( 2 \frac{2}{3} + 1 \frac{1}{2} + 3 \frac{3}{4} \), we first convert the mixed numbers to improper fractions. For \( 2 \frac{2}{3} \): \[ 2 \frac{2}{3} = \frac{8}{3} \] For \( 1 \frac{1}{2} \): \[ 1 \frac{1}{2} = \frac{3}{2} \] For \( 3 \frac{3}{4} \): \[ 3 \frac{3}{4} = \frac{15}{4} \] Next, we find a common denominator to add these fractions. The least common multiple of 3, 2, and 4 is 12. Now converting each fraction: \[ \frac{8}{3} = \frac{32}{12} \] \[ \frac{3}{2} = \frac{18}{12} \] \[ \frac{15}{4} = \frac{45}{12} \] Adding them together: \[ \frac{32}{12} + \frac{18}{12} + \frac{45}{12} = \frac{95}{12} \] Finally, converting back to a mixed number: \[ \frac{95}{12} = 7 \frac{11}{12} \] So, \( 2 \frac{2}{3} + 1 \frac{1}{2} + 3 \frac{3}{4} = 7 \frac{11}{12} \).
