Add or subtract. \( \begin{array}{lll}\text { 25. } 2 \frac{1}{3}+\frac{3}{4} & \text { 26. } 16 \frac{4}{5}-9 \frac{2}{3} & \text { 27. } \frac{6}{x}+\frac{3}{5}\end{array} \)
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The Deep Dive
To tackle these problems, let's break them down step by step! For \( 25. 2 \frac{1}{3} + \frac{3}{4} \): First, convert \( 2 \frac{1}{3} \) to an improper fraction: \( 2 \frac{1}{3} = \frac{7}{3} \). Now we have: \( \frac{7}{3} + \frac{3}{4} \). To add these fractions, find a common denominator, which is 12. Convert both fractions: \( \frac{7}{3} = \frac{28}{12} \) and \( \frac{3}{4} = \frac{9}{12} \). Now add: \( \frac{28}{12} + \frac{9}{12} = \frac{37}{12} \) or \( 3 \frac{1}{12} \). For \( 26. 16 \frac{4}{5} - 9 \frac{2}{3} \): Convert both mixed numbers to improper fractions: \( 16 \frac{4}{5} = \frac{84}{5} \) and \( 9 \frac{2}{3} = \frac{29}{3} \). Next, find a common denominator (15 in this case): \( \frac{84}{5} = \frac{252}{15} \) and \( \frac{29}{3} = \frac{145}{15} \). Now subtract: \( \frac{252}{15} - \frac{145}{15} = \frac{107}{15} \) or \( 7 \frac{2}{15} \). For \( 27. \frac{6}{x} + \frac{3}{5} \): To combine these, you can find a common denominator, which would be \( 5x \): \( \frac{6}{x} = \frac{30}{5x} \) and \( \frac{3}{5} = \frac{3x}{5x} \). Now add: \( \frac{30}{5x} + \frac{3x}{5x} = \frac{30 + 3x}{5x} \). So the final answers are: 25. \( 3 \frac{1}{12} \) 26. \( 7 \frac{2}{15} \) 27. \( \frac{30 + 3x}{5x} \)
