\( \begin{array}{lll}\text { a) } \frac{1}{8}+\frac{1}{6}= & \text { b) } \frac{9}{10}-\frac{1}{7}= & \text { c) } 1 \frac{3}{5}+\frac{3}{5}= \\ \text { d fractions of numbers: } \\ \begin{array}{ll}\text { a) } \frac{2}{5} \text { of } 45= & \text { b) } \frac{6}{10} \times 120=\end{array}\end{array} \)

Calculate the value by following steps: - step0: Calculate: \(\frac{1}{8}+\frac{1}{6}\) - step1: Reduce fractions to a common denominator: \(\frac{3}{8\times 3}+\frac{4}{6\times 4}\) - step2: Multiply the numbers: \(\frac{3}{24}+\frac{4}{6\times 4}\) - step3: Multiply the numbers: \(\frac{3}{24}+\frac{4}{24}\) - step4: Transform the expression: \(\frac{3+4}{24}\) - step5: Add the numbers: \(\frac{7}{24}\) Calculate or simplify the expression \( 6/10 * 120 \). Calculate the value by following steps: - step0: Calculate: \(\frac{6}{10}\times 120\) - step1: Reduce the fraction: \(\frac{3}{5}\times 120\) - step2: Reduce the numbers: \(3\times 24\) - step3: Multiply the numbers: \(72\) Calculate or simplify the expression \( 9/10 - 1/7 \). Calculate the value by following steps: - step0: Calculate: \(\frac{9}{10}-\frac{1}{7}\) - step1: Reduce fractions to a common denominator: \(\frac{9\times 7}{10\times 7}-\frac{10}{7\times 10}\) - step2: Multiply the numbers: \(\frac{9\times 7}{70}-\frac{10}{7\times 10}\) - step3: Multiply the numbers: \(\frac{9\times 7}{70}-\frac{10}{70}\) - step4: Transform the expression: \(\frac{9\times 7-10}{70}\) - step5: Multiply the numbers: \(\frac{63-10}{70}\) - step6: Subtract the numbers: \(\frac{53}{70}\) Calculate or simplify the expression \( 1 + 3/5 + 3/5 \). Calculate the value by following steps: - step0: Calculate: \(1+\frac{3}{5}+\frac{3}{5}\) - step1: Reduce fractions to a common denominator: \(\frac{5}{5}+\frac{3}{5}+\frac{3}{5}\) - step2: Transform the expression: \(\frac{5+3+3}{5}\) - step3: Add the numbers: \(\frac{11}{5}\) Calculate or simplify the expression \( 2/5 * 45 \). Calculate the value by following steps: - step0: Calculate: \(\frac{2}{5}\times 45\) - step1: Reduce the numbers: \(2\times 9\) - step2: Multiply the numbers: \(18\) Let's solve each part step by step. ### a) \( \frac{1}{8} + \frac{1}{6} \) To add these fractions, we need a common denominator. The least common multiple of 8 and 6 is 24. \[ \frac{1}{8} = \frac{3}{24}, \quad \frac{1}{6} = \frac{4}{24} \] Now we can add them: \[ \frac{3}{24} + \frac{4}{24} = \frac{7}{24} \] ### b) \( \frac{9}{10} - \frac{1}{7} \) For this subtraction, we also need a common denominator. The least common multiple of 10 and 7 is 70. \[ \frac{9}{10} = \frac{63}{70}, \quad \frac{1}{7} = \frac{10}{70} \] Now we can subtract: \[ \frac{63}{70} - \frac{10}{70} = \frac{53}{70} \] ### c) \( 1 \frac{3}{5} + \frac{3}{5} \) First, convert the mixed number to an improper fraction: \[ 1 \frac{3}{5} = \frac{5}{5} + \frac{3}{5} = \frac{8}{5} \] Now add: \[ \frac{8}{5} + \frac{3}{5} = \frac{11}{5} = 2 \frac{1}{5} \] ### d) Fractions of numbers #### a) \( \frac{2}{5} \text{ of } 45 \) To find this, multiply: \[ \frac{2}{5} \times 45 = \frac{90}{5} = 18 \] #### b) \( \frac{6}{10} \times 120 \) This can be simplified first: \[ \frac{6}{10} = \frac{3}{5} \] Now multiply: \[ \frac{3}{5} \times 120 = \frac{360}{5} = 72 \] ### Summary of Results - a) \( \frac{1}{8} + \frac{1}{6} = \frac{7}{24} \) - b) \( \frac{9}{10} - \frac{1}{7} = \frac{53}{70} \) - c) \( 1 \frac{3}{5} + \frac{3}{5} = 2 \frac{1}{5} \) - d) - a) \( \frac{2}{5} \text{ of } 45 = 18 \) - b) \( \frac{6}{10} \times 120 = 72 \)