Question: Topic Quiz B 1. Consider the expression shown. \[ \frac{1}{2} + \frac{1}{3} \] Rename…

Topic Quiz B

1. Consider the expression shown. \[ \frac{1}{2} + \frac{1}{3} \]

Rename each fraction. Then find the sum. Write one value from the given answer choices in the box. Values may be used more than once.

Answer Choices: \[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 \]

2. Complete each equation. \[ \frac{6}{12} + \frac{1}{3} = \frac{13}{36} \]

\[ \frac{11}{12} - \frac{1}{6} = \frac{3}{4} \]

\[ \frac{5}{6} - \frac{7}{10} = \frac{1}{6} \]

\[ \frac{2}{5} + \frac{4}{3} + \frac{1}{2} = \frac{2}{5} \]

\[ \left( \frac{3}{4} + \frac{5}{6} \right) - \frac{2}{3} = \frac{1}{6} \]

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Solution

Problem a) \[ \frac{5}{12} + \frac{1}{3} = \frac{}{{36}} \] Find a common denominator for the fractions. \[ \frac{1}{3} = \frac{12}{36} \] \[ \frac{5}{12} = \frac{15}{36} \] Add the fractions. \[ \frac{15}{36} + \frac{12}{36} = \frac{27}{36} \] Answer: \(\frac{27}{36}\) --- Problem b) \[ \frac{9}{12} - \frac{1}{3} = \frac{}{{6}} \] Find a common denominator for the fractions. \[ \frac{9}{12} = \frac{3}{4} \] \[ \frac{1}{3} = \frac{2}{6} \] Subtract the fractions. \[ \frac{3}{4} - \frac{2}{6} = \frac{9}{12} - \frac{4}{12} = \frac{5}{12} \] Express the result with denominator 6. \[ \frac{5}{12} = \frac{5 \times 0.5}{12 \times 0.5} = \frac{2.5}{6} \] Since we need an integer numerator: \[ \frac{5}{12} = \frac{5}{12} \] Answer: \(\frac{5}{12}\) --- Problem c) \[ \frac{5}{6} \div \frac{7}{10} = \frac{}{{42}} \] Divide the fractions by multiplying by the reciprocal. \[ \frac{5}{6} \times \frac{10}{7} = \frac{50}{42} \] Simplify the fraction. \[ \frac{50}{42} = \frac{25}{21} \] Answer: \(\frac{25}{21}\) --- Problem d) \[ \frac{2}{5} + \frac{4}{3} + \frac{1}{2} = \] Find a common denominator for the fractions. \[ \text{Common denominator} = 30 \] Convert each fraction: \[ \frac{2}{5} = \frac{12}{30} \] \[ \frac{4}{3} = \frac{40}{30} \] \[ \frac{1}{2} = \frac{15}{30} \] Add the fractions. \[ \frac{12}{30} + \frac{40}{30} + \frac{15}{30} = \frac{67}{30} \] Answer: \(\frac{67}{30}\) --- Problem e) \[ \left(\frac{3}{4} + \frac{5}{6}\right) - \frac{2}{3} = \] Find a common denominator for the fractions inside the parentheses. \[ \frac{3}{4} = \frac{9}{12} \] \[ \frac{5}{6} = \frac{10}{12} \] Add the fractions inside the parentheses. \[ \frac{9}{12} + \frac{10}{12} = \frac{19}{12} \] Subtract \(\frac{2}{3}\): \[ \frac{2}{3} = \frac{8}{12} \] \[ \frac{19}{12} - \frac{8}{12} = \frac{11}{12} \] Answer: \(\frac{11}{12}\)