5. Basir took a science test on Friday. One-eighth of the questions were multiple choice, and \( \frac{3}{4} \) of the questions were true-false questions. What part of the total number of questions are either multiple choice or true-false questions?
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The Deep Dive
To determine the part of the total number of questions that are either multiple choice or true-false, we can first express these categories as fractions of the total. Let’s denote the total number of questions as \( Q \). 1. The multiple choice questions account for \( \frac{1}{8}Q \). 2. The true-false questions account for \( \frac{3}{4}Q \). To find the total fraction of questions that are either multiple choice or true-false, we add the two fractions: \[ \frac{1}{8}Q + \frac{3}{4}Q \] To add these fractions, we need a common denominator, which is 8 in this case: \[ \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \] Now we can add: \[ \frac{1}{8}Q + \frac{6}{8}Q = \frac{7}{8}Q \] Thus, \( \frac{7}{8} \) of the total number of questions are either multiple choice or true-false questions.