³/₈ of a hospital day staff consists of registered nurses. Another ¹/₆ of the staff consists of phlebotomists.
What fraction of the day staff do the registered nurses and phlebotomists make up, combined?

Question

Quizplus · Accepted Answer

This problem can be solved by adding the fraction of the day staff that consists of registered nurses (³/₈) and the fraction of the day staff that consists of phlebotomists (¹/₆). Step 1: Find the least common denominator for both fractions. In order to add (or subtract) two fractions, they must have the same denominator. To determine the least common denominator, find the least common multiple between the two denominators (6 and 8). To find the least common multiple: List the multiples of each number until you find one in common. 6: 6, 12, 18, 24, 30…. 8: 8, 16, 24, 32, 40…. In this case, the least common denominator between ³⁄₈ and ¹⁄₆ is 24. Step 2: Make the two denominators the same as the least common denominator. First, determine what number needs to multiply each denominator in order to get to the least common denominator. In the case of ³⁄₈ , we would need to multiply the denominator (8) by 3 to get to the least common denominator (24). In order to make the denominator equal to 24, we multiply both the numerator and denominator by the same number (3). ^{3 • 3} / _{8 • 3} → ⁹⁄₂₄ In the case of ¹⁄₆ , we would need to multiply the denominator (6) by 4 to get to the least common denominator (24). In order to make the denominator equal to 24, we multiply both the numerator and denominator by the same number (4). ^{1 • 4} / _{6 • 4} → ⁴⁄₂₄ Now, we have: ⁹⁄₂₄ + ⁴⁄₂₄ Step 3: Add the fractions. ⁹⁄₂₄ + ⁴⁄₂₄ = ^{9 + 4}⁄₂₄ Step 4: Simplify ^{9 + 4}⁄₂₄ = ¹³⁄₂₄ Finally, if possible, we reduce the fraction. In this case, it is not possible. Answer: ¹³/₂₄

3/8 of a Hospital Day Staff Consists of Registered Nurses

³/₈ of a Hospital Day Staff Consists of Registered Nurses