Martha and Jordan were given a list of tasks to complete for work. Martha completed ¹/₄ of the tasks on the list and Jordan completed ²/₅ of the tasks on the list.
What fraction of the list of tasks do they still have left?

Question

Quizplus · Accepted Answer

This problem can be solved by adding the tasks that Martha (¹/₄) and Jordan ( ²/₅) completed and then subtracting that from the original list (1). 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 (4 and 5). To find the least common multiple: List the multiples of each number until you find one in common. 4: 4, 8, 12, 16, 20, 24…. 5: 5, 10, 15, 20, 25…. In this case, the least common denominator between ¹⁄₄ and ²⁄₅ is 20. 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 ¹⁄₄ , we would need to multiply the denominator (4) by 5 to get to the least common denominator (20). In order to make the denominator equal to 20, we multiply both the numerator and denominator by the same number (5). ^{1 • 5} / _{4 • 5} → ⁵⁄₂₀ In the case of ²⁄₅ , we would need to multiply the denominator (5) by 4 to get to the least common denominator (20). In order to make the denominator equal to 20, we multiply both the numerator and denominator by the same number (4). ^{2 • 4} / _{5 • 4} → ⁸⁄₂₀ Now, we have: ⁵⁄₂₀ + ⁸⁄₂₀ Step 3: Add the fractions. ⁵⁄₂₀ + ⁸⁄₂₀ = ^{5 + 8}⁄₂₀ Step 4: Simplify ^{5 + 8}⁄₂₀ = ¹³⁄₂₀ Finally, if possible, we reduce the fraction. In this case, it is not possible. Next, we need to subtract the completed tasks (¹³⁄₂₀) from the whole (1) to see how much they have left. Step 5: Find the 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 (1 and 20). Remember that to make a whole number into a fraction, the whole number becomes the numerator and 1 becomes the denominator (¹⁄₁). To find the least common multiple: List the multiples of each number until you find one in common. 20: 20, 40, 60, 80…. 1: 1, 2, 3, 4, 5, 6, 7, 8, 9 ,10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20…. In this case, the least common denominator between ¹⁄₁ and ¹³⁄₂₀ is 20. Step 6: 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 ¹³⁄₂₀, we don't need to take any further steps because the denominator is already 20. In the case of ¹⁄₁ , we would need to multiply the denominator (1) by 20 to get to the least common denominator (20). In order to make the denominator equal to 20, we multiply both the numerator and denominator by the same number (20). ^{1 • 20} / _{1 • 20} → ²⁰⁄₂₀ So, we have: ²⁰⁄₂₀ - ¹³⁄₂₀ Step 3: Subtract the fractions. ²⁰⁄₂₀ - ¹³⁄₂₀ = ^{20 - 13}⁄₂₀ Step 4: Simplify ^{20 - 13}⁄₂₀ = ⁷⁄₂₀ Finally, if possible, we reduce the fraction. In this case, it is not possible. Answer: ⁷⁄₂₀

Martha and Jordan Were Given a List of Tasks to Complete