Catwalk Duration: During rehearsals, Maria takes $\frac{1}{8}$ of an hour to complete her walk, while Susan takes $\frac{3}{15}$ of an hour. Who spends more time on the catwalk?
Select one of two
Maria
Susan
Answer (1)
Simplify Susan's time: 15 3 = 5 1 .
Find a common denominator to compare 8 1 and 5 1 . The least common multiple of 8 and 5 is 40.
Convert the fractions: 8 1 = 40 5 and 5 1 = 40 8 .
Compare the fractions: Since \frac{5}{40}"> 40 8 > 40 5 , Susan spends more time on the catwalk. The answer is S u s an .
Explanation
Problem Analysis Let's analyze the problem. Maria takes 8 1 of an hour, and Susan takes 15 3 of an hour. We need to determine who spends more time on the catwalk.
Simplify Susan's Time First, simplify Susan's time: 15 3 can be simplified by dividing both the numerator and the denominator by 3: 15 3 = 15 ÷ 3 3 ÷ 3 = 5 1
Find a Common Denominator Now, we need to compare the two fractions, 8 1 and 5 1 , to see which one is larger. To do this, we can find a common denominator. The least common multiple of 8 and 5 is 40.
Convert to Common Denominator Convert both fractions to have a denominator of 40: 8 1 = 8 × 5 1 × 5 = 40 5 5 1 = 5 × 8 1 × 8 = 40 8
Compare the Fractions Now we can easily compare the fractions: 40 5 and 40 8 . Since 8 > 5, we have \frac{5}{40}"> 40 8 > 40 5 . Therefore, \frac{1}{8}"> 5 1 > 8 1 .
Conclusion Since \frac{1}{8}"> 5 1 > 8 1 , Susan spends more time on the catwalk than Maria.
Examples
Understanding fractions and comparing them is crucial in many real-life situations. For instance, when baking, you might need to compare the amount of flour or sugar used in different recipes. If one recipe calls for 4 1 cup of sugar and another calls for 8 2 cup, recognizing that 8 2 simplifies to 4 1 helps you realize both recipes use the same amount of sugar. This skill is also useful in managing time, comparing distances, or understanding proportions in various fields.
