Ralph spends $15 \frac{1}{3}$ hours per month playing tennis. How many hours does he play tennis in a year? (There are twelve months in a year.)
Answer (1)
Convert the mixed number to an improper fraction: 15 3 1 = 3 46 .
Multiply the hours per month by the number of months in a year: 3 46 × 12 .
Simplify the expression: 3 46 × 12 = 3 552 = 184 .
Ralph plays tennis for a total of 184 hours in a year.
Explanation
Convert mixed number to improper fraction First, we need to determine how many hours Ralph spends playing tennis each month. We are given that he spends 15 3 1 hours per month. To make this easier to work with, we'll convert this mixed number to an improper fraction.
Calculate improper fraction To convert 15 3 1 to an improper fraction, we multiply the whole number (15) by the denominator (3) and add the numerator (1). This gives us 15 × 3 + 1 = 45 + 1 = 46 . So, 15 3 1 = 3 46 .
Multiply by the number of months Now we know Ralph spends 3 46 hours per month playing tennis. Since there are 12 months in a year, we need to multiply the number of hours per month by 12 to find the total number of hours per year: 3 46 × 12
Perform multiplication To calculate 3 46 × 12 , we can write 12 as a fraction: 1 12 . Then we have: 3 46 × 1 12 = 3 × 1 46 × 12 = 3 552
Simplify the fraction Now we simplify the fraction 3 552 by dividing 552 by 3: 3 552 = 184
State the final answer So, Ralph spends a total of 184 hours per year playing tennis.
Examples
Understanding how to calculate total time spent on an activity over a year can help in budgeting and planning. For example, if you know you spend a certain amount of time commuting each day, you can calculate the total time spent commuting in a year. This can help you understand how much time you're investing in different activities and make informed decisions about your schedule.
