# Portions of Time

**1.** Start by thinking about the **time conversion.**

**2.** Remember that **"of"** means **multiplication.**

**3.** Ask yourself at the end "Does the answer make sense?" If it doesn't make sense, you probably did something wrong.

**Example 1**

**How many hours are in**

**1**

**4**

**of a day?**

**Solution:**

There are 24 hours in a day.

**1**

**4**

**of 24.**

**Remember that "of" means multiplication.**

**1**

**4**

**of 24 is the same as**

**1**

**4**

**times 24.**

**1**

**4**

**x 24 =**

**1**

**4**

**x**

**24**

**1**

**= 6**

**Remember that there's an understood 1 underneath the 24 and that to multiply fractions you must multiply the numerators then the denominators. At the end, 24 divided by 4 is 6.**

**Answer: 6 hours.**

**Example 2**

**How many years are in**

**3**

**4**

**of a century?**

**Solution:**

**There are 100 years in a century.**

Remember that **"of"** means **multiplication.**

**3**

**4**

**3**

**4**

Let's solve this.

**3**

**4**

**x 100 =**

**3**

**4**

**x**

**100**

**1**

**=**

**300**

**4**

**= 75**

**Remember that there's an understood 1 underneath the 100, and that to multiply fractions you must multiply the numerators then the denominators. At the end, 300 divided by 4 is 75.**

**Answer: 75 years**

**Example 3**

**Mark practiced playing the piano for**

**2**

**5**

**of an hour. How many minutes make**

**2**

**5**

**of an hour?**

**Solution:**

**There are 60 minutes in an hour.**

**So if there are 60 minutes in an hour and we need to find out how many minutes are in**

**2**

**5**

**"of"**means

**multiplication**.

**2**

**5**

**of 60 is the same as**

**2**

**5**

**times 60.**

Let's solve this:

**2**

**5**

**x 60 =**

**2**

**5**

**x**

**60**

**1**

**=**

**120**

**5**

**= 24**

**Remember that there's an understood 1 underneath the 60, and that to multiply fractions you must multiply the numerators then the denominators. At the end, 120 divided by 5 is 24.**

**Answer: 24 minutes. **

**Time conversions:**

- 60 seconds = 1 minute
- 60 minutes = 1 hour
- 24 hours = 1 day
- 7 days = 1 week
- 12 months = 1 year
- 52 weeks = 1 year
- 365 days = 1 year (366 for leap year)
- 10 years = 1 decade
- 100 years = 1 century
- 1000 years = 1 millennium

**Conversion rule:**

Large to small: **Multiply**

Small to large: **Divide**

**Quick tips for solving 'portions of time' problems:**

- Start by thinking about the time conversion.
- Remember that
**"of"**means**multiplication.** - Ask yourself at the end "Does my answer make sense?" If it doesn't make sense, you probably did something wrong.