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# Portions of Time

Tips to solve problems that involve 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.

Let's take a look at some examples:

Example 1

How many hours are in
1
4
of a day?

Solution:

There are 24 hours in a day.

So if there are 24 hours in a day and we need to find how many hours are in
1
4
of a day, we need to figure out what is
1
4
of 24.

Remember that "of" means multiplication.

So,
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.

Example 2

How many years are in
3
4
of a century?

Solution:

There are 100 years in a century.

So, if there are 100 years in a century and we need to find how many years are in
3
4
of a century, we need to figure out what is
3
4
of 100.

Remember that "of" means multiplication.

So,
3
4
of 100 is the same as
3
4
times 100.

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.

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 an hour.
We need to determine what is
2
5
Remember that "of" means multiplication.
So,
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.

Summary

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.