Let’s Master Time Interconversion!
Hello! Welcome to the world of Speed. Before we can figure out how fast a racing car travels or how long a marathon takes, we need to become experts at switching between different units of time. This is called Interconversion.
Don't worry if this seems a bit tricky at first. Think of it like changing a large \(\$1\) coin into smaller \(10\)-cent coins—it’s the same amount of money, just written in a different way!
The Golden Rule of 60
In most math topics, we use groups of \(10\) or \(100\). But time is special! Time uses the Rule of 60. To move between hours, minutes, and seconds, the number \(60\) is your best friend.
Quick Review:
1. \(1 \text{ hour (h)} = 60 \text{ minutes (min)}\)
2. \(1 \text{ minute (min)} = 60 \text{ seconds (s)}\)
How do I know whether to Multiply or Divide?
Here is a simple trick to remember what to do:
Big unit to Small unit (e.g., Hour to Minute): You are breaking a "big" thing into many "small" pieces. MULTIPLY by \(60\).
Small unit to Big unit (e.g., Minute to Hour): You are grouping "small" pieces into one "big" thing. DIVIDE by \(60\).
Memory Aid: "Big to Small, give it a Multiply call! Small to Big, do the Division jig!"
Section 1: Changing Minutes to Hours
When we change minutes to hours, we are moving from a smaller unit to a bigger unit. This means we must divide by \(60\).
Example 1: Whole Numbers
How many hours are there in \(180\) minutes?
Step 1: Identify the units. We are going from minutes to hours (Small to Big).
Step 2: Divide by \(60\).
\(180 \div 60 = 3\)
Answer: \(3 \text{ hours}\).
Example 2: Decimals and Fractions
Sometimes, the answer isn't a whole number. Let’s look at \(90\) minutes.
Step 1: Divide \(90\) by \(60\).
\(90 \div 60 = 1.5\)
Step 2: You can also write this as a fraction.
\(\frac{90}{60} = \frac{9}{6} = \frac{3}{2} = 1\frac{1}{2}\)
Answer: \(1.5 \text{ hours}\) or \(1\frac{1}{2} \text{ hours}\).
Key Takeaway: To turn minutes into hours, divide the number of minutes by \(60\). Your answer can be a whole number, a decimal, or a fraction!
Section 2: Changing Seconds to Minutes
This works exactly the same way as changing minutes to hours because there are \(60\) seconds in every minute.
Example:
A song is \(240\) seconds long. How many minutes is that?
Step 1: We are going from seconds to minutes (Small to Big).
Step 2: Divide by \(60\).
\(240 \div 60 = 4\)
Answer: \(4 \text{ minutes}\).
Did you know?
The reason we use \(60\) for time goes back thousands of years to the Ancient Sumerians! They found \(60\) very useful because it can be divided easily by \(2, 3, 4, 5, 6, 10, 12, 15, 20,\) and \(30\).
Section 3: Changing Hours to Minutes
Now let's go the other way! When we move from a bigger unit (hours) to a smaller unit (minutes), we multiply by \(60\).
Example:
How many minutes are in \(2.5\) hours?
Step 1: Identify the units. Hours to Minutes (Big to Small).
Step 2: Multiply by \(60\).
\(2.5 \times 60 = 150\)
Answer: \(150 \text{ minutes}\).
Key Takeaway: To turn hours into minutes, multiply the number of hours by \(60\).
Common Mistakes to Avoid
The "100" Trap: Many students accidentally divide or multiply by \(100\) because they are used to the metric system (like cm and m). Always double-check and ask yourself: "Am I using the Rule of 60?"
Wrong Operation: If you turn \(2\) hours into minutes and get a tiny number (like \(2 \div 60 = 0.03\)), stop and think! \(2\) hours should be a lot of minutes, so you should have multiplied instead.
Quick Review Box
To change...
Minutes \(\rightarrow\) Hours: Divide by \(60\)
Seconds \(\rightarrow\) Minutes: Divide by \(60\)
Hours \(\rightarrow\) Minutes: Multiply by \(60\)
Minutes \(\rightarrow\) Seconds: Multiply by \(60\)
Practice Tip: Try converting your favorite TV show's length from minutes to hours. If it's \(30\) minutes long, that's \(30 \div 60 = 0.5\) or \(\frac{1}{2}\) an hour!