Calculate Running Pace: Converting 2km in 4½ Minutes to Minutes per Kilometer

Q: Why do I need to convert the mixed number first?

Converting $ 4\frac{1}{2} $ to $ \frac{9}{2} $ makes division much easier! Mixed numbers are harder to divide because you have to work with both whole and fractional parts separately.

Q: How do I remember which number goes on top when dividing?

Think about what you're looking for: minutes per kilometer. The word "per" means "divided by," so it's minutes ÷ kilometers, which is time ÷ distance.

Q: Can I just use decimals instead of fractions?

Yes! $ 4\frac{1}{2} = 4.5 $ minutes, so 4.5 ÷ 2 = 2.25 minutes per km. Then convert 2.25 back to $ 2\frac{1}{4} $ if needed.

Q: What does 'average pace' actually mean?

Average pace means how long it takes to complete each unit of distance. Even if Chris ran faster or slower during different parts, we calculate the overall average time per kilometer.

Q: How can I check if my answer makes sense?

Ask yourself: "If Chris runs each kilometer in $ 2\frac{1}{4} $ minutes, how long for 2 km?" The answer should be $ 4\frac{1}{2} $ minutes, matching the original problem!

Rate Division with Mixed Number Fractions

Chris runs 2 km in $4\frac{1}{2}$ minutes.

How many minutes does he run on average per km?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 How many minutes does Idan run on average per km?

00:03 Divide the number of minutes by the number of km to find the average

00:11 First, convert mixed fraction to fraction

00:28 Convert division to multiplication by reciprocal

00:41 Make sure to multiply numerator by numerator and denominator by denominator

00:45 Calculate the multiplications

00:49 Now convert to mixed fraction

00:53 Break down 9 into 8 plus 1

00:57 Break down the fraction into whole number and remainder

01:02 Convert proper fraction to whole number, and add to mixed fraction

01:08 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Chris runs 2 km in $4\frac{1}{2}$ minutes.

How many minutes does he run on average per km?

Step-by-step solution

To solve this problem, we need to calculate the average time Chris spends running per kilometer. We are given that Chris runs 2 km in $4\frac{1}{2}$ minutes.

First, let's convert the mixed fraction $4\frac{1}{2}$ into an improper fraction. The whole number 4 and the fraction $\frac{1}{2}$ combine as follows:

4\frac{1}{2} = \frac{4 \times 2 + 1}{2} = \frac{9}{2}

This means that the total time taken is $\frac{9}{2}$ minutes.

Next, we find the average time Chris runs per kilometer by dividing the total time by the distance:

\text{Average time per km} = \frac{\text{Total time}}{\text{Total distance in km}} = \frac{\frac{9}{2}}{2}

To divide by a fraction, we multiply by its reciprocal:

\frac{\frac{9}{2}}{2} = \frac{9}{2} \times \frac{1}{2} = \frac{9}{4}

The fraction $\frac{9}{4}$ can be converted back into a mixed number:

\frac{9}{4} = 2\frac{1}{4}

Therefore, the average time Chris runs per kilometer is $2\frac{1}{4}$ minutes.

Final Answer

$2\frac{1}{4}$

Key Points to Remember

Essential concepts to master this topic

Rate Formula: Divide total time by total distance for average rate
Technique: Convert mixed numbers like $4\frac{1}{2} = \frac{9}{2}$ before dividing
Check: Multiply answer by distance: $2\frac{1}{4} \times 2 = 4\frac{1}{2}$ minutes ✓

Common Mistakes

Avoid these frequent errors

Dividing distance by time instead of time by distance
Don't calculate 2 ÷ 4½ = 4/9 minutes per km! This gives you kilometers per minute, not minutes per kilometer. Always divide total time by total distance to find time per unit.

Practice Quiz

Test your knowledge with interactive questions

$2\times\frac{5}{7}=$

FAQ

Everything you need to know about this question

Why do I need to convert the mixed number first?

Converting $4\frac{1}{2}$ to $\frac{9}{2}$ makes division much easier! Mixed numbers are harder to divide because you have to work with both whole and fractional parts separately.

How do I remember which number goes on top when dividing?

Think about what you're looking for: minutes per kilometer. The word "per" means "divided by," so it's minutes ÷ kilometers, which is time ÷ distance.

Can I just use decimals instead of fractions?

Yes! $4\frac{1}{2} = 4.5$ minutes, so 4.5 ÷ 2 = 2.25 minutes per km. Then convert 2.25 back to $2\frac{1}{4}$ if needed.

What does 'average pace' actually mean?

Average pace means how long it takes to complete each unit of distance. Even if Chris ran faster or slower during different parts, we calculate the overall average time per kilometer.

How can I check if my answer makes sense?

Ask yourself: "If Chris runs each kilometer in $2\frac{1}{4}$ minutes, how long for 2 km?" The answer should be $4\frac{1}{2}$ minutes, matching the original problem!

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