Convert and Calculate: Finding Average Daily Progress in 5km Wall Construction

Q: Why can't I just divide 5 by 2 to get 2.5?

You could get 2.5, but that would be 2.5 kilometers per day. The question asks for meters per day, so you must convert first: $5 \text{ km} = 5000 \text{ m}$, then $5000 \div 2 = 2500 \text{ m}$.

Q: How do I remember the conversion from km to m?

Remember that kilo means 1000! Just like 1 kilogram = 1000 grams, we have 1 kilometer = 1000 meters. So multiply kilometers by 1000 to get meters.

Q: What if the problem gave me the answer choices in kilometers?

Then you'd convert your final answer back to kilometers! $2500 \text{ m} = 2500 \div 1000 = 2.5 \text{ km}$. Always check what units the question wants.

Q: Is this the same as finding an average?

Yes! Finding average daily progress means total work ÷ number of days. Whether it's meters of wall, pages read, or problems solved, the method is the same.

Unit Conversion with Division Applications

Nigel builds a 5 km long wall over a period of two days.

How many meters on average does he build each day?

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Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Nigel builds a 5 km long wall over a period of two days.

How many meters on average does he build each day?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Convert the total length of the wall Nigel builds from kilometers to meters.
Step 2: Calculate the average number of meters built each day.

Now, let's work through each step:

Step 1: Nigel builds a wall that is 5 kilometers long. Since $1 \text{ km} = 1000 \text{ m}$ , we convert kilometers to meters:

5 \text{ km} = 5 \times 1000 \text{ m} = 5000 \text{ m}

Step 2: Since the wall is built over 2 days, we divide the total length in meters by the number of days to find the average:

\text{Average meters per day} = \frac{5000 \text{ m}}{2 \text{ days}} = 2500 \text{ m/day}

Therefore, on average, Nigel builds 2500 meters of the wall each day.

Thus, the correct answer is choice $\boxed{3}$ with 2500 m per day.

Final Answer

2500

Key Points to Remember

Essential concepts to master this topic

Conversion Rule: Always convert kilometers to meters using 1 km = 1000 m
Calculation Technique: Divide total length by number of days: 5000 ÷ 2 = 2500
Check: Multiply answer by days: 2500 × 2 = 5000 m = 5 km ✓

Common Mistakes

Avoid these frequent errors

Forgetting to convert kilometers to meters
Don't divide 5 km directly by 2 days = 2.5 km per day! This gives the answer in wrong units (kilometers instead of meters). Always convert kilometers to meters first: 5 km = 5000 m, then divide.

Practice Quiz

Test your knowledge with interactive questions

Convert to cm:
$$ 0.6 $$ meters

FAQ

Everything you need to know about this question

Why can't I just divide 5 by 2 to get 2.5?

You could get 2.5, but that would be 2.5 kilometers per day. The question asks for meters per day, so you must convert first: $5 \text{ km} = 5000 \text{ m}$ , then $5000 \div 2 = 2500 \text{ m}$ .

How do I remember the conversion from km to m?

Remember that kilo means 1000! Just like 1 kilogram = 1000 grams, we have 1 kilometer = 1000 meters. So multiply kilometers by 1000 to get meters.

What if the problem gave me the answer choices in kilometers?

Then you'd convert your final answer back to kilometers! $2500 \text{ m} = 2500 \div 1000 = 2.5 \text{ km}$ . Always check what units the question wants.

Is this the same as finding an average?

Yes! Finding average daily progress means total work ÷ number of days. Whether it's meters of wall, pages read, or problems solved, the method is the same.

What if Nigel worked for 3 days instead of 2?

Same process: convert to meters first (5000 m), then divide by days. $5000 \div 3 = 1666.67 \text{ m per day}$ . More days means less work per day!

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