Math Problem: Converting Cm And Mm To Meters

Let's break down this math problem step by step, guys! We need to figure out what number fills in the blank in the equation: 400 cm + 500 mm = ... m. The options are a) 405, b) 40.5, c) 4.5, and d) 0.45. Don't worry, it's not as tricky as it looks! We just need to make sure we're all on the same page with our units of measurement.

Understanding the Units

First, let's quickly recap the relationships between centimeters (cm), millimeters (mm), and meters (m). This is super important for getting the right answer. Remember these conversions:

• 1 meter (m) = 100 centimeters (cm)
• 1 centimeter (cm) = 10 millimeters (mm)
• 1 meter (m) = 1000 millimeters (mm)

Knowing these conversions is like having a secret decoder ring for this problem! Now, let's get to solving it. Let's dive into converting everything into meters so we can easily add them together. We're aiming to express both 400 cm and 500 mm in terms of meters. Once we've done that, a simple addition will give us our answer.

To convert 400 cm to meters, we use the conversion factor 1 m = 100 cm. So, we divide 400 by 100:

400 cm ÷ 100 = 4 meters

Next, we need to convert 500 mm to meters. We know that 1 m = 1000 mm. Therefore, we divide 500 by 1000:

500 mm ÷ 1000 = 0.5 meters

Now that both values are in meters, we can add them together:

4 meters + 0.5 meters = 4.5 meters

Therefore, the missing number is 4.5, which corresponds to option c).

Converting to Meters

The key to solving this problem is converting everything to the same unit – in this case, meters. We have 400 cm and 500 mm. Let's convert each of these to meters individually.

• Converting 400 cm to meters: To convert centimeters to meters, we divide by 100 (since there are 100 cm in 1 meter). So, 400 cm / 100 = 4 meters.
• Converting 500 mm to meters: To convert millimeters to meters, we divide by 1000 (since there are 1000 mm in 1 meter). So, 500 mm / 1000 = 0.5 meters.

Now that we have both values in meters, we can simply add them together:

4 meters + 0.5 meters = 4.5 meters

So, 400 cm + 500 mm = 4.5 m.

The Answer

Looking at our options, we see that the correct answer is:

c) 4.5

Therefore, the number that should fill in the blank is 4.5.

Why the Other Options Are Wrong

It's also helpful to understand why the other options are incorrect. This helps reinforce your understanding of unit conversions.

• a) 405: This is way off! It seems like someone might have just added the numbers without converting the units first. You can't just add centimeters and millimeters directly without converting them to the same unit.
• b) 40.5: This is also incorrect. It's closer to the right answer, but still not quite there. Maybe a mistake was made in the conversion process.
• d) 0.45: This is too small. It's possible someone divided instead of multiplied, or mixed up the conversion factors. It's important to double-check your work to avoid these kinds of errors.

Key Takeaways

• Always pay attention to units: Units are super important in math and science. Make sure you're always working with the same units before adding or subtracting.
• Know your conversions: Memorize the common conversions between units, like centimeters, millimeters, and meters. This will make these types of problems much easier.
• Double-check your work: It's always a good idea to double-check your work, especially when dealing with unit conversions. A small mistake can lead to a wrong answer.

Real-World Applications

Understanding unit conversions isn't just for math class! It's actually really useful in everyday life. For example:

• Home improvement: When you're measuring for furniture or calculating how much paint to buy, you need to be able to convert between different units of measurement.
• Cooking: Recipes often use different units of measurement, like cups, ounces, and milliliters. Knowing how to convert between these units is essential for following recipes accurately.
• Travel: When you're traveling to a different country, you may need to convert between miles and kilometers, or between Fahrenheit and Celsius.

So, mastering unit conversions is a valuable skill that will serve you well in many different situations.

Practice Problems

Want to test your understanding of unit conversions? Try these practice problems:

1. 250 cm + 750 mm = ? m
2. 1.5 m - 80 cm = ? cm
3. 3000 mm + 2 m = ? m

Answers:

1. 3.25 m
2. 70 cm
3. 5 m

Conclusion

So, there you have it! The answer to the question "What number should fill in the blank? 400 cm + 500 mm = ... m" is 4.5. Remember to always pay attention to units, know your conversions, and double-check your work. With a little practice, you'll become a unit conversion master in no time! Keep practicing, and you'll be a math whiz in no time! Math can be fun, and mastering these basic concepts is super helpful in everyday life. Keep up the great work, everyone!