Math Challenge: Which Expression Yields The Highest Value?
Hey guys! Let's dive into a fun math challenge where we'll be calculating some expressions and figuring out which one gives us the biggest number. We'll also tackle a word problem about comparing the lengths of travel books. So, grab your calculators (or your mental math skills!) and let's get started!
Expression Evaluation: Finding the Highest Value
In this section, we're going to break down each expression step-by-step, making sure we follow the order of operations (PEMDAS/BODMAS, if you remember that!). Our main goal here is to accurately calculate each one and then compare the results to find the ultimate winner – the expression with the highest value. It's like a mathematical race, and we're the judges!
Evaluating Expression A
Let's start with expression A: (31 500-900)-5-46 800: 9. The first crucial step in solving this expression is understanding and applying the order of operations correctly. Remember PEMDAS/BODMAS? It tells us the sequence in which we should perform calculations: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). Adhering to this order is essential for arriving at the correct answer.
So, following the order of operations, we'll first handle the parentheses. Inside the parentheses, we have 31 500 - 900. Doing this subtraction, 31,500 minus 900 equals 30,600. Now our expression looks like this: 30600 - 5 - 46 800 : 9.
Next up, according to PEMDAS/BODMAS, we need to tackle any division before we do subtraction. We have 46 800 divided by 9. When we perform this division, 46,800 ÷ 9 equals 5,200. So, we can update the expression again, and it now reads: 30600 - 5 - 5200.
Now we're left with only subtraction operations. We perform subtraction from left to right. First, we subtract 5 from 30,600, which gives us 30,595. The expression simplifies to: 30595 - 5200.
Finally, we subtract 5,200 from 30,595. Performing this final subtraction, 30,595 minus 5,200, we get 25,395. So, the value of expression A is 25,395.
In summary, by carefully following the order of operations (PEMDAS/BODMAS), we've successfully evaluated expression A. We started by subtracting within the parentheses, then performed the division, and finally completed the subtraction operations from left to right. This methodical approach is key to solving mathematical expressions accurately. The result we obtained for expression A is 25,395, which we'll use later when we compare it with the values of expressions B and C to determine which expression has the highest value.
Tackling Expression B
Now, let's move on to expression B: 581 000:7-100-400000. Just like with expression A, we need to carefully follow the order of operations to get the correct result. Remembering PEMDAS/BODMAS will be our guiding principle here.
Looking at expression B, the first operation we need to perform is the division, as it comes before subtraction in the order of operations. We have 581 000 divided by 7. When we do this division, 581,000 ÷ 7 equals 83,000. So, we can rewrite the expression as: 83000 - 100 - 400000.
Now we're left with a series of subtractions. We'll perform these subtractions from left to right. First, we subtract 100 from 83,000. Doing this, 83,000 minus 100 gives us 82,900. Our expression now looks like: 82900 - 400000.
Finally, we need to subtract 400,000 from 82,900. This is where things get interesting because we're subtracting a larger number from a smaller number, which will give us a negative result. When we subtract 400,000 from 82,900, we get -317,100. So, the value of expression B is -317,100.
To recap, we've evaluated expression B by first performing the division and then carrying out the subtractions from left to right. The important thing to note here is that the result is a negative number. This is perfectly valid, but it means that when we compare the values of the expressions later, expression B will likely be the smallest since it's negative.
Cracking Expression C
Alright, let's dive into expression C: 2 450 000:5:8+10000 - 90. By now, we know the drill – we're going to follow the order of operations (PEMDAS/BODMAS) to make sure we calculate this one accurately. Get ready to put those math skills to the test!
Looking at expression C, we see that we have a series of divisions, an addition, and a subtraction. According to the order of operations, we need to perform the divisions first. We have 2 450 000 divided by 5, and then the result of that division divided by 8. Let's tackle these one at a time.
First, let's divide 2,450,000 by 5. When we do this division, 2,450,000 ÷ 5 equals 490,000. Now our expression looks like this: 490000 : 8 + 10000 - 90.
Next up, we need to divide 490,000 by 8. Performing this division, 490,000 ÷ 8 gives us 61,250. So, the expression simplifies to: 61250 + 10000 - 90.
Now we have addition and subtraction left. We perform these operations from left to right. First, we add 10,000 to 61,250. Doing this addition, 61,250 plus 10,000 equals 71,250. The expression now reads: 71250 - 90.
Finally, we subtract 90 from 71,250. Performing this subtraction, 71,250 minus 90, we get 71,160. So, the value of expression C is 71,160.
To sum it up, we've carefully evaluated expression C by following the order of operations. We performed the divisions from left to right, then the addition, and finally the subtraction. This step-by-step approach is crucial for ensuring accuracy in mathematical calculations. The result we obtained for expression C is 71,160, which we'll now compare with the values of expressions A and B.
Comparing and Contrasting: The Grand Finale
Now that we've done the hard work of calculating expressions A, B, and C, it's time for the exciting part: comparing their values to see which one reigns supreme! This is where all our careful calculations pay off, and we get to see the final results of our mathematical journey.
Let's remind ourselves of the values we found for each expression:
- Expression A: 25,395
- Expression B: -317,100
- Expression C: 71,160
When we look at these numbers, the first thing that jumps out is that Expression B is a negative number. Remember, negative numbers are always smaller than positive numbers, so we can immediately say that Expression B is the smallest of the three. It's like being in debt – not a great place to be in this mathematical competition!
Now we need to compare Expression A and Expression C. Expression A has a value of 25,395, while Expression C has a value of 71,160. It's pretty clear that 71,160 is much larger than 25,395. So, Expression C is the winner!
Therefore, after evaluating and comparing all three expressions, we can confidently say that Expression C (2 450 000:5:8+10000 - 90) has the highest value.
Word Problem: Aziza's Travel Books
Let's switch gears a bit and tackle a word problem. These are like little stories with a mathematical twist, and they're a great way to see how math applies to real-life situations. In this case, we're going to help Aziza compare the lengths of her travel books.
Understanding the Problem
Here's the problem: Aziza compared 3 travel books. The first book has 51,200 words, and the second book has 3,200 fewer words than the first. We need to figure out how many words are in the second book.
Solving the Word Count
This problem is actually quite straightforward once we break it down. The key phrase here is "3,200 fewer words." This tells us that we need to subtract 3,200 from the number of words in the first book to find the number of words in the second book.
So, we'll take the number of words in the first book (51,200) and subtract 3,200 from it. The equation looks like this: 51200 - 3200 = ?
When we do the subtraction, 51,200 minus 3,200 equals 48,000. So, the second book has 48,000 words.
The Final Word (Count) on Aziza's Books
We've successfully solved the word problem! By carefully reading the problem and identifying the key information ("3,200 fewer words"), we knew that we needed to subtract. This is a crucial skill in problem-solving – understanding what the words are telling you to do mathematically.
So, to recap, the first book has 51,200 words, and the second book has 48,000 words. Great job, guys!
Conclusion: Math Adventures!
Wow, we've covered a lot in this math challenge! We tackled some complex expressions, carefully following the order of operations to find the highest value. We also dove into a word problem, using our subtraction skills to compare the lengths of Aziza's travel books. Math can be an adventure, and you guys aced it!
Remember, the key to math success is to take things step-by-step, pay attention to the details, and don't be afraid to ask questions. Keep practicing, keep exploring, and who knows what mathematical discoveries you'll make next! Keep up the awesome work!
