Math Expressions: Calculate The Differences And Sums
Hey guys! Let's dive into some math problems where we'll be crafting expressions and crunching numbers. We're going to tackle differences, sums, and even throw in some odd and even number fun. Get your thinking caps on, and let's get started!
a) The Difference Between an Odd Number and 4,956
Okay, so this first problem is all about finding a difference. Specifically, we need to figure out the odd number that comes right after 35,749 and then subtract 4,956 from it. Sounds like a plan, right?
First things first, what's the odd number that follows 35,749? Well, 35,749 itself is odd, so the very next number, 35,750, is even. That means we need to go one step further to 35,751. Bingo! That's our odd number.
Now, for the mathematical expression, we're looking at:
35,751 - 4,956 = ?
Let's break this down. When we subtract, we're finding the difference between two numbers. In this case, we want to know how much bigger 35,751 is compared to 4,956. You can set this up as a standard subtraction problem, making sure to align the place values (ones, tens, hundreds, etc.).
When you perform the subtraction, you'll find that:
35,751 - 4,956 = 30,795
So, the difference between the odd number following 35,749 and 4,956 is 30,795. See? We nailed it! It’s all about breaking the problem down step-by-step. Always identify the key information – in this case, spotting the odd number and understanding we needed to find a difference through subtraction. Keep practicing these steps, and these kinds of problems will become second nature. The key takeaway here is to carefully read the problem and pull out the important details before you even start calculating. This approach is super helpful for all sorts of math challenges, not just these specific ones. Math isn't about just crunching numbers; it’s about understanding what the numbers represent and how they relate to each other.
b) Sum of 67,365 and the Difference Between 793,475 and 356,723
Alright, let's tackle the next part of our mathematical adventure! This time, we're dealing with both a sum and a difference, so we've got a two-part calculation ahead of us. We need to add 67,365 to the result of subtracting 356,723 from 793,475. Don't worry; we'll take it one step at a time.
First up, let's find the difference between 793,475 and 356,723. Remember, the difference means we need to subtract. So, our first expression is:
793,475 - 356,723 = ?
Go ahead and set that up like a regular subtraction problem, making sure those place values are lined up neatly. When you subtract, you should get:
793,475 - 356,723 = 436,752
Great! We've got the difference. Now, the second part of the problem asks us to find the sum of 67,365 and this difference we just calculated. Sum, of course, means addition. So, our next expression is:
67,365 + 436,752 = ?
Set this up as an addition problem, again making sure your place values are aligned. When you add these numbers together, you'll find:
67,365 + 436,752 = 504,117
So, the final answer is 504,117. How cool is that? We took a problem that looked a little complex and broke it down into smaller, manageable steps. This is a fantastic strategy for tackling math problems (and really, lots of other kinds of problems too!). When you see something that looks intimidating, try to identify the individual pieces and solve them one by one. Think of it like climbing a ladder – you focus on one rung at a time, and before you know it, you're at the top. Always remember, the key is to carefully identify what operations you need to perform (subtraction for difference, addition for sum) and then work through them in the correct order. With practice, you'll become a pro at these multi-step calculations!
c) Sum of the Largest Four-Digit and Five-Digit Even Numbers
Okay, mathletes, let's wrap things up with a challenge that involves finding the largest even numbers within specific digit ranges and then adding them together. This one’s going to test our understanding of place value and what makes a number even.
So, we need to find: a) the largest four-digit even number and b) the largest five-digit even number, and then we need to find their sum. Let's start by figuring out those numbers.
What's the largest four-digit number you can think of? Most people would say 9,999. But wait! There's a catch. We need an even number. Remember, even numbers are divisible by 2. 9,999 is odd (it ends in a 9), so it won't work for us. To get the largest even number, we need to go down one from 9,999. That gives us 9,998. Perfect! 9,998 is the largest four-digit even number.
Now, let's tackle the five-digit number. What's the biggest five-digit number in general? It's 99,999. But just like before, this is an odd number. To make it even, we simply subtract 1, resulting in 99,998. That's our largest five-digit even number!
Alright, we've identified our players: 9,998 and 99,998. The problem asks for the sum, so we need to add these two numbers together. The expression looks like this:
9,998 + 99,998 = ?
Set this up as an addition problem, being extra careful to align your place values correctly (thousands with thousands, hundreds with hundreds, and so on). When you add them together, you get:
9,998 + 99,998 = 109,996
Therefore, the sum of the largest four-digit and five-digit even numbers is 109,996. Awesome job! We conquered another math problem by thinking carefully about what the question asked. We had to remember what makes a number even and then apply our knowledge of place value to find the largest numbers within the given constraints. These kinds of problems are a great way to solidify your understanding of different mathematical concepts and how they relate to each other. Always remember to double-check your work and make sure your answer makes sense in the context of the problem. Keep up the great work, guys!
So, there you have it! We've worked through three different math problems, each with its own little twist. Remember, the key to solving these kinds of problems isn't just about knowing how to add and subtract; it's also about reading carefully, understanding what the problem is asking, and breaking it down into smaller, more manageable steps. Keep practicing, and you'll become a math whiz in no time!
