Solving Math Expressions: A Step-by-Step Guide

by Dimemap Team 47 views

Hey guys! Let's dive into solving some math expressions today. We're going to break down the steps and make it super easy to understand. Our main goal is to take these word problems, turn them into math equations, and then find the answers. We'll tackle three different problems, so you'll get plenty of practice. Ready? Let's jump in!

1) Adding Sums: -1.4 + 3.7 and 5.3 + -7.6

In this first problem, we need to add the sum of two sets of numbers. The key here is to take it one step at a time. First, let’s focus on the sum of -1.4 and 3.7. Think of this as combining a debt of 1.4 with a gain of 3.7. What do we get?

The expression for this part is: (-1.4) + 3.7. To solve it, we subtract the absolute values (3.7 - 1.4) which equals 2.3. Since 3.7 is greater and positive, the result is positive 2.3. Great! We've nailed the first part.

Next up, we need to find the sum of 5.3 and -7.6. This is another addition problem, but this time we're adding a positive and a negative number. The expression here is: 5.3 + (-7.6). Again, think of it as combining a gain of 5.3 with a debt of 7.6. To solve, we subtract the absolute values (7.6 - 5.3) which gives us 2.3. But remember, 7.6 is greater and negative, so our result is negative 2.3.

Now, we're at the final step. The problem asks us to add these two sums together. So, we're adding the result from the first part (2.3) to the result from the second part (-2.3). The expression is: 2.3 + (-2.3). What happens when you add a number and its negative? They cancel each other out! So, the final answer here is 0.

Let's recap quickly:

  1. Sum of -1.4 and 3.7 = 2.3
  2. Sum of 5.3 and -7.6 = -2.3
  3. Add the sums: 2.3 + (-2.3) = 0

So, the value of the entire expression is 0. See? Breaking it down makes it much simpler.

2) Combining Sums: 7.24 + 5.16 and -15.3 + -6.2

Alright, let's tackle our second problem! This one is similar to the first, but with slightly different numbers. Again, we're asked to add the sums of two sets of numbers. Our first task? Find the sum of 7.24 and 5.16. This is a straightforward addition, guys. The expression is 7.24 + 5.16.

Let's add these up: 7. 24 + 5.16 = 12.40. So, the sum of 7.24 and 5.16 is 12.40. Easy peasy!

Now, let’s find the sum of -15.3 and -6.2. When we're adding negative numbers, it’s like adding debts. The expression here is: (-15.3) + (-6.2). Both numbers are negative, so we're essentially adding their absolute values and keeping the negative sign. So, 15. 3 + 6.2 = 21.5. Since both numbers were negative, the result is -21.5.

We're almost there! The final step is to add these two sums together. So, we need to add 12.40 and -21.5. The expression is: 12.40 + (-21.5). This is like combining a gain of 12.40 with a debt of 21.5. To solve, we subtract the absolute values (21.5 - 12.40) which equals 9.1. But remember, 21.5 is greater and negative, so the result is negative 9.1.

Let's quickly summarize:

  1. Sum of 7.24 and 5.16 = 12.40
  2. Sum of -15.3 and -6.2 = -21.5
  3. Add the sums: 12.40 + (-21.5) = -9.1

So, the final value of this expression is -9.1. You're getting the hang of this, right?

3) Sum and Difference: 40.2 + -8.4 and the Difference of Numbers

Okay, let’s move on to our third and final problem. This one introduces a slight twist – we're dealing with both a sum and a difference. First, we need to find the sum of 40.2 and -8.4. This is like the problems we’ve already tackled. The expression is: 40.2 + (-8.4).

Think of this as combining a gain of 40.2 with a debt of 8.4. To solve, we subtract the absolute values (40.2 - 8.4). Let's do that: 40. 2 - 8.4 = 31.8. Since 40.2 is greater and positive, our result is positive 31.8. Got it!

The problem also asks us to add this sum to the difference of numbers. But wait, the sentence ends abruptly. We need more information! It seems like there's some missing information in the original problem. We can't complete this without knowing what numbers we're finding the difference between.

However, let’s discuss how we would approach this if we had that information. Suppose the problem had said: “add the sum of the numbers 40.2 and -8.4 to the difference of the numbers 10 and 5.” Then we'd proceed like this:

First, find the difference between 10 and 5: 10 - 5 = 5. Then, add this difference to the sum we already calculated (31.8): 31.8 + 5 = 36.8.

If we had those numbers, the final answer would be 36.8. But since we don't have the complete problem, we can only solve the first part.

So, for the part we can solve, the sum of 40.2 and -8.4 is 31.8.

Wrapping Up

Awesome work, guys! We've walked through how to break down math expressions, handle sums and differences, and even tackle problems with both positive and negative numbers. Remember, the key is to take it step by step, and don't be afraid of those negative signs! Once you practice a bit, you'll be solving these like a pro.

If you have any questions or want more practice, let me know. Keep up the great work, and I'll catch you in the next one!