Solving Addition And Subtraction Problems A Step-by-Step Guide
Hey guys! Are you ready to dive into some math problems? We're going to break down some addition and subtraction challenges, making sure you understand each step along the way. Whether you're prepping for an exam or just want to brush up on your skills, this guide will help you master these calculations. Let's get started!
A) 6786.98 + 87.654 + 37.98: Adding Decimals Like a Pro
When it comes to adding decimals, the key is alignment. Think of it as making sure everyone is standing in the right line before the race starts. You need to align the decimal points so that you're adding tenths to tenths, hundredths to hundredths, and so on. Let's break down this problem step by step to make it super clear.
First, write down the numbers, aligning the decimal points:
6786.98
87.654
+ 37.98
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Notice how each decimal point is right above the other? That's crucial. Now, some of you might be wondering what to do about those empty spaces. Well, we can fill them with zeros. Think of it as adding invisible placeholders so everything lines up perfectly. Our problem now looks like this:
6786.980
87.654
+ 37.980
--------
Much better, right? Now we can start adding column by column, from right to left. Start with the thousandths column (the last column on the right). We have 0 + 4 + 0, which equals 4. So, we write down 4 in the thousandths place.
Next, let's move to the hundredths column. We have 8 + 5 + 8, which equals 21. Write down the 1 in the hundredths place and carry over the 2 to the tenths column. Think of it as having too many hundredths to fit in one spot, so you pass some along to the next column.
In the tenths column, we have 9 + 6 + 9, plus the 2 we carried over, which equals 26. Write down the 6 in the tenths place and carry over the 2 to the ones column.
Now, let's tackle the ones column. We have 6 + 7 + 7, plus the 2 we carried over, which equals 22. Write down the 2 in the ones place and carry over the 2 to the tens column.
In the tens column, we have 8 + 3, plus the 2 we carried over, which equals 13. Write down the 3 in the tens place and carry over the 1 to the hundreds column.
Finally, in the hundreds column, we have 7 plus the 1 we carried over, which equals 8. Write down 8 in the hundreds place.
And in the thousands column, we simply have 6. So, we write down 6.
Now, let's put it all together:
6786.980
87.654
+ 37.980
--------
6912.614
So, 6786.98 + 87.654 + 37.98 = 6912.614. See? Not so scary when you break it down! Always remember to keep those decimals aligned, and you'll be adding like a math whiz in no time!
B) 567.23 + 234.567 + 128.542: Mastering Multi-Digit Decimal Addition
Alright, let's jump into another addition problem! This time, we're tackling 567.23 + 234.567 + 128.542. The same rules apply here as before: alignment is key. Decimals need to line up perfectly to ensure we're adding the correct place values together. Let’s walk through this step-by-step to make sure we nail it.
First, write down the numbers, aligning the decimal points. Remember those empty spaces? We'll fill them with zeros to keep everything neat and tidy. This makes the addition process much smoother and helps prevent errors.
567.230
234.567
+ 128.542
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Now that everything is aligned and our placeholders are in place, let's start adding column by column, moving from right to left. We'll begin with the thousandths column, which includes the digits 0, 7, and 2. Adding these together gives us 0 + 7 + 2 = 9. So, we write down 9 in the thousandths place.
Next, we move to the hundredths column. Here, we have 3 + 6 + 4. Adding these gives us 13. We write down the 3 in the hundredths place and carry over the 1 to the tenths column. Carrying over is essential when the sum of a column is greater than 9, as it ensures we account for the extra value in the next higher place value.
In the tenths column, we have 2 + 5 + 5, plus the 1 we carried over, which equals 13. Again, we write down the 3 in the tenths place and carry over the 1 to the ones column.
Now, let's tackle the ones column. We have 7 + 4 + 8, plus the 1 we carried over, giving us a total of 20. We write down the 0 in the ones place and carry over the 2 to the tens column.
Moving to the tens column, we have 6 + 3 + 2, plus the 2 we carried over, which equals 13. Write down the 3 in the tens place and carry over the 1 to the hundreds column.
Finally, in the hundreds column, we have 5 + 2 + 1, plus the 1 we carried over, which equals 9. So, we write down 9 in the hundreds place.
Let's put it all together and see our final sum:
567.230
234.567
+ 128.542
--------
930.339
So, 567.23 + 234.567 + 128.542 = 930.339. Great job! Remember, practice makes perfect. The more you work through these problems, the more comfortable you’ll become with decimal addition. Keep those decimals aligned, and you'll be adding multi-digit decimals like a pro in no time!
C) 7896.76 - 789.765: Subtracting Decimals with Precision
Now, let's switch gears and dive into subtraction. We're going to tackle 7896.76 - 789.765. Just like with addition, aligning those decimal points is super important. It ensures we're subtracting the correct place values from each other. So, let's break down this subtraction problem step by step to make sure we get it right.
First, we write down the numbers, making sure the decimal points are aligned. Notice that 7896.76 has only two decimal places, while 789.765 has three. To make things easier, we can add a zero to the end of 7896.76 so that both numbers have the same number of decimal places.
7896.760
- 789.765
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Now we’re ready to subtract. We start from the rightmost column, which is the thousandths place. We have 0 - 5. Since we can't subtract 5 from 0, we need to borrow from the hundredths place. The 6 in the hundredths place becomes 5, and the 0 in the thousandths place becomes 10. Now we have 10 - 5, which equals 5. So, we write down 5 in the thousandths place.
Next, we move to the hundredths place. We now have 5 - 6. Again, we can't subtract 6 from 5, so we need to borrow from the tenths place. The 7 in the tenths place becomes 6, and the 5 in the hundredths place becomes 15. Now we have 15 - 6, which equals 9. So, we write down 9 in the hundredths place.
Moving to the tenths place, we have 6 - 7. Once again, we need to borrow. We borrow from the ones place. The 6 in the ones place becomes 5, and the 6 in the tenths place becomes 16. Now we have 16 - 7, which equals 9. So, we write down 9 in the tenths place.
Now let's tackle the ones place. We have 5 - 9. We need to borrow again, this time from the tens place. The 9 in the tens place becomes 8, and the 5 in the ones place becomes 15. Now we have 15 - 9, which equals 6. We write down 6 in the ones place.
Moving to the tens place, we have 8 - 8, which equals 0. So, we write down 0 in the tens place.
In the hundreds place, we have 8 - 7, which equals 1. We write down 1 in the hundreds place.
Finally, in the thousands place, we simply have 7. So, we write down 7.
Let’s put it all together:
7896.760
- 789.765
--------
7106.995
So, 7896.76 - 789.765 = 7106.995. See, subtraction is all about borrowing and being precise. Keep practicing, and you’ll become a subtraction superstar!
D) 8567.54 - 2345.767: Mastering Decimal Subtraction with Borrowing
Okay, guys, let's dive into another subtraction problem! This time, we're tackling 8567.54 - 2345.767. Just like before, the key to success here is aligning those decimal points. When the decimals are aligned, we can ensure that we're subtracting the correct place values from each other. So, let's break down this problem step by step to make it super clear and easy to understand.
First things first, let's write down the numbers, making sure those decimal points are perfectly aligned. Notice that 8567.54 has only two decimal places, while 2345.767 has three. To make our subtraction process smoother, we can add a zero to the end of 8567.54. This way, both numbers have the same number of decimal places, which helps avoid any confusion.
8567.540
- 2345.767
--------
Now that everything is nicely aligned, we can start subtracting column by column, moving from right to left. Let's begin with the thousandths place. We have 0 - 7. Uh-oh, we can't subtract 7 from 0 without getting into negative numbers, so we need to borrow. We borrow 1 from the hundredths place. The 4 in the hundredths place becomes 3, and the 0 in the thousandths place becomes 10. Now we have 10 - 7, which equals 3. We write down 3 in the thousandths place.
Next up, the hundredths place. We now have 3 - 6. Again, we can't subtract 6 from 3, so we need to borrow. This time, we borrow 1 from the tenths place. The 5 in the tenths place becomes 4, and the 3 in the hundredths place becomes 13. Now we have 13 - 6, which equals 7. So, we write down 7 in the hundredths place.
Moving on to the tenths place, we have 4 - 7. We need to borrow again! We borrow 1 from the ones place. The 7 in the ones place becomes 6, and the 4 in the tenths place becomes 14. Now we have 14 - 7, which equals 7. We write down 7 in the tenths place.
Now, let's tackle the ones place. We have 6 - 5, which is nice and simple. It equals 1. So, we write down 1 in the ones place.
Moving to the tens place, we have 6 - 4, which equals 2. We write down 2 in the tens place.
In the hundreds place, we have 5 - 3, which equals 2. We write down 2 in the hundreds place.
Finally, in the thousands place, we have 8 - 2, which equals 6. We write down 6 in the thousands place.
Let’s put it all together and see our final result:
8567.540
- 2345.767
--------
6221.773
So, 8567.54 - 2345.767 = 6221.773. Fantastic! See, even with all that borrowing, if we take it step by step, we can solve any subtraction problem. Remember, practice is the name of the game. The more you work on these problems, the more confident you’ll become with decimal subtraction. Keep those decimals aligned, and you'll be subtracting like a math whiz in no time!
Final Thoughts: You've Got This!
So there you have it, guys! We've tackled some tricky addition and subtraction problems with decimals. Remember, the key is to align those decimal points, take it one step at a time, and don't be afraid to borrow when you need to. Math might seem tough sometimes, but with a little practice, you can conquer anything. Keep up the great work, and you'll be a math master before you know it!
