Solve: ${5.12 + 3.79}$

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Introduction

In mathematics, addition is one of the fundamental operations that involves combining two or more numbers to get a total or a sum. It is a basic arithmetic operation that is used in various mathematical expressions and equations. In this article, we will focus on solving a simple addition problem, which is $5.12 + 3.79$. We will break down the problem step by step and provide a clear explanation of the solution.

Understanding the Problem

The problem $5.12 + 3.79$ involves adding two decimal numbers. To solve this problem, we need to understand the concept of decimal numbers and how to add them. Decimal numbers are numbers that have a decimal point, which separates the whole number part from the fractional part. In this problem, we have two decimal numbers: $5.12$ and $3.79$.

Step 1: Line Up the Numbers

To add decimal numbers, we need to line up the numbers correctly. We start by lining up the decimal points of the two numbers. In this case, the decimal points are already lined up.

  5.12
+ 3.79

Step 2: Add the Numbers

Next, we add the numbers. We start by adding the numbers in the ones place (the rightmost digit). In this case, we have $2 + 9$, which equals $11$. However, since we are dealing with decimal numbers, we need to carry over the $1$ to the tenths place.

  5.12
+ 3.79
------
  8.91

Step 3: Add the Tenths Place

Now, we add the numbers in the tenths place. In this case, we have $1 + 7$, which equals $8$. We write the $8$ in the tenths place.

  5.12
+ 3.79
------
  8.91

Step 4: Add the Hundredths Place

Finally, we add the numbers in the hundredths place. In this case, we have $0 + 9$, which equals $9$. We write the $9$ in the hundredths place.

  5.12
+ 3.79
------
  8.91

Conclusion

In conclusion, the solution to the problem $5.12 + 3.79$ is $8.91$. We broke down the problem step by step and provided a clear explanation of the solution. We lined up the numbers correctly, added the numbers in the ones place, tenths place, and hundredths place, and obtained the final answer.

Tips and Tricks

Here are some tips and tricks to help you solve addition problems with decimal numbers:

• Always line up the decimal points of the two numbers correctly.
• Add the numbers in the ones place, tenths place, and hundredths place separately.
• Carry over any numbers that are greater than $9$ to the next place value.
• Use a calculator or a computer program to check your answer.

Real-World Applications

Addition with decimal numbers has many real-world applications. For example, in finance you may need to add two or more decimal numbers to calculate the total cost of a product or service. In science, you may need to add decimal numbers to calculate the total amount of a substance or the total distance traveled by an object.

Common Mistakes

Here are some common mistakes to avoid when solving addition problems with decimal numbers:

• Not lining up the decimal points correctly.
• Not adding the numbers in the correct place value.
• Not carrying over numbers that are greater than $9$.
• Not using a calculator or a computer program to check your answer.

Conclusion

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Q: What is the correct order of operations when adding decimal numbers?

A: The correct order of operations when adding decimal numbers is to line up the decimal points, add the numbers in the ones place, tenths place, and hundredths place separately, and carry over any numbers that are greater than $9$ to the next place value.

Q: How do I add decimal numbers with different numbers of decimal places?

A: To add decimal numbers with different numbers of decimal places, you need to line up the decimal points by adding zeros to the number with fewer decimal places. For example, if you want to add $5.12$ and $3.79$, you would line up the decimal points like this:

  5.12
+ 3.79

Q: What is the difference between adding decimal numbers and adding whole numbers?

A: The main difference between adding decimal numbers and adding whole numbers is that decimal numbers have a decimal point, which separates the whole number part from the fractional part. When adding decimal numbers, you need to line up the decimal points and add the numbers in the correct place value.

Q: Can I use a calculator to add decimal numbers?

A: Yes, you can use a calculator to add decimal numbers. In fact, using a calculator can be a quick and easy way to check your answer. However, it's still important to understand the concept of decimal numbers and how to add them manually.

Q: What is the rule for adding decimal numbers with the same decimal place value?

A: When adding decimal numbers with the same decimal place value, you can add the numbers in that place value without carrying over to the next place value. For example, if you want to add $5.12$ and $3.79$, you can add the numbers in the tenths place like this:

  5.12
+ 3.79
------
  8.91

Q: Can I add decimal numbers with different signs?

A: Yes, you can add decimal numbers with different signs. When adding decimal numbers with different signs, you need to subtract the number with the negative sign from the number with the positive sign. For example, if you want to add $5.12$ and $-3.79$, you would subtract $3.79$ from $5.12$ like this:

  5.12
- 3.79
------
  1.33

Q: What is the rule for adding decimal numbers with a zero in the ones place?

A: When adding decimal numbers with a zero in the ones place, you can add the numbers in the tenths place without carrying over to the next place value. For example, if you want to add $5.00$ and $3.79$, you can add the numbers in the tenths place like this:

  5.00
+ 3.79
------
  8.79

Q: Can I add decimal numbers with a decimal point in the middle of the number?

A: Yes, you can add decimal with a decimal point in the middle of the number. When adding decimal numbers with a decimal point in the middle of the number, you need to line up the decimal points and add the numbers in the correct place value. For example, if you want to add $5.12.34$ and $3.79.56$, you would line up the decimal points like this:

  5.12.34
+ 3.79.56
------
  8.91.90

Conclusion

In conclusion, adding decimal numbers requires attention to detail and a clear understanding of the concept of decimal numbers. By following the steps outlined in this article, you can add decimal numbers with confidence. Remember to always line up the decimal points correctly, add the numbers in the correct place value, and carry over numbers that are greater than $9$ to the next place value.