Question

Find the sum. $$6.8+3.3+(-4.1)$$

Short answer

The sum of \(6.8, 3.3\) and \(-4.1\) is \(6\).

Step-by-step solution

Identify the numbers

The numbers given here are \(6.8, 3.3, -4.1\).

Add the positive numbers

Firstly, add the positive numbers \(6.8 + 3.3\) which equals to \(10.1\).

Subtract the negative number

Next, subtract the absolute value of the negative number from the result obtained from the previous step. That is \(10.1 - 4.1\).

Find the final sum

Perform the subtraction to get the final answer. \(10.1 - 4.1 = 6\)

Key concepts

Decimal Addition

Understanding decimal addition is fundamental in arithmetic and it's often one of the first steps when coming across math problems involving numbers with fractions. To add decimals effectively, align the numbers by their decimal points and sum up each column as you would with whole numbers, carrying over any excess to the next column when needed. Consider the example from the exercise:

When adding the positive numbers 6.8 and 3.3, align the decimal points and add column by column:

  6.8
+ 3.3
-------
10.1

The result is 10.1. This is a straightforward process similar to addition without decimals, just remember to keep the decimal points lined up!

Adding decimals properly is a valuable skill in everyday life, such as when managing finances or measuring quantities.

Subtracting Negative Numbers

Subtracting negative numbers can be a bit confusing, but there's a simple rule that makes it much easier: when you subtract a negative number, it's the same as adding the positive version of that number. This is because subtraction of a negative number reverses the negative into a positive. This concept is fundamental to understanding and solving many types of math problems.

Let's return to the exercise. After adding the positive decimals, we have 10.1. The next step is to subtract -4.1 from this sum:

10.1
-(-4.1)
---------
10.1 + 4.1

Here, the double negative turns into a positive, leading to simply adding 4.1 to 10.1, resulting in 6 as the final answer.

Arithmetic Operations

Mastering arithmetic operations is crucial for further study in mathematics and practical application in real-life situations. Arithmetic involves not only the ability to perform operations such as addition and subtraction but also the understanding of the rules that govern these operations, particularly when it comes to dealing with positive and negative numbers.

In our current exercise, we applied these principles by first adding positive numbers, which is a direct operation, and then dealing with the subtraction of a negative number. The sequence in which we perform these operations is important, especially as math problems become more complex. Using methods like the above ensures accuracy and helps in building a strong mathematical foundation.

In conclusion, arithmetic operations form the groundwork for problem-solving in math. They are essential, from simple calculations to complex equations, making them a vital part of a student's educational journey.