Problem 45 - Basic College Mathematics

Question

Simplify. $$ 6.1-4.32+0.8 $$

Step-by-Step Solution

Answer

2.58

Step 1 - Understand the problem

Simplifying the expression involves performing addition and subtraction operations on the given numbers: 6.1, -4.32, and 0.8.

Step 2 - Add 6.1 and 0.8

First, add 6.1 and 0.8. The calculation is: \[ 6.1 + 0.8 = 6.9 \]

Step 3 - Subtract 4.32 from the result

Now, subtract 4.32 from the sum obtained in Step 2. The calculation is: \[ 6.9 - 4.32 \] We can perform the subtraction by lining up the decimal points: \[ 6.90 \]\[ -4.32 \]\[ 2.58 \]

Key Concepts

Addition and Subtraction

Addition and subtraction are the basic operations of arithmetic. These operations are essential to learn and understand as they form the foundation for more complex math topics.
When adding or subtracting numbers, it is important to line up the digits according to their place values (units, tenths, hundredths, etc.).
This way, you can ensure that your calculations are accurate.
For instance, when working with decimal numbers, ensure that you align the decimal points directly one above the other.
In our example, we first add 6.1 and 0.8 which results in 6.9. Then, we subtract 4.32 from 6.9 by placing the numbers such that their decimal points are aligned perfectly.

Decimal Numbers

Decimal numbers are a way of representing fractions or numbers that are not whole.
They have a whole number part and a fractional part, separated by a decimal point.
For example, in the number 6.1, '6' is the whole number part, and '1' is the fractional part.
Understanding how to work with decimal numbers is crucial when performing arithmetic operations like addition and subtraction.
In our problem, we worked with the decimal numbers 6.1, 0.8, and 4.32. It was important to ensure we aligned the decimal points correctly to get accurate results.
The alignment of decimal points ensures that each digit is in the correct place value, which helps in accurate calculations.

Step-by-Step Solution

Following a step-by-step solution helps break down complex problems into manageable parts.
Let's see the three main steps used to solve our exercise:

Step 1: Understand the problem. Know that you need to perform addition and subtraction on 6.1, -4.32, and 0.8.

Step 2: Add 6.1 and 0.8. First, align the decimal points and then perform the addition: \( 6.1 + 0.8 = 6.9 \).

Step 3: Subtract 4.32 from 6.9. Again, align the decimal points and then perform the subtraction:
\[ 6.90\]
\[ -4.32\]
\[ 2.58\]

Through these steps, we can simplify the expression accurately. Always take it one step at a time and verify your results.