Problem 45 - Algebra 1: Concepts and Skills

Question

Find the sum. $$5.4+2.6+(-3)$$

Step-by-Step Solution

Answer

The sum of 5.4, 2.6, and -3 is 5.0.

Step 1: Adding decimals

Add the two decimal numbers together: \(5.4 + 2.6 = 8.0\).

Step 2: Subtracting a negative

Subtract the negative integer from the result of step 1: \(8.0 - 3 = 5.0\).

Key Concepts

Addition of Decimals

Understanding how to add decimal numbers is vital for solving a wide range of mathematical problems, from simple arithmetic to complex equations. When adding decimals, it's important to align the decimal points vertically before carrying out the addition. This ensures each place value (tenths, hundredths, thousandths, etc.) is correctly lined up.

For example, if you have to add the numbers 5.4 and 2.6, you would align the decimal points and add as if they were whole numbers, taking care to put the decimal point in the result directly below the decimal points in the numbers being added:

• 5.4
• + 2.6
• -----
• = 8.0

Notice how the decimal places are stacked on top of each other. This process helps to avoid confusion and enables us to arrive at a precise sum. In this case, adding the tenths place, 4 + 6 equals 10, which we record as 0 with a carryover of 1 to the ones place. The final result is 8.0.

Subtracting Integers

Subtracting integers, whether they are positive or negative, follows specific rules that help maintain the correct number value and direction. To subtract a positive integer from another number, you can think of it as 'taking away' or moving to the left on a number line.

The process involves subtracting each digit starting from the rightmost end, moving towards the left, and borrowing from the next left digit when necessary. For instance:

• If you have the number 8.0 and need to subtract 3, simply decrease the total amount by 3.
• This looks like: 8.0 - 3
• Which becomes: 5.0

It's straightforward when subtracting whole numbers, but it's critical to manage borrowing correctly when dealing with mixed integers (numbers which have both whole numbers and decimal portions).

Negative Numbers Arithmetic

Arithmetic with negative numbers can be a bit puzzling at first, but some simple rules help to demystify this topic. When adding a negative number, it is equivalent to subtracting its absolute value. The absolute value is the distance of the number from zero without considering its sign, so the absolute value of -3 is 3.

For example, when we add -3 to 8.0, it's similar to subtracting 3 from 8.0:

• 8.0 + (-3) = 8.0 - 3
• Resulting in 5.0

Remember, adding a negative number moves you left on a number line, while adding a positive number moves you right. In this course, always keep an eye on the signs of the numbers you're working with and apply these guidelines to handle negative numbers correctly.