Problem 39 - Prealgebra and Introductory Algebra

Question

Simplify. $$-18.39+4.9-23.7$$

Step-by-Step Solution

Answer

Therefore, the simplified result of -18.39 + 4.9 - 23.7 is -37.19.

Step 1: Understand the problem

We are given the expression -18.39 + 4.9 - 23.7. We have to simplify this and get a result by adding and subtracting these given decimal numbers. Note that between two addition/subtraction operations, the operation must be performed from left to right.

Step 2: Perform the first operation

Firstly, add -18.39 and 4.9. To simplify, you can consider this as subtracting 4.9 from -18.39. \(-18.39 + 4.9 = -13.49 \). After doing this step, our expression becomes \(-13.49 - 23.7\).

Step 3: Perform the second operation

Next, subtract 23.7 from -13.49. This is equivalent to adding -23.7 to -13.49. We get \(-13.49 - 23.7 = -37.19\).

Key Concepts

Decimal Numbers

Decimal numbers are numbers that are expressed using a decimal point to separate the whole part of the number from the fractional part. This is one of the most commonly used number systems, especially when dealing with money, measurements, and precise computations. When dealing with decimal numbers, it's important to remember:

• Each digit to the right of the decimal point represents a fraction of a whole number, often powers of ten (e.g., tenths, hundredths).
• Aligning the decimal points is crucial when adding or subtracting them; this ensures that digits of the same place value are lined up.
• Decimals can be simplified by removing trailing zeros. For instance, 3.500 can be simplified to 3.5 without any loss of value.

Understanding these basics can make it much easier to solve problems involving decimal operations.

Addition and Subtraction

Addition and subtraction are fundamental arithmetic operations, and they follow similar rules whether you're dealing with whole numbers or decimal numbers.

• For decimal numbers, the key is to line up the decimal points to maintain proper place value alignment. This makes the arithmetic straightforward and accurate.
• In addition, start from the rightmost digit and move leftward, carrying over any extra value to the next place value if necessary.
• For subtraction, starting from the rightmost digit also helps, borrowing from the next left digit if needed.

In our example exercise with -18.39 + 4.9, we treat it as subtracting the smaller number from the larger one while keeping track of the negative sign. The operation becomes simpler when considering it as moving along a number line, where adding moves to the right, and subtracting moves to the left.

Order of Operations

Order of operations is a principal rule in mathematics that defines the order in which different operations (addition, subtraction, multiplication, division, etc.) should be performed to get correct results. For simple operations like addition and subtraction, the rule generally followed is "from left to right" unless parentheses indicate otherwise.

• This rule is important to ensure consistency in mathematical calculations and expressions.
• For the given expression -18.39 + 4.9 - 23.7, handle each operation in sequence from left to right, ensuring you apply subtraction and addition correctly as you proceed.
• Complex expressions might require paying attention to additional rules such as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication/Division, Addition/Subtraction).

Consistently applying these rules ensures that the simplified answer to any expression is both accurate and universally confirmed.