Problem 68 - Algebra 1: Concepts and Skills

Question

Evaluate the expression $$ 1.4-6.2-9.1 $$

Step-by-Step Solution

Answer

The answer to the expression '1.4-6.2-9.1' is -13.9.

Step 1: Identify the operation

The instruction '1.4-6.2-9.1' involves two subtraction operations which should be performed from left to right.

Step 2: Perform the first operation

Subtraction is performed between the first two numbers: \(1.4 - 6.2 = -4.8\).

Step 3: Perform the second operation

The result of the first operation (-4.8) is then subtracted from the third number: \(-4.8 - 9.1 = -13.9\).

Key Concepts

Subtraction of Decimals

Understanding how to subtract decimals is a fundamental aspect of arithmetic, pivotal when working with money, measurements, and various scientific calculations where precision is essential. When subtracting decimal numbers, it's important to align the decimal points vertically. This ensures every digit is subtracted from its counterpart in the correct place value.

For example, in the operation presented in the exercise, when you align 1.4 and 6.2:

• Start from the rightmost digit, which is in the tenths place.
• Subtract each digit in the tenths place.
• If necessary, borrow from the next left digit in the units place, and continue the subtraction.

After performing the subtraction operations properly, you find that 1.4 minus 6.2 results in -4.8, as decimals allow for negative results. It confirms correctness, suggesting the calculation acknowledges the value of the difference and the relative positions of each number on the number line.

Order of Operations

The order of operations, often simplified by the acronym PEMDAS or BODMAS, provides a consistent framework for solving mathematical expressions. It stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

For the given exercise, we only need to focus on the last part: addition and subtraction. These should be carried out sequentially from left to right, as they appear in the expression. Hence, after subtracting 6.2 from 1.4, we then proceed to subtract 9.1 from the result of the first operation. Therefore, despite subtraction being the only operation in question, the sequence in which we perform these operations is crucial to arriving at the correct result, -13.9.

Arithmetic Operations

Arithmetic operations form the cornerstone of mathematics and consist of addition, subtraction, multiplication, and division. These operations are the building blocks for more complex mathematical concepts. Each operation has a specific set of rules that govern their execution.

When focusing on subtraction, it's key to remember the following points:

• Subtraction is not commutative, which means that changing the order changes the result (e.g., 7 - 5 is not the same as 5 - 7).
• The operation can yield negative numbers.
• Absorbing the rules of subtraction within the broad scope of arithmetic is necessary for computational fluency.

To reiterate, with the given expression, we start by subtracting the second number from the first and then we subtract the third number from that result, fully aligning with predefined arithmetic protocols.