Problem 13 - Algebra A Combined Function

Question

Subtract. \(16-(-21)\)

Step-by-Step Solution

Answer

The result is 37.

Step 1: Recognize the Operation

The operation given is subtraction of a negative number: \(16 - (-21)\). When you subtract a negative number, it is the same as adding its positive counterpart.

Step 2: Convert Subtraction to Addition

Rewrite the expression \(16 - (-21)\) as \(16 + 21\). This changes the subtraction of a negative to the addition of a positive.

Step 3: Perform the Addition

Now, add the numbers together: \(16 + 21\). Add the ones first: \(6 + 1 = 7\). Then add the tens: \(1 + 2 = 3\). This gives us \(37\).

Step 4: Check Your Work

Verify your result to ensure accuracy. Adding \(16\) and \(21\) indeed gives \(37\), so our result is correct.

Key Concepts

Addition of Integers

When it comes to adding integers, remember this simple rule: adding a positive number moves you further to the right on the number line, while adding a negative number moves you to the left. In the context of integer addition, this means:

• If you add two positive integers, you'll get a positive sum.
• If you add two negative integers, the result is also negative.
• If you add a positive and a negative integer, you'll need to find the difference between their absolute values, and the sign of the larger absolute value will be the sign of the sum.

Understanding this concept can help when converting and managing operations, like turning subtraction of a negative integer into addition. For instance, subtracting -21 is the same as adding +21, simplifying our original problem into a straightforward addition task: 16 + 21.

Integer Operations

Integer operations encompass addition, subtraction, multiplication, and division involving whole numbers. To confidently perform these operations, one must understand their rules and how integers interact positively and negatively. Here's a brief rundown:

• Addition: Combine values, respecting their signs. Positive with positive yields a positive sum, and negative with negative results in a negative sum.
• Subtraction: Often transform it into addition by changing the sign of the number being subtracted. This trick simplifies the operation and reduces errors.
• Multiplication and Division: With two integers, the sign of the result depends on the signs involved. Equal signs yield positive results, while opposite signs produce negative results.

Knowing these rules helps in solving problems more efficiently and understanding the nature of any arithmetic expression.

Mathematical Expressions

Mathematical expressions are combinations of numbers, operators, and sometimes variables arranged in a meaningful way to represent calculations. To simplify and interpret these expressions, certain conventions are followed:

• Parentheses: Operations within parentheses are performed first.
• Order of Operations: Follow PEMDAS/BODMAS rules (Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction).
• Equivalent Expressions: Expressions that yield the same result are considered equivalent, such as changing subtraction of a negative to addition of a positive in 16 - (-21).

By mastering these guidelines, tackling mathematical expressions becomes much easier, making complex problems simpler to handle.