Problem 39 - Prealgebra

Question

Add the following numbers left to right. $$24+(-6)+(-8)$$

Step-by-Step Solution

Answer

The result is 10.

Step 1: Start with the first two numbers

The first two numbers we need to add are 24 and -6. Adding them involves subtracting 6 from 24. So, calculate \( 24 + (-6) = 24 - 6 = 18 \).

Step 2: Add the next number

Now that we have 18 from the first step, add it to the next number, which is -8. This involves subtracting 8 from 18.So, calculate \( 18 + (-8) = 18 - 8 = 10 \).

Key Concepts

Understanding Negative Numbers

Negative numbers can be puzzling at first, but you'll find them quite simple once you get the hang of it. In mathematics, negative numbers are numbers that are less than zero. They are usually denoted with a minus sign, such as -1, -2, or -6. When you add a negative number, it is essentially like subtracting its positive counterpart.

For instance, adding -6 is the same as subtracting 6. So, when you encounter an expression like 24 + (-6), you should read it as "24 minus 6." This notation helps in simplifying calculations, especially when multiple operations are involved.

Keep in mind:

• Negative numbers decrease the overall value.
• They behave oppositely to addition when paired with positive numbers.
• Visualizing them on a number line can help; moves to the left for negative values.

Step-by-Step Solutions for Clarity

Tackling math problems step-by-step is a great way to ensure you understand each part of the process. This method is particularly helpful with integer operations involving both positive and negative numbers. When you approach a problem like adding integers, breaking it down into steps can prevent confusion.

A step-by-step approach usually involves:

• Identifying the numbers and their signs.
• Performing operations sequentially rather than trying to solve it all at once.
• Checking each step to ensure accuracy before moving to the next one.

Step-by-Step Example

In the exercise, the problem 24 + (-6) + (-8) was solved by first tackling the addition of 24 and -6 separately from -8. By focusing on two numbers at a time, you reduce the chance of making mistakes and make the math more manageable. Start with 24 and -6, and you simplify by recognizing it as a subtraction, leading to 18. Then, take 18 and handle the next number, -8, similarly. This breakdown makes each step clear and manageable.

Mastering the Order of Operations

The order of operations is a crucial concept in math, ensuring that everyone solves problems the same way. Although this exercise seems simple with just addition, understanding the order of operations helps in solving more complex problems.

For basic expressions without parentheses, you can add or subtract numbers from left to right as they appear. This means when you face the equation 24 + (-6) + (-8), you proceed by performing the operation from the far left to the right, dealing with pairs sequentially.

• Start by adding the first two numbers: 24 + (-6), treating it as 24 - 6.
• Then, take your result and add the next number, as we did with 18 + (-8).
• This left-to-right approach ensures consistency across different problems.

In more advanced expressions, remember to apply rules such as PEMDAS/BODMAS (Parentheses/Brackets, Exponents/Orders, Multiplication, and Division, Addition, and Subtraction). This structured approach keeps calculations orderly and predictable.