Problem 71 - Prealgebra

Question

If the sum of -3 and 5 is increased by 8, what number results?

Step-by-Step Solution

Answer

The number that results is 10.

Step 1: Calculate the Initial Sum

First, let's find the sum of the two numbers given: -3 and 5. To do this, simply add them together: \[-3 + 5 = 2\]

Step 2: Increase the Sum

Next, increase the resulting sum from Step 1 by adding 8 to it. So, take the sum from the previous step which is 2 and add 8: \[2 + 8 = 10\]

Step 3: Identify the Resulting Number

The result of increasing the initial sum by 8 is the final solution to the exercise. Therefore, the number that results is 10.

Key Concepts

Addition

Addition is one of the most basic yet essential operations in arithmetic. It involves combining two or more numbers to find the total or sum. For instance, if you have three apples and then get two more, you can find out how many apples you have altogether by adding the two numbers: 3 + 2 = 5. This simple process forms the foundation for more complex mathematics.

In the context of integers, addition works the same. When adding positive numbers, you count up, thereby increasing the total. When negative numbers are involved, it gets slightly more interesting. Remember, an easy way to think of negative numbers is like debts. If you owe someone three dollars and get five dollars, paying off your debt results in having two extra dollars. Thus, adding -3 and 5 gives you 2, as shown in the exercise.

Understanding addition helps in various life skills, from calculating expenses to understanding complex equations later in mathematics.

Negative Numbers

Negative numbers represent values less than zero, often indicating a deficit or opposite direction than positive ones. They are important in understanding the full spectrum of real-world situations where not everything is positive.

Negative numbers are easily spotted by the minus sign (-) in front of them. For example, -3 suggests a position three steps below zero. In terms of money, negative numbers can represent debts; thus, -3 dollars signify owing three dollars.

In arithmetic operations such as addition, negative numbers impact the sum differently than positive numbers.

• Adding a negative number is akin to subtraction. For instance, 5 + (-3) effectively means 5 - 3.
• When combining two negative numbers, their absolute values are added, and the result is negative.
• Adding a larger positive number to a smaller negative number results in a positive sum, such as -3 + 5 = 2.

Familiarity with negative numbers is crucial in various fields, including science, engineering, and finance.

Problem Solving Steps

Problem-solving in mathematics often involves understanding a situation, breaking it down into manageable steps, and then systematically proceeding through those steps.

In our exercise, we start by comprehending what the question asks and restating it in simpler terms. Then, we identify the known elements and operations required—addition, in this case. We outline each step:

• Step 1: Calculate the initial sum. Given numbers -3 and 5, we find their sum by adding them: -3 + 5 = 2.
• Step 2: Increase this sum by adding 8, which means 2 + 8 = 10.
• Step 3: Identify the result as the final answer, which is 10.

Each step builds upon the previous one, ensuring you progress toward the solution logically and clearly. This problem-solving method is useful not just in math but in approaching any challenge systematically and with clarity. Mastering this approach leads to greater confidence and efficiency in dealing with problems.