Problem 47 - Prealgebra and Introductory Algebra

Question

What is 16 more than \(-5 ?\)

Step-by-Step Solution

Answer

Therefore, 16 more than -5 is \(11\).

Step 1: Identify numbers and operation

The problem is asking for a value that is 16 more than -5. Here, -5 is being increased by 16.

Step 2: Perform the operation

To find the answer, add 16 to -5. The operation is \(-5 + 16\)

Step 3: Calculate the result

When you add 16 and -5, the result is \(11\).

Key Concepts

Integers

Integers are a set of numbers that include both positive and negative whole numbers, as well as zero. They do not include fractions or decimals.
Examples of integers are:

• Negative integers: -3, -2, -1
• Zero: 0
• Positive integers: 1, 2, 3

The key characteristic of integers is that they extend infinitely in both the positive and negative directions on the number line. This means there is no largest or smallest integer, as you can always find a higher or lower one by simply adding or subtracting another whole number.
In problems involving integers, understanding their position relative to one another is crucial, especially when performing arithmetic operations such as addition or subtraction.

Arithmetic Operations

Arithmetic operations are basic mathematical processes used to perform calculations. The main arithmetic operations are addition, subtraction, multiplication, and division.
In the context of integers, each operation follows specific rules, especially when negative numbers are involved.

• Addition: Combines numbers to get a sum.
• Subtraction: Finds the difference between numbers.

For instance, when adding a positive number to a negative number, like in rack -5 + 16 rack, you are essentially moving up the number line towards zero and beyond, which results in a positive number. Understanding these operations helps in handling more complex math problems accurately.

Negative Numbers

Negative numbers are less than zero and are represented with a minus sign (-) before them.
Common examples include temperatures below zero or debts, like owing money.
When working with negative numbers in math problems, it's important to remember:

• They are located to the left of zero on the number line.
• When adding a positive number to a negative number, you "move" right on the number line towards the positive side.

For rack -5 + 16 rack, starting from -5, you count 16 steps to the right, which lands you at 11. This process reflects the idea of offsetting a lesser value with a greater positive value.

Basic Math Problem Solving

Basic math problem solving often involves identifying what is being asked and breaking down the operations needed.
To solve problems efficiently, follow these steps:

• Identify the numbers and the operation required.
• Perform the operations systematically.
• Verify the result.

Looking at the problem rack 16 more than -5 rack, it defines that -5 needs to increase by 16 through addition, which simplifies the operation to rack -5 + 16 rack. Calculating this gives the result of 11, reflecting a straightforward approach to arithmetic problems and ensuring accuracy.