Problem 44 - Algebra 1: Concepts and Skills

Question

Find the sum. $$-24.5+6+8$$

Step-by-Step Solution

Answer

The sum of '-24.5+6+8' is \(-10.5\).

Step 1: Identify the numbers

The numbers given are \(-24.5\), \(6\), and \(8\).

Step 2: Treat -24.5 as subtraction

As \(-24.5\) is a negative number, it can be treated as subtraction. So, the given problem becomes \(6+8-24.5\).

Step 3: Perform the operation

Perform the operation as it is now presented: \(6 + 8 = 14\). Then, subtract \(24.5\) from \(14\) to give \(-10.5\).

Key Concepts

Negative Numbers

Negative numbers are numbers less than zero. They have a minus sign (-) in front of them. Negative numbers can be challenging at first because they work opposite to positive numbers.
In the exercise, you see

• -24.5, which is a negative number.

This means you treat it like money owed. Negative numbers can be added or subtracted like positive numbers, but they follow some interesting rules.
When you add a negative number, you are essentially subtracting that number from the total. This is why

• '-24.5' can be rewritten as '- 24.5' when adding to the sum.

Understanding how negative numbers work is crucial for many areas of mathematics and science!

Order of Operations

The order of operations is a set of rules that tells you the correct sequence to solve math problems. These rules ensure that everyone gets the same answer to a problem by agreeing on which steps to follow first. The common mnemonic to remember it is PEMDAS:

• Parentheses
• Exponents
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In this exercise, we focused on addition and subtraction operations. Even though there were no parentheses or exponents, understanding the sequence is still important. You first handle operations on the same level from left to right, as seen in the examples:

• First add
• Then subtract, taking into account whether numbers are positive or negative.

Mastering the order of operations helps avoid confusion and ensures accurate solutions!

Rational Numbers

Rational numbers include all numbers that can be expressed as a fraction or ratio of two integers. They also include integers, fractions, and repeating or terminating decimals.
In this exercise, the numbers

• -24.5 (which is a negative decimal but still rational),
• 6, and
• 8

are all rational. Understanding rational numbers means recognizing patterns like decimals that end or repeat. This helps in simplifying problems and operations involving them. Whether you are adding or subtracting, the result should stay rational if you start with rational numbers. Grasping rational numbers is important for solving many mathematical problems effectively.