Problem 81 - Algebra A Combined Function

Question

Translate each phrase; then simplify. See Example 22. Find the sum of -6 and 25.

Step-by-Step Solution

Answer

The sum of -6 and 25 is 19.

Step 1: Understanding the Phrase

The problem asks us to find the sum of two numbers, -6 and 25. The word 'sum' in mathematics means to add, so we are looking to add these two numbers together.

Step 2: Translate the Phrase to an Expression

To translate the phrase "the sum of -6 and 25" into a mathematical expression, write it as \(-6 + 25\).

Step 3: Simplify the Expression

To find the sum, calculate \(-6 + 25\). Start with the number 25 and move 6 units to the left on the number line since you're adding a negative number. This gives you 19.

Key Concepts

Mathematical Expressions

In mathematics, expressions are a combination of numbers, operators, and sometimes variables. In this context, we want to translate verbal phrases into mathematical expressions.
For instance, the phrase "the sum of -6 and 25" becomes the expression \(-6 + 25\). Here are some key points to consider:

• **Sum** indicates addition. When you see this word, you are typically adding the numbers that follow.
• Negative numbers, like -6, will be shown with a "-" sign before the number itself.
• Mathematical expressions allow you to perform calculations and reach a numerical answer.

Developing the skill to translate words into expressions is fundamental in solving many math problems. You'll use operators such as \(+\), \(-\), \(\times\), and \(\div\) to connect numbers in a meaningful way. Keep this in mind as you advance to more complex problems.

Number Line

A number line is a visual representation that helps us to understand numbers and their relationships better. It is a straight line with numbers placed at equal intervals or segments along its length.

When dealing with addition, especially involving negative numbers, the number line becomes an invaluable tool. Here's how you can use it:

• Start with the first number. If you begin at positive or zero, mark your starting point on the line.
• If you add a positive number, move to the right. If it's negative, move to the left.
• Each movement represents a unit increase or decrease.

For the expression \(-6 + 25\), begin at 25 and move 6 units to the left, landing at 19. The number line simplifies understanding how adding negative numbers affects a total. By visualizing these steps, you can better grasp changes in value.

Negative Numbers

Negative numbers are numbers less than zero, represented with a "-" sign. They are crucial in various mathematical operations and real-life situations. Here are some foundational aspects:

• They represent values below zero, like debts or temperatures below freezing.
• When adding a negative number, it's like subtracting a positive number equivalent.
• Negative numbers play a significant role in expressions, affecting the outcome based on the arithmetic operation applied.

In our context, adding \(-6\) to 25 is interpreted as finding the difference between 25 and 6, which results in 19. Understanding negative numbers allows you to confidently handle operations that could initially seem tricky. Whether in finance or science, they help describe quantities that go below the baseline.