Problem 8 - Algebra 1

Question

Use the subtraction rule to rewrite the subtraction expression as an equivalent addition expression. Then evaluate the expression. $$ -2.4-3 $$

Step-by-Step Solution

Answer

The equivalent addition expression for \( -2.4 - 3 \) is \( -2.4 + (-3) \) and the evaluated answer is -5.4.

Step 1: Rewrite the subtraction expression as an equivalent addition expression

Use the subtraction rule to rewrite \( -2.4 - 3 \) as \( -2.4 + (-3) \). The rule is based on understanding that subtracting a number is the same as adding its negative.

Step 2: Evaluate the expression

Now, simply add the numbers. When you add a negative number, you are essentially moving to the left on the number line. So, -2.4 to the left another 3 units gives -5.4

Key Concepts

Subtraction Rule

The subtraction rule is a fundamental concept in algebra that helps simplify subtraction expressions. Essentially, this rule states that subtracting a number is the same as adding its opposite, or negative. For instance, if you have the expression \( a - b \), it can be rewritten as \( a + (-b) \). Here, \( b \) is simply replaced by \(-b\), which means you are adding the inverse of \( b \).This concept is incredibly useful because turning subtraction into addition can make calculations more straightforward, especially when dealing with negative numbers. Understanding this rule allows you to more easily manipulate and evaluate algebraic expressions.

Addition of Negative Numbers

Adding negative numbers is an extension of basic addition and involves understanding how values change direction on the number line. When you add a negative number, you are essentially moving to the left, or decreasing, on the number line. For example, if you start at \(-2.4\) and add \(-3\), you move 3 units to the left from \(-2.4\).This movement can be visualized step-by-step:

• Begin at \(-2.4\) on the number line.
• Add \(-3\) means moving 3 units left.
• The new position on the number line is \(-5.4\).

Hence, adding negative numbers essentially reduces the value of the original number, aligning closely with the visual concept of shifting left on a number line.

Number Line

A number line is a visual representation that helps in understanding arithmetic operations involving real numbers. It is a straight line with numbers placed at intervals, where each point on the line corresponds to a real number. Zero is typically in the center, with positive numbers to the right and negative numbers to the left.When dealing with operations like subtraction or addition of negative numbers, the number line offers a clear illustration:

• Subtracting a number is like adding its negative counterpart, which moves you left.
• Adding a negative number also moves you left, reinforcing the reduction of the initial value.

For the expression \(-2.4 + (-3)\), locating \(-2.4\) on the line first, and then moving 3 units to the left simplifies understanding this operation visually, landing you on \(-5.4\). The number line thus makes complex concepts more tangible by offering a spatial perspective.