Problem 54 - Algebra 1: Concepts and Skills

Question

Determine whether the equation is true or false. $$ 1.3-2.7=1.4 $$

Step-by-Step Solution

Answer

false

Step 1: Perform the Left-Side Operation

First, perform the subtraction operation on the left side of the equation, which is \(1.3 - 2.7\).

Step 2: Compare the Result with the Right-Side

After performing the operation, compare the obtained value with the number on the right-side of the equation, which is \(1.4\).

Step 3: Determine whether the Equation is True or False

If the left-side operation result equals the right-side number, then the equation is true. Otherwise, the equation is false.

Key Concepts

Subtraction

Subtraction is a fundamental arithmetic operation, where we remove a number from another number. Understanding subtraction is crucial for solving equations and comparing values. In our exercise, we have the expression \(1.3 - 2.7\). To perform this operation, consider the numerical value and order:

• Ensure values are aligned correctly if working with decimals.
• Subtract smaller values from larger ones, remembering that order matters.
• If needed, use borrowing techniques to simplify subtraction.

For \(1.3 - 2.7\), you essentially subtract a larger number from a smaller one, which often results in a negative value. This computation gives us \(-1.4\). It's important to practice subtraction to become comfortable with equations and calculations in broader math contexts.

True or False Statements

True or false statements are logical assertions about whether an equation holds or not. In mathematics, these statements confirm if both sides of an equation are equivalent after transformations. When evaluating our exercise:

• First, complete any operations on either side of the equation.
• Next, compare the resulting value from operations to the other side of the equation.
• If both sides match exactly, the statement is true. Otherwise, it is false.

In our example, after performing \(1.3 - 2.7\) we got \(-1.4\). Since \(-1.4\) is not equal to \(1.4\), the equation is false. Recognizing true or false statements is key to understanding logical consistency and correctness in mathematics.

Comparing Values

Comparing values in mathematics involves determining the relationship between numbers. This could mean deciding if they are equal, greater than, or less than one another. It is essential when evaluating equations like our example or solving inequalities. Here’s a simple way to approach this process:

• First, compute or simplify the expressions on both sides of an equation.
• Assess the numerical result of both sides.
• If the values are equal, it indicates balance; otherwise, identify which side is larger or smaller.

With \(1.3 - 2.7 = 1.4\), the computed value \(-1.4\) does not match \(1.4\). This signifies that \(-1.4\) is less than \(1.4\) (since negative numbers are lesser). Comparing values helps to verify and conclude the truth value of mathematical statements accurately.