Problem 57 - Algebra 1: Concepts and Skills

Question

Determine whether the equation is true or false. $$ 14.4+0.14=2.88 $$

Step-by-Step Solution

Answer

The given equation is false.

Step 1: Addition of given numerals

We begin by adding the numbers on the left side of the equation, namely, 14.4 and 0.14. When we add these together, we get \(14.4 + 0.14 = 14.54\)

Step 2: Comparison

After getting the sum, we need to verify if this is equal to the number on the right side of the equation, which is 2.88. However, 14.54 is not equal to 2.88.

Step 3: Final Verification

Since the left and right side of the equation aren't equal, this means the given equation \(14.4+0.14=2.88\) is false

Key Concepts

Addition of Decimals

Understanding how to add decimal numbers is fundamental to many aspects of math and real life applications, such as handling money or measuring distances. To add decimals, align them by the decimal point and then proceed to add each digit column starting from the farthest to the right, similar to how whole numbers are added. Always remember to place the decimal point in the sum directly below the other decimal points.

In the exercise given, when you add 14.4 (which has one decimal place) to 0.14 (which has two decimal places), you should mentally align them as follows:

 14.4+ 0.14-------- 14.54

This process shows the importance of ensuring each decimal place is correctly aligned to avoid errors in calculations.

Equality Verification

Equality verification is a process to determine if two values, or in this case, two sides of an equation, are identical. After calculating the sum of the numbers on one side of an equation, like we did in the addition step, the next phase is to compare this sum to the value on the other side of the equal sign.

It is important to understand that an equation represents a balance; the values on both sides must be equivalent for the equation to be true. For example, the exercise provided requires us to check if 14.54 is equal to 2.88. Since they are different, the equation is false. This step helps in detecting mistakes and is a pillar of not just mathematics, but also of logical reasoning.

Comparing Numbers

To compare numbers, especially decimals, you should first check the digits before the decimal point. Numbers with more digits before the decimal point are larger. If the count of digits is the same, compare each decimal place from left to right until you find a difference.

When we compare 14.54 and 2.88, we immediately see that 14 is greater than 2, meaning overall, 14.54 is greater than 2.88 without a need for further comparison. This concept is crucial to understanding numerical value and ordering of numbers.

Basic Algebra Concepts

Algebra is the branch of mathematics that deals with symbols and rules for manipulating those symbols. Basic algebra concepts include understanding variables, coefficients, and the concept of equality. In the context of our example, the exercise doesn't present a typical algebraic problem since there are no variables to solve for. However, the properties of equality used in algebra apply: for an equation to be true, whatever is done to one side must be done to the other to maintain balance.

Our example didn't involve these steps since it was a straightforward comparison, but it's important to grasp these foundational aspects of algebra to tackle more complex problems in the future.