Problem 52 - Prealgebra

Question

Add and subtract as indicated. What number is added to 0.043 to obtain \(6.054 ?\)

Step-by-Step Solution

Answer

6.011 is added to 0.043 to obtain 6.054.

Step 1: Understand the Problem

We need to find a number that, when added to 0.043, results in 6.054. This can be expressed by the equation: \(x + 0.043 = 6.054\).

Step 2: Isolate the Variable

To find the number \(x\), we need to isolate it by subtracting 0.043 from both sides of the equation. This gives us: \(x = 6.054 - 0.043\).

Step 3: Perform the Subtraction

Now, perform the subtraction: \(6.054 - 0.043\). Align the decimal points to ensure accuracy:\[\begin{array}{c} 6.054 \- 0.043 \\hline 6.011\end{array}\]

Step 4: Conclusion

The number that when added to 0.043 yields 6.054 is 6.011.

Key Concepts

Algebraic Equations

Algebraic equations are mathematical statements where two expressions are set equal to each other, using the equality sign \( = \). These equations can include numbers, variables, operations like addition and subtraction, and sometimes functions. They are used to express relationships between different quantities. In our exercise, the equation is:

• \( x + 0.043 = 6.054 \)

This equation tells us that some unknown value \( x \) when added to 0.043 equals 6.054. The goal is to find the value of \( x \). Through the exploration of algebraic equations, we can solve real-world problems by finding unknowns based on given information. It simplifies the process of deducing logical conclusions in math.

Isolation of a Variable

Isolation of a variable is a fundamental skill in solving algebraic equations. The aim is to "isolate" or "get the variable on its own" on one side of the equation, so you can determine its value. In this exercise, the variable is \( x \). We start with the equation:

• \( x + 0.043 = 6.054 \)

To isolate \( x \), we perform operations that remove other numbers from its side of the equation. Since 0.043 is added to \( x \), we do the opposite operation, which is subtraction. By subtracting 0.043 from both sides, we preserve the equality:

• \( x + 0.043 - 0.043 = 6.054 - 0.043 \)

This simplifies to:

• \( x = 6.011 \)

By isolating \( x \), we have effectively solved for the unknown variable.

Problem-Solving Steps

Problem-solving in math often involves a series of logical steps that guide you from the problem statement to the solution. Here are the essential steps we followed in this exercise:1. **Understand the Problem:** Here, we identified that the exercise requires us to find what number, when added to 0.043, results in 6.054.2. **Set Up the Equation:** We expressed the problem using the equation \( x + 0.043 = 6.054 \).3. **Isolate the Variable:** By subtracting 0.043 from both sides, we found \( x = 6.011 \).4. **Verify the Solution:** Finally, ensure the solution is correct by plugging \( x = 6.011 \) back into the original equation to see if it holds true.Following these steps helps maintain organization and ensures all aspects of the problem are covered.

Decimal Operations

Working with decimals requires careful attention, especially during operations like addition and subtraction. Decimals represent fractions and have a point (the decimal point) which separates the whole part from the fractional part. In our problem, to perform the subtraction of decimals accurately, it’s crucial to align the decimal points:

• Subtract \( 0.043 \) from \( 6.054 \)

To perform:\[\begin{array}{c} 6.054 \ - 0.043 \ \hline \ 6.011\end{array}\]Make sure the decimal points are in a straight line vertically. It helps to fill in any missing spaces with zeros if necessary. This ensures that you are subtracting each digit correctly according to its place value. Decimal operations become intuitive with practice, allowing you to manage more complex problems involving decimals.