Problem 51 - Prealgebra

Question

Add and subtract as indicated. What number is added to 0.035 to obtain \(4.036 ?\)

Step-by-Step Solution

Answer

The number is 4.001.

Step 1: Understand the Problem

We are given a number, 0.035, and we want to find out what number needs to be added to it to result in 4.036. Mathematically, this can be expressed as 0.035 + x = 4.036, where x is the unknown number we need to find.

Step 2: Set Up the Equation

Write down the equation based on the problem statement: 0.035 + x = 4.036.

Step 3: Isolate the Variable

To solve for x, we need to isolate it on one side of the equation. Subtract 0.035 from both sides of the equation to achieve this: x = 4.036 - 0.035.

Step 4: Perform the Subtraction

Carry out the subtraction by aligning the decimal points and subtracting one number from the other: 4.036 - 0.035 = 4.001.

Step 5: Verify the Solution

To ensure the solution is correct, add 0.035 to the result of step 4: 0.035 + 4.001 = 4.036. Since the addition gives us the original number, the solution is verified.

Key Concepts

Adding Decimals

Adding decimals is a fundamental math skill, and it is quite simple once you master the basic concept. When you add decimals, the key is to align the numbers by their decimal points. This ensures that you are adding each digit in the correct place value, just as you would with whole numbers.
Start by writing the numbers one on top of the other, ensuring the decimal points are in a vertical line. If the numbers have different lengths, fill any gaps with zeros, so each number has the same amount of decimal places. This doesn't change the value of the number but helps in keeping the numbers aligned.
Once lined up, add the numbers just as you would normally, moving from right to left. Remember to carry over any numbers if the sum of a column is greater than 9, just like in standard addition. Finally, place the decimal point in the sum directly beneath the other decimal points, maintaining alignment. This simple alignment is crucial in avoiding mistakes when working with decimals.

Subtracting Decimals

Subtracting decimals uses a similar process to adding decimals, with the main difference being, of course, that you are subtracting! Begin by aligning the decimal points of the numbers you are working with, placing them one over the other.
Just like when adding, adjust the numbers if necessary by filling gaps with zeros to ensure they have the same number of decimal places. This alignment helps ensure accuracy in performing the operation.
Subtract each column starting from the right. If the top digit in the ones place is smaller than the bottom digit, you will need to "borrow" from the next column to the left, similar to whole number subtraction. After you have borrowed, subtract each of the columns as adjusted.

• Line up the decimals
• Borrow if needed
• Calculate each column

Ultimately, make sure to place the decimal point in the result correctly, directly aligning with the original numbers. This alignment ensures that your answer is accurate.

Equations with Decimals

Equations involving decimals can feel daunting at first, but they follow the same principles as equations with whole numbers. When given an equation like 0.035 + x = 4.036, the goal is to find the value of x, the unknown number, which represents a missing piece in the equation.
To solve such an equation, the first step is often to isolate the variable on one side of the equation. In this scenario, you would subtract 0.035 from both sides to get x by itself: \[x = 4.036 - 0.035\]

This operation is straightforward; align the decimals to perform the subtraction accurately. Once you've calculated the value of x, it's always a good idea to plug it back into the original equation to verify the solution. This means adding 0.035 back to your found value of x and checking that it equals 4.036:

• Isolate the variable
• Perform arithmetic operations
• Verify your solution

Understanding this process boosts your math skills substantially, ensuring you're well-prepared for any math challenges involving decimals.