Problem 254 - Intermediate Algebra

Question

In the following exercises, add or subtract. $$ 59.08-4.6 $$

Step-by-Step Solution

Answer

54.48

Step 1: Line up the decimals

Align the numbers by their decimal points to make the subtraction easier. Write 59.08 on top and 4.6 below, ensuring the decimal points are aligned.

Step 2: Add zeros to align digits

To ensure that both numbers have the same number of decimal places, add an extra zero to 4.6, making it 4.60. This helps in easy subtraction.

Step 3: Subtract column by column

Starting from the rightmost digit, subtract each column. If needed, borrow from the next column to the left. .

Step 4: Perform the subtraction

1. Subtract the hundredths place: 8 - 0 = 8.2. Subtract the tenths place: 0 - 6 (borrow 1 from the units place): becomes 10 - 6 = 4.3. Subtract the units place: 8 (since you borrowed 1) - 4 = 4.4. Subtract the tens place: 5 - 0 = 5.So, 59.08 - 4.60 = 54.48.

Step 5: Write the final answer

After performing the subtraction, the final result is 54.48.

Key Concepts

step-by-step math solutions

Step-by-step math solutions are crucial for understanding complex problems. Let's break down the problem of subtracting 4.6 from 59.08. First, always align the numbers by their decimal points. This ensures that each digit is in the correct place value column.
Next, if the numbers do not have the same number of digits after the decimal, add zeros to the end of the shorter number. In this case, rewrite 4.6 as 4.60. This way, each digit will align neatly for easy subtraction.
Then, start subtracting from the rightmost column, moving left. If you need to borrow, do so from the next column on the left. For example, when subtracting 0 from 8, no borrowing is needed. But when subtracting 6 from 0, you'll need to borrow. Following these steps will lead you to the correct solution.

aligning decimals

Aligning decimals is an essential step in subtraction or addition of decimal numbers. Misalignment can cause errors, producing incorrect results. To align decimals:

• Write each number in a column format, ensuring decimal points are directly above one another.
• Fill in any blanks with zeros to match the number of decimal places in both numbers.

In our example, we rewrite 4.6 as 4.60 to ensure alignment with 59.08. Proper alignment helps maintain accurate place values, ensuring the subtraction is performed correctly and systematically.

borrowing in subtraction

Borrowing is a fundamental part of subtraction, especially when dealing with large numbers or decimals. Here's how it works:

• If a digit in a column is smaller than the digit you're subtracting, borrow 1 from the next column to the left.
• Reduce the left column by 1 and add 10 to the current column.

In the exercise given, while subtracting 0 from 6 in the tenths column, we borrow from the units place. This makes the subtraction possible: 10 - 6 = 4. This step-by-step borrowing ensures every column is correctly handled, leading to accurate results.

basic arithmetic operations

Basic arithmetic operations include addition, subtraction, multiplication, and division. Understanding these operations is fundamental to solving math problems. Today, we focus on subtraction, which involves taking one number away from another.
This process is straightforward:

• Align the numbers by their decimal points.
• Make sure all digits in each column are compared correctly.
• If necessary, borrow from the next column to the left to ensure each subtraction step is possible.

Using these steps in our problem, 59.08 - 4.6 becomes a simple task. Always treat subtraction, especially with decimals, methodically to avoid mistakes and ensure precision.