Problem 256 - Intermediate Algebra

Question

In the following exercises, add or subtract. $$ 3.84-6.1 $$

Step-by-Step Solution

Answer

-2.26

Step 1 - Align the Numbers

Write 3.84 and 6.1 vertically, aligning the decimal points to ensure proper subtraction.

Step 2 - Pad with Zeros

Since 6.1 has fewer digits after the decimal point, add a zero to make it 6.10.

Step 3 - Subtract Digit by Digit

Subtract each digit starting from the rightmost column. Subtract 0 from 4, 1 from 8, and 6 from 3. Borrow as needed.

Step 4 - Borrowing

When subtracting 6 from 3 in the ones place, you need to borrow 1 from the next left column making it 13-6 instead of 3-6.

Step 5 - Perform the Subtraction

Now perform the subtraction: 4 - 0 = 4 8 - 1 = 7 Since we borrowed 1, we now have 13 - 6 = 7.This gives us a result of -2.26.

Key Concepts

Aligning Decimal Points

When subtracting decimals, the first step is to align the decimal points of the numbers vertically. This ensures that digits with the same place value are in the same column. For example, in the problem 3.84 - 6.1, write 3.84 above 6.1, aligning the decimal points directly one over the other. This helps avoid mistakes and ensures that digits are correctly subtracted from their corresponding place values.

Padding with Zeros

Sometimes, the numbers being subtracted might have different numbers of digits after the decimal point. In such cases, to make subtraction easier, we pad the shorter number with zeros. In the example 3.84 - 6.1, adding a zero to 6.1 makes it 6.10. This makes the decimal places even:

• 3.84
• - 6.10

Padding with zeros ensures that each decimal place has a corresponding digit to subtract from, making the process clearer and more accurate.

Borrowing in Subtraction

Borrowing is crucial when a digit in the minuend (the number from which another number is subtracted) is smaller than the corresponding digit in the subtrahend (the number being subtracted). In our example, when subtracting the digit in the ones place, we have 3.84 - 6.10. We can't subtract 6 from 3 without borrowing.
So we borrow 1 from the tenths place (making 3 a 13 and reducing the next left column by 1).

• Now perform the subtraction: 4 - 0 = 4
• 8 - 1 = 7
• 13 - 6 = 7

This will give the result: -2.26. Borrowing helps ensure that we can still subtract larger digits accurately.