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Chapter 5: Problem 117

In the following exercises, add or subtract. $$91.75-(-10.462)$$

Short Answer

Expert verified
102.212

Step by step solution

01

Identify the Operation

The given expression is 91.75 - (-10.462). This involves subtracting a negative number.
02

Convert Subtraction to Addition

Subtracting a negative number is equivalent to adding its positive counterpart. Therefore, 91.75 - (-10.462) can be rewritten as 91.75 + 10.462.
03

Align Decimal Points

Write the numbers 91.75 and 10.462 such that their decimal points are aligned: \[ \begin{array}{r} 91.750 \ +10.462 \ \ \ \ \ \end{array} \]
04

Add the Numbers

Add the numbers column by column, ensuring to carry over any values where necessary: \[ \begin{array}{r} 91.750 \ +10.462 \ \ \ \ \ \ 102.212 \ \end{array} \]
05

Write the Final Answer

The result of 91.75 + 10.462 is 102.212.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

decimal points alignment
When adding or subtracting decimals, it is essential to align the decimal points properly. This ensures that each column corresponds to the correct place value.
This method makes it easier to avoid mistakes in calculation.
For example, if you want to add 91.75 and 10.462, format them like this:

91.750
+10.462

Notice how every digit and decimal point is in an organized column.
Once properly aligned, you can proceed to the actual addition or subtraction.
addition of decimals
Once the decimal points are aligned, you can add the numbers column by column just like you would with whole numbers.
Let's add 91.75 and 10.462:

91.750
+10.462
------
102.212

Here are some tips to ensure you do it right:
  • Start from the rightmost column and move towards the left.
  • Add each column as you go, including any carry-over to the next column if necessary.
  • Ensure that the decimal point in the result is directly below the decimal points in the numbers being added.
  • Don鈥檛 forget to add zeros to make the number of decimal places equal (as shown above).
This makes the addition process simple and error-free.
subtraction of negative numbers
Subtracting a negative number can initially seem confusing, but there鈥檚 a straightforward trick to it:
  • First, convert the subtraction of the negative number into an addition.
    Remember: Subtracting a negative is equivalent to adding the corresponding positive number.
For example, with the problem 91.75 - (-10.462), rewrite it as:
91.75 + 10.462

Now you no longer have a subtraction problem; instead, you have a simpler addition problem, which can be solved using the steps discussed earlier.
This conversion makes dealing with negative numbers much simpler and helps ensure accuracy in your calculations.

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