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Chapter 5: Problem 118

In the following exercises, add or subtract. $$94.69-(-12.678)$$

Short Answer

Expert verified
107.368

Step by step solution

01

Understand the Operation

Identify that the exercise requires subtraction involving a negative number: \(94.69 - (-12.678)\). Remember that subtracting a negative number is equivalent to addition.
02

Convert the Operation

Rewrite the subtraction as an addition: \(94.69 - (-12.678) = 94.69 + 12.678\). This simplifies the calculation.
03

Perform the Addition

Add the two numbers together. Align them by their decimal points for accuracy:\[\begin{array}{r} 94.690 \+ 12.678 \hline107.368\end{array}\]Adding the numbers gives a result of \(107.368\).

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Key Concepts

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

adding decimals
Decimal addition is quite similar to adding whole numbers but with a very important rule: always line up the decimal points! This ensures that each place value (units, tenths, hundredths, etc.) matches correctly. Start by writing the numbers vertically so the decimal points are in a straight line. Add zeros if necessary to make sure each number has the same number of decimal places. Add from right to left, just like with whole numbers.
For example, in the exercise, we had to add 94.690 to 12.678. By aligning the decimal points, we ensure accuracy in our calculation. Each digit corresponds to the correct place value, making the math easier. The sum of those numbers is 107.368.
subtracting negatives
Subtracting a negative number can be tricky at first, but the concept is straightforward. Subtracting a negative is the same as adding the absolute value of that number. This happens because of the two negative signs cancel each other out.
Consider the problem: \(94.69 - (-12.678)\). The two negatives become a positive sign: \(94.69 + 12.678\). This is a crucial step in simplifying the problem. Remember, whenever you see a negative sign followed by another negative sign, you can replace them with a positive sign.
This concept helps simplify many arithmetic problems involving negative numbers.
arithmetic operations
Arithmetic operations include addition, subtraction, multiplication, and division. Understanding how to properly perform these operations with decimals and negative numbers is critical in math.
  • **Addition**: Line up the numbers by their decimal points, apply the operation from right to left.
  • **Subtraction**: Also line up by decimal points, subtract normally from right to left.
  • **Multiplication and Division**: Decimal places need special care. For multiplication, count the total number of decimal places in both numbers. This will be the number of decimal places in the result. For division, move the decimal point in both the divisor and dividend to make the divisor a whole number, then proceed with the operation.
Using the exercise as an example, we used fundamental arithmetic concepts to solve \(94.69 - (-12.678) \). By converting it to an addition problem and already knowing how to add decimals, we solved it easily.

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