Problem 18 - Fundamentals of Mathematics

Question

Use a calculator to find each difference. $$ -31.89-44.17 $$

Step-by-Step Solution

Answer

The difference is -76.06.

Step 1: Rewriting the Expression

The original expression we have to solve is \[ -31.89 - 44.17 \]We can rewrite this expression as the sum of two negative numbers:\[ -31.89 + (-44.17) \]

Step 2: Adding the Numbers

Since both numbers are negative, we can add their absolute values together and keep the negative sign. Compute:\[ 31.89 + 44.17 = 76.06 \]Thus, our result will be:\[ -76.06 \]

Step 3: Verifying the Result with a Calculator

Input the original expression from Step 1 into a calculator:\[ -31.89 - 44.17 \]The calculator should output:\[ -76.06 \]

Key Concepts

Understanding Negative Numbers

Negative numbers might seem confusing at first, but they are just numbers less than zero. Imagine a number line with zero in the middle, positive numbers to the right, and negative numbers to the left. Negative numbers are crucial when dealing with temperatures below freezing, debts, or elevations below sea level. When subtracting a negative number, it can be helpful to think of it as adding a positive number. This means that subtracting a larger negative number results in a more negative value. For example, subtracting a negative from another negative becomes more straightforward when converted into addition.

What is Absolute Value?

The absolute value of a number is the distance of that number from zero on a number line, regardless of direction. It is always a positive number or zero. Simply put, the absolute value of a number disregards its sign. The symbols for absolute value are double vertical bars on either side of the number, like this: \( |x| \\). For example:

• The absolute value of \( |-3| \) is 3.
• The absolute value of \( |5| \) is 5.

Understanding absolute values is particularly helpful when dealing with the addition or subtraction of negative numbers, as it allows for a simplified calculation by considering only the numeric part without worrying about the sign.

Using Calculators Effectively

Calculators are handy tools for solving mathematical problems quickly and accurately. When working with negative numbers, it's important to enter expressions correctly. For subtraction or adding negatives, ensure to use the correct buttons to input the negative sign. Here are some tips:

• Double-check the minus signs before hitting "equals" to avoid errors in the output.
• Use parentheses to clarify operations, especially when dealing with multiple negative numbers.
• Review the calculator's display to confirm each step correctly represents what you intend to compute.
• Practice entering complex expressions so it becomes second nature.

By mastering calculator usage, you increase your ability to solve advanced mathematical problems efficiently and with confidence.