Problem 48 - Fundamentals of Mathematics

Question

Find the sums in the following 27 problems. If possible, use a calculator to check each result. $$ -47.03+(-22.71) $$

Step-by-Step Solution

Answer

The sum is -69.74.

Step 1: Understanding the Problem

The problem requires us to find the sum of two negative numbers: -47.03 and -22.71. When adding negative numbers, you add their absolute values and attach a negative sign to the result.

Step 2: Calculate the Sum

Add the absolute values of the two numbers: \[ 47.03 + 22.71 = 69.74 \] Since both numbers were negative, the sum is also negative. Thus, the result is -69.74.

Step 3: Verify with a Calculator

Use a calculator to verify the result by entering -47.03 + (-22.71). The calculator should display -69.74, confirming our manual calculation.

Key Concepts

Negative Numbers

Negative numbers are values that fall below zero on the number line. They are represented with a minus sign (-) in front of the number.

• Negative numbers are to the left of zero on the number line.
• They represent values such as debts or temperatures below freezing.

Understanding negative numbers is crucial because they have unique properties, especially when combined through operations like addition or subtraction.
When you add negative numbers, you essentially combine their absolute values and assign a negative sign to the sum. This is because adding two debts results in a larger debt.

Absolute Value

Absolute value refers to the magnitude of a number, ignoring its sign. It's like asking how far a number is from zero on the number line, regardless of direction.

• The absolute value of a number is always positive.
• For instance, the absolute values of -5 and 5 are both 5.

When dealing with negative numbers, finding the absolute value is a crucial step in addition.
For example, in adding -47.03 and -22.71, we first find their absolute values, 47.03 and 22.71.
Then, we add these numbers together, which helps to simplify the process before applying the sign.

Calculator Use

Using a calculator can be very helpful to confirm your math work, especially with decimals or negative numbers.

• Always ensure your calculator is set to the correct operation mode for the task.
• Use it to double-check your results after doing a manual calculation.

For example, after calculating the sum of -47.03 + (-22.71) manually, you can use a calculator to verify.
Simply enter the expression as is into the calculator: -47.03 + (-22.71).
The calculator should read -69.74, giving you confidence in your manual work.