Problem 35 - Fundamentals of Mathematics

Question

Find the sums in the following 27 problems. If possible, use a calculator to check each result. $$ -5+(-12)+(-4) $$

Step-by-Step Solution

Answer

The sum is -21.

Step 1: Understand the Operation

We need to find the sum of the three numbers: -5, -12, and -4. All are negative numbers.

Step 2: Add the First Two Numbers

Start by adding the first two numbers: \(-5 + (-12) = -5 - 12 = -17\).

Step 3: Add the Result with the Third Number

Now add the result from Step 2 to the third number:\(-17 + (-4) = -17 - 4 = -21\).

Step 4: Verify with a Calculator

Using a calculator, verify that \(-5 + (-12) + (-4) = -21\). The result should be the same, confirming our previous steps.

Key Concepts

Understanding Integer Addition

Integer addition involves combining two or more numbers, which can be positive or negative, to find their total amount. In this exercise, we're dealing with negative numbers specifically. Remember that integers are whole numbers that can be positive, negative, or zero. Additionally, adding integers doesn't change the identity of integers, meaning you will still get a whole number as a result.

When adding integers, follow these simple guidelines:

• Positive numbers add up to increase the total.
• Negative numbers add up to decrease the total value.
• If you have both positive and negative numbers, think of this as adding gains and losses. Combine accordingly.

In the original exercise, you add -5, -12, and -4. Each step involves adding further negative numbers, which means you're going deeper into negative territory, effectively "losing" more each time.

Negative Number Operations

Working with negative numbers can sometimes feel a bit tricky, but it's all about perspective. Think of negative numbers as movements to the left on a number line. Adding -5, for instance, means you're moving 5 steps to the left.

Here's what happens as you perform negative number operations:

• Adding a negative number is equivalent to subtracting the positive version of that number.
• When you see expressions like -5 + (-12), you interpret it as -5 taking an additional 12 steps left, resulting in -17.
• Continuing this, adding -4 takes the sum from -17 to -21.

Remembering these movements on the number line can simplify working with negatives. They are not just opposites of positives but also represent a shift in direction.

Calculator Verification

A calculator is a great tool for verifying your results, especially in complex calculations. Knowing how to double-check your math manually is crucial, but confirming the numbers with a calculator ensures accuracy and builds confidence.

Here’s how to do calculator verification:

• Enter each number with the correct sign in sequence, exactly as the problem states.
• After each operation, check flash results to make sure no input errors.
• Compare the calculator result to your manual solution. If they match, your work is correct; otherwise, re-check each step to find discrepancies.

In this exercise, after combining -5, -12, and -4 and obtaining -21, using a calculator to confirm reinforces accuracy. It's a reliable method that saves time and provides peace of mind.