Problem 34 - Fundamentals of Mathematics

Question

Find the value of each of the following. Use a calculator to check each result. $$ 14-(-20) $$

Step-by-Step Solution

Answer

The value is 34.

Step 1: Identify the Expression

The expression given is a subtraction involving a negative number: \( 14 - (-20) \).

Step 2: Apply the Rule for Subtracting Negatives

Subtracting a negative number is equivalent to adding the positive of that number. So, \( 14 - (-20) \) becomes \( 14 + 20 \).

Step 3: Perform the Addition

Now, add the two numbers: \( 14 + 20 = 34 \).

Step 4: Verify Using a Calculator

Enter the expression \( 14 - (-20) \) into a calculator to check your manual calculation. The calculator should also return \( 34 \).

Key Concepts

Subtracting Negative Numbers

Subtracting negative numbers might seem tricky at first, but it follows a simple rule that makes everything clear. When you subtract a negative number, it's like taking away something that is not there, which essentially means you're adding. To make this clearer, consider this rule: **Subtracting a negative number is the same as adding its positive counterpart.** For example, if you have the expression \(14 - (-20)\), you can rewrite it as \(14 + 20\). This rule works because negative signs can "cancel out" each other. Imagine having two negatives, they kind of cancel out, making it positive. This is a concept that applies very often in mathematics, especially when dealing with numbers on the number line. Every time you see subtraction with a negative number, think of it as an opportunity to switch to addition.

Addition

Addition is one of the most fundamental operations in arithmetic, and it's used for combining numbers to find their total value. To add two numbers, you simply count upwards from one of them. In our exercise, after changing the subtraction of a negative to an addition, we have \(14 + 20\). Here's a breakdown:

• Start with 14.
• Add 20 more. If you're counting along, start at 14 and count to 34.

As a result, we get 34. Addition helps in tallying numbers together for a combined total and is easy to verify by counting.

Verification with Calculator

Verifying calculations with a calculator is a great strategy to ensure accuracy. Calculators can quickly handle complex and simple calculations alike, reducing the chance of manual errors. To verify the arithmetic operation \(14 - (-20)\), you would follow these steps on a calculator:

• Enter 14.
• Use the subtraction sign \(-\).
• Enter the negative number with its negative sign: \(-20\).
• Press equals \(=\).

You should see the result \(34\) displayed on the calculator. The technology helps reaffirm your manual work and provides peace of mind that the operation was correctly interpreted and calculated.