Problem 42 - Fundamentals of Mathematics

Question

Find the sums in the following 27 problems. If possible, use a calculator to check each result. $$ 13+(-56) $$

Step-by-Step Solution

Answer

The sum is -43.

Step 1: Identify the Numbers

We are asked to find the sum of two numbers: 13 and -56. Here, 13 is a positive number and -56 is a negative number.

Step 2: Understand the Operations

When adding a positive number and a negative number, you're essentially subtracting the smaller number from the larger one and taking the sign of the larger number. The sign of -56 is negative, so the result will also be negative.

Step 3: Perform the Calculation

Subtract the smaller absolute value from the larger: \[|56| - |13| = 56 - 13 = 43\]Since 56 (from -56) has a greater absolute value than 13, the result is -43.

Step 4: Verify with a Calculator

Use a calculator to verify the result by entering: 13 + (-56). The calculator should display -43, confirming our manual calculation.

Key Concepts

Positive Numbers

Positive numbers are the numbers greater than zero. They can be whole numbers like 1, 2, 3, and so on, fractions, or decimals. The main thing is they are all above zero, indicating profit, gain, or increase.
When you add two positive numbers together, you continue to move to the right on the number line. For example, adding 3 and 5 results in 8. You would simply count up.

• Stay to the right side of zero.
• Results are always positive.
• Indicate amounts above the zero mark.

Negative Numbers

Negative numbers are less than zero, represented with a minus sign (-) before them. They can also be whole numbers, fractions, or decimals. These numbers are like depths below sea level, debts, or temperatures below zero.
When you add a positive number and a negative number, you essentially subtract their absolute values. The result takes the sign of the larger absolute value. This is crucial to understand.

• Consider 13 + (-56): The operation is a subtraction because signs differ.
• Subtracting the smaller absolute value from the larger: 56 - 13 = 43.
• Because 56 is larger, and its original sign is negative, the result is -43.

Calculator Verification

Using a calculator to verify your results is a great practice. Even if you're confident in your math skills, calculators help confirm your answers quickly and efficiently.
For the operation 13 + (-56), entering these numbers in your calculator should show -43, verifying your manual calculations.

• Double-check work, especially with complex problems.
• Boosts confidence by confirming manual results.
• Minimizes small errors that can occur with paper calculations.

Having a calculator handy means you can tackle even larger, more complex sums with ease, supporting your learning effectively.