Problem 89 - Elementary Algebra

Question

$$ -12-5 $$

Step-by-Step Solution

Answer

-7

Step 1: Identify the numbers

The given numbers are -12 and -5.

Step 2: Understand the operation

The operation to be performed is subtraction of -5 from -12.

Step 3: Rewrite the operation as addition

Rewrite the subtraction of a negative number as adding its positive counterpart: -12 - (-5) = -12 + 5.

Step 4: Perform the addition

Add 5 to -12: -12 + 5 = -7.

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They are found to the left of zero on the number line. Think of negative numbers as debts or temperatures below freezing. They are denoted with a minus sign (-). For example, -3 is 3 units left of zero on the number line. Negative numbers are used in various real-world scenarios like banking (debts), temperatures, and elevations below sea level. When performing arithmetic operations with negative numbers, understanding their behavior is crucial.
For example: -5, -10, -15 are all negative numbers.
Negative numbers can be added, subtracted, multiplied, and divided just like positive numbers. However, some special rules apply to ensure accurate calculations.

Subtraction

Subtraction is one of the basic arithmetic operations, and it involves taking away a number from another. When dealing with negative numbers, the operation can seem tricky. Subtracting a negative number is the same as adding its positive counterpart. This is because two negatives make a positive. For example, in the exercise -12 - (-5), subtracting -5 from -12 can be rewritten as -12 + 5. Here’s how you do it:

• Identify the numbers involved
• Rewrite the subtraction as addition by changing the sign of the number being subtracted
• Perform the addition

This makes it easier to handle and leads to the correct result.

Addition

Addition involves combining two or more numbers to get their total. When adding positive and negative numbers, keep the following in mind:

• If both numbers are positive, the result is positive.
• If both numbers are negative, the result is negative, and you add their absolute values.
• If one number is positive and the other is negative, subtract the smaller absolute value from the larger absolute value, and take the sign of the number with the larger absolute value.

For example, adding -12 and 5, as in the exercise, means subtracting 5 from 12, because -12 has the larger absolute value, and the result will be negative. So, -12 + 5 = -7. Practicing these rules will help make integer addition a breeze.