Problem 32 - Prealgebra and Introductory Algebra

Question

Add. $$-89+62$$

Step-by-Step Solution

Answer

-27

Step 1: Understand the numbers

In this problem, the numbers are -89 and +62. The number -89 is negative, and the number +62 is positive. These are the numbers we need to add.

Step 2: Addition of positive and negative numbers

When adding a negative number (-89) and a positive number (+62), the rule is to subtract the numbers without considering the signs, and to take the sign of the larger number (in terms of absolute value).

Step 3: Compute the operation

Subtract the absolute value of the numbers: \(|89| - |62| = 27\). The result will take the sign of -89 (which has the larger absolute value), which results in -27.

Key Concepts

Negative Numbers

Negative numbers are numbers that are less than zero. They are shown with a minus sign, like \(-89\). Negative numbers can represent many things, like temperatures below freezing or financial debts.

• Whenever you see a negative sign, it indicates that the number is less than zero.
• These numbers are found to the left of zero on a number line.
• Adding negative numbers usually means you're subtracting in the real world.

Understanding negative numbers is crucial, especially when it comes to performing operations like addition and subtraction.

Absolute Value

The absolute value of a number is how far it is from zero on a number line, regardless of its direction. It's always a positive value or zero.

• The absolute value of \(+5\) and \(-5\) is the same, which is 5.
• It's denoted by two vertical bars around the number, for example, \(|-89| = 89\).

When dealing with integer addition, especially with negative numbers, absolute value helps us determine which number has a larger magnitude without worrying about the sign.

Addition Rules

When adding numbers, there are specific rules to follow based on the signs of the numbers involved:

• If both numbers are positive, simply add them together.
• If both are negative, add their absolute values and make the result negative.
• When one is positive and the other is negative, subtract the smaller absolute value from the larger absolute value.
• The sign of the result will be the same as the number with the larger absolute value.

Understanding these rules allows you to correctly solve addition problems, no matter the combination of positive and negative numbers.

Positive Numbers

Positive numbers are those greater than zero and are found to the right of zero on a number line. They are numbers without a sign or with a plus sign, like \(+62\).

• Positive numbers are associated with gains, like income or increasing temperatures.
• Adding positive numbers increases their overall value.

In operations with integers, recognizing positive numbers helps you apply the correct addition rules, especially when combined with negative numbers.