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Chapter 2: Problem 5

Solve the following addition problems. $$ (+4)+(-4) $$

Short Answer

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Step by step solution

01

Identify the numbers

In the problem, we have two numbers: 1. The first number is +4.2. The second number is -4.
02

Understand the addition rules for integers

When adding integers, if one is positive and the other is negative, subtract the smaller absolute value from the larger absolute value. The result takes the sign of the number with the larger absolute value.
03

Apply the rule

In this case, the absolute values are the same: 1. Absolute value of +4 is 4.2. Absolute value of -4 is also 4.Since they are equal, the result is zero.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

absolute value
In mathematics, the **absolute value** of a number is its distance from zero on a number line, disregarding whether it is positive or negative. The absolute value is always non-negative. For example, the absolute value of both +4 and -4 is 4. The term 'absolute value' is often represented by two vertical bars, so the absolute value of **a** is written as \(|a|\). The idea behind absolute value is to measure how large a number is without considering its direction on the number line.
addition rules
Addition rules for integers can be simplified with a few basic principles. Knowing these rules is crucial for solving many types of math problems:
  • **Adding two positive integers** results in a positive integer. For example, \( +3 + +2 = +5 \).
  • **Adding two negative integers** results in a negative integer. For example, \( -3 + -2 = -5 \).
However, adding a positive integer with a negative integer requires extra care:
  • If the absolute value of the positive integer is greater than the absolute value of the negative integer, the result is positive. For example, \( +5 + -3 = +2 \).
  • If the absolute value of the negative integer is greater, the result is negative. For example, \( -5 + +3 = -2 \).
  • If the absolute values are equal, the result is zero. For example, \( +4 + -4 = 0 \).
Understanding these rules helps to simplify and solve addition problems quickly, ensuring accuracy.
integers
**Integers** are a set of numbers that include all the whole numbers, their negatives, and zero. They do not include fractions or decimals. Examples of integers include -3, 0, and +5. Integers are represented by the letter **Z** in mathematics. They play a crucial role in various math concepts and everyday situations. For example, when adding or subtracting integers, it's important to understand their properties. Knowing that -4 means moving four units to the left on the number line and +4 means moving four units to the right helps in visualizing and solving problems. Mastering integer operations is essential in building a strong foundation for higher-level math.

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Most popular questions from this chapter

Solve these division problems. $$ (-6) \div(-3) $$

Mark each statement true (T) or false (F). 5 is an integer.

See if you can figure out the sign of the correct answer to each problem. Then circle the letter next to the correct answer and spell a phrase. $$ (-4)+(-7)=\quad(-) P \text { or }(+) H $$

Solve the following addition problems. $$ (+5)+0 $$

Solve the following addition problems. $$ (-5)+(+2) $$
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