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Chapter 2: Problem 42

Add the numbers with different signs. $$45+(-45)$$

Short Answer

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Step by step solution

01

Understand the Problem

The task requires adding 45 and -45. Note that these numbers have different signs.
02

Identify that the Numbers are Opposites

45 is a positive number and -45 is its negative equivalent. They are opposite numbers.
03

Apply the Rule of Adding Opposites

When you add a number to its opposite, the sum is always zero. Therefore, 45 + (-45) equals 0.

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Key Concepts

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

opposite numbers
Opposite numbers are numbers that are the same distance from zero on a number line but in opposite directions.
For example, 45 and -45 are opposite numbers.
Here are some key points about opposite numbers:
  • If you imagine a number line, positive numbers are to the right of zero, and negative numbers are to the left of zero.
  • The opposite of a positive number is negative, and the opposite of a negative number is positive.
  • Opposite numbers cancel each other out when added together.
A simple example is 3 and -3. When you place them on a number line, you can see they are an equal distance from zero but in opposite directions. Understanding opposite numbers is crucial in further understanding addition of integers and the sum of opposites.
addition of integers
Adding integers, especially with different signs, can be tricky at first, but it's based on straightforward rules.
There are two main cases to consider:
  • Adding integers with the same sign: When both numbers are either positive or both are negative, you simply add their absolute values and keep the common sign. For example, 5 + 7 = 12, and -4 + (-6) = -10.
  • Adding integers with different signs: This requires a bit more thought. You subtract the smaller absolute value from the larger absolute value and take the sign of the number with the larger absolute value. For example, 5 + (-3) = 2 and -8 + 3 = -5.
To add 45 and -45, you notice they have different signs and are actually opposites. This brings us to the next concept: the sum of opposites.
sum of opposites
The sum of opposites is a fundamental concept in adding integers. Opposites are pairs of numbers like 45 and -45.
When you add a number to its opposite, their absolute values are the same but signs are different. The result is always zero.
To visualize this:
  • Picture the number 45 on the number line, 45 units to the right of zero.
  • Now picture -45 on the number line, 45 units to the left of zero.
When you add 45 and -45, you're essentially moving 45 units to the right and then 45 units back to the left, landing you back at zero.
Mathematically, it's expressed as:
45 + (-45) = 0
Understanding that the sum of opposites is zero can simplify calculations and enhance your grasp of integer operations.

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Most popular questions from this chapter

Simplify. $$(-1)^{2}$$

Divide the real numbers, if possible. $$\frac{0}{-6}$$

Fill in the blank with \(<,>,\) or \(=\) $$-(82) \square|46|$$

Rank the numbers from least to greatest. If \(d\) represents a negative number, then what is the sign of \(-(-d) ?\)

Divide the real numbers, if possible. $$\frac{30}{-6}$$
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