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Chapter 1: Problem 79

Subtract. $$ -31-(-31) $$

Short Answer

Expert verified
-31 - (-31) = 0

Step by step solution

01

Understand the Problem

We are given the expression \(-31 - (-31)\), and asked to find its value.
02

Simplify the Expression

Notice that we are subtracting a negative number. Subtracting a negative number is the same as adding its positive counterpart. Therefore, \(-31 - (-31)\) becomes \(-31 + 31\).
03

Add the Numbers

Now we add the numbers \-31\ and \31\. Since they are opposites, their sum is 0. Hence, \(-31 + 31 = 0\).

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Key Concepts

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

Subtracting Negative Numbers
Understanding how to subtract negative numbers is essential in math. It can seem tricky at first, but it becomes simple with practice. When you subtract a negative number, you are essentially adding a positive one. This is because subtracting a negative is the same as adding its positive counterpart.

Consider the problem \( -31 - (-31) \). At a glance, this might look confusing. However, you can simplify it by recognizing that subtracting \( -31 \) is the same as adding \(+31\). This converts the original problem to \( -31 + 31 \). Now you see, subtracting a negative number transforms the problem into an addition problem!
Simplify Expressions
Simplifying expressions is a key skill in math that helps solve problems more easily. Breaking down complex expressions into simpler components can often make the problem much clearer.

In the example \( -31 - (-31) \), we simplified the subtraction of a negative by turning it into an addition: \( -31 + 31 \). This simplification step is crucial because it reduces the complexity of the original problem. Learn to identify when and how to simplify math expressions, as this skill will come handy in algebra and beyond.
Adding Integers
Adding integers is one of the basic operations in math that forms the foundation for more complex arithmetic. When adding integers, consider their signs.
Here are some quick tips:
  • When adding a positive and a negative integer, think about which number has the greater absolute value. The result takes the sign of that number.
  • If the integers have the same sign (both positive or both negative), simply add their absolute values and keep the sign.
Back to our example: \( -31 + 31 \). Here, \( -31 \) and \( 31 \) are opposites. Their absolute values are the same, so they cancel each other out, leaving \ 0 \. This is why \( -31 + 31 = 0 \)!

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Most popular questions from this chapter

Classify each statement as either true or false. The following sets are used: \(\mathrm{N}=\) the set of natural numbers; \(W=\) the set of whole numbers; \(\mathbb{Z}=\) the set of integers; \(\mathbb{C}=\) the set of rational numbers; \(\mathrm{H}=\) the set of irrational numbers; \(\mathrm{R}=\) the set of real numbers. $$ \mathrm{W} \subseteq Z $$

Find an equivalent expression by factoring. $$ 7 x-21 y+14 z $$

Find an equivalent expression by factoring. $$ 5 d+30 $$

Find an equivalent expression by factoring. $$ 9 p-3 $$

Use set-builder notation to write each set. The set of all multiples of 5 between 7 and 79
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