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Chapter 2: Problem 105

Use a commutative law to write an expression equivalent to $7+t

Short Answer

Expert verified
The expression equivalent to \[7 + t\] is \[t + 7\].

Step by step solution

01

Identify the Commutative Law

The commutative law states that for addition, the order in which numbers are added does not change the sum. For any two numbers, say a and b, the law is expressed as \[ a + b = b + a \].
02

Apply the Commutative Law

Apply the commutative law to the given expression. Here, the expression is \[7 + t\] and we need to rewrite it by swapping the positions of 7 and t using the commutative law.
03

Rewrite the Expression

By applying the commutative law, the original expression \[7 + t\] becomes \[t + 7\].

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Key Concepts

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

Commutative Property
The commutative property is a fundamental principle in mathematics that applies to both addition and multiplication. It asserts that the order in which you add or multiply numbers does not change the result. For example, in addition, if you have two numbers, say \(a\) and \(b\), the commutative property states that \(a + b = b + a\). This means you can swap the positions of the numbers, and the sum will remain the same. The same principle applies to multiplication as well, where \(a \times b = b \times a\). Understanding this property helps simplify many algebraic expressions and makes calculations more flexible and easier to handle.
Addition
Addition is one of the most basic operations in arithmetic and mathematics. It corresponds to the process of combining two or more numbers to get a total or sum. When you add two numbers, you're typically combining quantities together. For instance, if you have 3 apples and you get 2 more, you have a total of 5 apples, which is the result of adding 3 and 2. In algebra, addition extends to combining algebraic expressions as well, where variables and constants can be added to form new expressions. The commutative property of addition makes it easier to rearrange numbers and variables to simplify these expressions and solve equations more efficiently.
Algebraic Expressions
An algebraic expression is a mathematical phrase that can include numbers, variables (like \(t\) or \(x\)), and operations (such as addition, subtraction, multiplication, and division). Algebraic expressions are used to represent real-world problems in a symbolic form. For instance, the expression \(7 + t\) can represent the sum of 7 and some unknown number \(t\). By using the commutative property, we can rearrange this expression as \(t + 7\) without changing its value. Simplifying and manipulating algebraic expressions is a key skill in algebra that allows us to solve equations, understand relationships between quantities, and model real-life situations.

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Most popular questions from this chapter

Assume that \(r, p,\) and \(s\) are nonzero constants and that \(x\) and \(y\) are variables. Determine whether each equation is linear. $$ r^{2} x=p y+5 $$

Determine whether each equation is linear. Find the slope of any nonvertical lines. $$ 5 x-3 y=15 $$

Find the indicated function values. $$ f(x)=\left\\{\begin{array}{ll}{x^{2}-10,} & {\text { if } x<-10} \\ {x^{2},} & {\text { if }-10 \leq x \leq 10} \\ {x^{2}+10,} & {\text { if } x>10}\end{array}\right. $$ a) \(f(-10) \quad\) b) \(f(10)\) c) \(f(11)\)

Determine whether each equation is linear. Find the slope of any nonvertical lines. $$ g(x)-x^{3}=0 $$

Find the intercepts. Then graph by using the intercepts, if possible, and a third point as a check. $$ 0.2 y-1.1 x=6.6 $$
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