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Chapter 11: Problem 13

In the expression \(7 r\), how many \(r\) 's are indicated?

Short Answer

Expert verified
There are 7 r's indicated in the expression 7r.

Step by step solution

01

Understanding the Expression

In the expression \(7r\), the number 7 and the letter \(r\) are connected through multiplication. This implies that \(r\) is repeated 7 times or is multiplied by 7.
02

Identifying Repetitions

The coefficient (number in front of \(r\)) tells us how many times \(r\) is used. Here, the coefficient is 7, meaning \(r\) is present seven times in the expression.

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Key Concepts

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

Coefficients in Algebra
In algebra, a **coefficient** is a number that multiplies a variable. It provides important information about how many times you are using or repeating a given variable within an algebraic expression. Let's consider the expression \(7r\). Here, the coefficient is 7.
This tells us that the variable \(r\) is to be multiplied by 7 or used seven times.
Coefficients are crucial because they:
  • Help determine the quantity of the variable involved.
  • Indicate whether the variable should increase or decrease its value.
  • Affect the overall value and outcome of the algebraic expression.
Understanding coefficients is key to analyzing and simplifying expressions in algebra effectively.
They set the base for quantifying expressions where variables are involved.
Multiplication in Algebra
**Multiplication in algebra** involves combining quantities in a manner similar to arithmetic multiplication, yet it includes variables. In expressions like \(7r\), the coefficient (7) and the variable (\(r\)) are multiplied together. This indicates repeated addition of \(r\); for example, you are adding the variable \(r\) seven times.
Considerations when dealing with multiplication in algebra include:
  • Understanding that a number next to a variable implies multiplication.
  • Recognizing that multiplication affects both the coefficient and the variable.
  • Being aware of the associative and commutative properties that often apply in multiplying variables and coefficients.
For example, in multiplying variables like \(3a \times 4b\), you can rearrange and group terms: \(12ab\).
This flexibility is helpful in simplifying complex expressions.
Variables in Expressions
A **variable** in algebra represents an unknown value and is usually symbolized by letters such as \(x\), \(y\), or, as in our example, \(r\). Variables allow us to express general relationships and mathematical rules.
The beauty of variables lies in their ability to hold different values based on the problem at hand.Key points about variables include:
  • They stand in for numbers that can change or that we wish to find.
  • They are often paired with coefficients to express equations or expressions.
  • Understanding their role is critical in setting up and solving algebraic problems.
In the expression \(7r\), \(r\) represents the variable that is multiplied by the coefficient 7.
This structure is foundational in crafting equations that describe real-world scenarios.

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Most popular questions from this chapter

Translate each phrase or sentence to a mathematical expression or equation. A number minus the opposite of five.

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Translate each phrase or sentence to a mathematical expression or equation. When twelve is subtracted from five times some number, the result is two less than the original number.

For problems \(57-140\), solve each equation. $$ -3 z=\frac{2 z}{5} $$

Translate each phrase or sentence to a mathematical expression or equation. When a number divided by six is increased by nine, the result is one.
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