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Chapter 7: Problem 67

In the following exercises, simplify. $$ (5.89 d+2.75 d)+1.25 d $$

Short Answer

Expert verified
9.89d

Step by step solution

01

Identify Like Terms

Notice that in the expression \(5.89d + 2.75d + 1.25d\), all the terms are like terms since they all contain the variable \(d\).
02

Combine Like Terms

Since all terms are like terms, add the coefficients together: \(5.89d + 2.75d + 1.25d = (5.89 + 2.75 + 1.25)d\).
03

Calculate the Sum of Coefficients

Compute the sum of the coefficients: \(5.89 + 2.75 + 1.25 = 9.89\).
04

Rewrite the Expression

Write the simplified expression by combining the coefficient with the variable: \(9.89d\).

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Key Concepts

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

Like Terms
In algebra, **like terms** are terms that have the same variable raised to the same power. For example, in the expression we are simplifying \(5.89d + 2.75d + 1.25d\), all the terms have the variable \(d\). This means they are like terms.When identifying like terms:
  • Make sure the variables are identical, including their exponents.
  • Like terms can be combined because they represent the same type of quantity.
A common beginner mistake is to attempt to combine terms that are not alike. For example, \(3x\) and \(4y\) cannot be combined because they involve different variables \(x\) and \(y\). In contrast, any terms with the same variable, such as \(4d\) and \(5d\), can be easily combined.
Combining Coefficients
Once you identify like terms, the next step is to combine their coefficients. The **coefficient** is the numerical factor of a term. In the expression \(5.89d + 2.75d + 1.25d\), the coefficients are \(5.89, 2.75\), and \(1.25\).To combine coefficients, you simply add or subtract the numbers in front of the like terms. For our example, add the coefficients as follows: \(5.89 + 2.75 + 1.25\). To break it down:
  • First, add \(5.89\) and \(2.75\) to get \(8.64\).
  • Then, add \(8.64\) to \(1.25\): \(8.64 + 1.25 = 9.89\).
So, the combined coefficient of the expression is \(9.89\). Once the coefficients are combined, the expression will be simplified to \(9.89d\).
Basic Algebra Operations
In this example, we also used **basic algebra operations** to simplify the expression. These operations usually include addition, subtraction, multiplication, and division.Here are some crucial points to remember:
  • Always perform operations on coefficients if the terms are like terms.
  • Make sure to adhere to the order of operations (PEMDAS/BODMAS) where applicable.
In our specific example, the operation involved was addition. We added the coefficients \(5.89, 2.75, \ \)and \(1.25\), to simplify the equation to its most basic form, \(9.89d\).Following these steps, algebra becomes more manageable. Remember, identify like terms, combine coefficients, and apply basic operations accurately!When you keep these principles in mind, simplifying algebraic expressions becomes much easier and less intimidating.

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