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Chapter 3: Problem 91

Use the rule for order of operations to combine the following. \((7-3)(8+2)\)

Short Answer

Expert verified
The expression evaluates to 40.

Step by step solution

01

Simplify Inside Parentheses

First, we need to simplify the expressions within each set of parentheses. For the expression \((7-3)\), subtract 3 from 7, which equals 4. For the expression \((8+2)\), add 8 and 2, which equals 10. So, the expression becomes \(4 \times 10\).
02

Multiply the Results

Now, apply the multiplication rule. Multiply the numbers obtained from the simplified parentheses: \(4 \times 10 = 40\).

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Key Concepts

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

Parentheses
Parentheses are an essential part of mathematical expressions and help dictate the correct order of operations. When you see expressions enclosed in parentheses, solve whatever is inside them first. By doing this, you ensure that you follow the operations in the correct sequence as outlined by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). For instance, consider an expression
  • Within \((7-3)\), subtract 3 from 7, resulting in 4.
  • Within \((8+2)\), add 8 and 2, resulting in 10.
Once simplified, the expression now looks cleaner and becomes easier to approach in the next steps.
Multiplication
Multiplication comes after dealing with operations inside parentheses. Once any expressions within parentheses are simplified鈥攁nd assuming there are no exponents鈥攜ou proceed with multiplication. Recall our example, where after simplifying parentheses, you are left with \(4 \times 10\).
  • Multiply these two numbers: \(4 \times 10 = 40\).
This key step shows the importance of executing operations in the correct order, as even a small mistake could lead to an entirely different result. Always verify your multiplications to ensure accuracy as this operation forms a pivotal step in solving expressions correctly.
Simplify Expressions
Simplifying expressions involves combining like terms and performing operations in the set sequence. The process requires careful execution of each step鈥攕tarting with parentheses, followed by multiplication, and continuing as needed based on the expression's complexity. This disciplined method ensures that the expressions are reduced to their simplest form.
  • Breaking it down: start by handling all operations within the parentheses.
  • Proceed to execute any multiplications.
  • By doing so, the original complicated expression simplifies, in this case, to a single number, \(40\).
Simplification is all about making expressions easier and cleaner to understand, ensuring that they convey results in the clearest and most concise form possible. By following these steps diligently, you gain confidence in managing more complex mathematical problems through a structured approach.

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Most popular questions from this chapter

Combine. \(\frac{1}{2}+\frac{2}{3}\)

Multiply or divide as indicated. $$\frac{35}{110} \cdot \frac{80}{63} \div \frac{16}{27}$$

The following problems all involve the concept of borrowing. Subtract in case. \(15-5 \frac{3}{10}\)

Find the following sums. (Add.) $$\begin{array}{r}8 \frac{2}{3} \\\9 \frac{1}{8} \\\\+6 \frac{1}{4} \\\\\hline\end{array}$$

Find the following sums. (Add.) $$\begin{array}{r}6 \frac{1}{7} \\\9 \frac{3}{14} \\\\+12 \frac{1}{2} \\\\\hline\end{array}$$
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