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Chapter 2: Problem 347

In the following exercises, simplify. $$ 4+3(10-1) $$

Short Answer

Expert verified
31

Step by step solution

01

Simplify inside the parentheses

Identify the expression inside the parentheses, which is \(10 - 1\). Simplify this expression.\[10 - 1 = 9\]
02

Multiply by the factor outside the parentheses

Multiply the result of the expression inside the parentheses by the factor outside the parentheses. The factor outside is 3. So, compute: \[3 \times 9 = 27\]
03

Add the remaining numbers

Add the result from the previous step with the remaining number in the original expression, which is 4. Thus,\[4 + 27 = 31\]

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Key Concepts

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

Order of operations
When simplifying arithmetic expressions, understanding the order of operations is crucial. This determines the sequence in which you should perform calculations to get the correct result. The acronym PEMDAS helps recall these rules:
  • Parentheses first
  • Exponents (ie powers and square roots, etc.)
  • Multiplication and Division (left-to-right)
  • Addition and Subtraction (left-to-right)
To simplify correctly, always start with operations inside parentheses, then handle exponents, followed by multiplication and division, and finally perform addition and subtraction.
In our example, \(4+3(10-1)\), we begin by simplifying the parentheses.
Parentheses simplification
Parentheses indicate which operations should be performed first. It's like gathering all smaller parts of the whole problem and solving each part before handling the entire expression. For the example given, \(4+3(10-1)\), look inside the parentheses first.
\(10 - 1\) simplifies to \9\. This gives us a new expression \(4 + 3 \times 9\). Now that parentheses are simplified, continue to the next step.
Multiplication in arithmetic
In expressions, multiplication is prioritized over addition and subtraction. Once you've handled parentheses and any exponents:
Continue with multiplication or division before addition or subtraction. Looking at \(4 + 3 \times 9\), perform the multiplication first:
\(3 \times 9 = 27\). Now the expression is simpler: \(4 + 27\). Finally, perform the addition: \4 + 27 = 31\.
We have simplified the expression following all proper arithmetic rules.

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