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Chapter 2: Problem 91

Simplify each of the following. $$2+3(4+1)$$

Short Answer

Expert verified
The simplified expression is 17.

Step by step solution

01

Solve Inside the Parentheses

Begin by solving the expression inside the parentheses. In this case, add the numbers inside the parentheses: \(4 + 1 = 5\).
02

Multiply by the Coefficient

Now that we've simplified the parentheses, multiply the result by the number outside the parentheses. The expression becomes: \(3 \times 5 = 15\).
03

Add the Remaining Numbers

Finally, add the result from Step 2 to the remaining number outside the parentheses. Thus, the expression becomes: \(2 + 15 = 17\).

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Key Concepts

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

Simplification of Expressions
Simplification of expressions is a key skill in mathematics. It involves reducing complex mathematical expressions into simpler forms while retaining their original meaning. This process often makes it easier to understand and solve problems.
  • Identify and address operations according to the order of operations.
  • Eliminate unnecessary parts or simplify fractions.
With practice, simplifying expressions becomes intuitive, allowing for quick and accurate calculations. Remember to always follow the rules of arithmetic operations for accurate results.
Parentheses in Mathematics
Parentheses play a vital role in mathematics by indicating which operations should be performed first. They override the normal precedence usually given in an equation. Let's break down their importance:
  • Grouping: Parentheses are used to group numbers and operations, ensuring that anything within them is treated as a single unit.
  • Order: Always perform calculations inside parentheses first, before tackling any other operations in the expression.
For instance, in the expression \(2+3(4+1)\), the parentheses around \(4+1\) mean this calculation is done first, giving a result of 5 before other operations.
Basic Arithmetic Operations
Basic arithmetic operations are the foundational blocks of mathematics, consisting of addition, subtraction, multiplication, and division. Understanding how these operations work independently and together is crucial for solving problems effectively. Here's how they relate to our example expression:
  • Addition: In the expression \(4+1\) within the parentheses, addition is the first step.
  • Multiplication: The result from the parentheses is multiplied by 3, following the basic rule that multiplication comes before addition in the absence of parentheses.
  • Final Addition: Finally, the previously obtained product is added to 2, completing the simplification process and resulting in 17.
Recognizing the sequence of these operations when they're combined is fundamental for tackling more complex problems.

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Most popular questions from this chapter

Simplify as much as possible by first changing all subtractions to addition of the opposite and then adding left to right. $$-29-53-37$$

Perform the indicated operations. $$2(5+8)$$

Apply the distributive property to each expression and then simplify the result. $$2(3+4)$$

Add or subtract. $$[2+12]+[7-5]$$

Add or subtract. $$12+15$$
See all solutions

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