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Chapter 1: Problem 31

Simplify the given expression. $$ 7 \cdot[8-5]-10 $$

Short Answer

Expert verified
The expression simplifies to 11.

Step by step solution

01

Simplify Inside the Brackets

Identify and simplify the expression inside the brackets. The bracket contains the operation \(8 - 5\). Solve this to get \(3\).
02

Multiply by 7

Now that we have simplified the bracket to \(3\), multiply it by \(7\). So, \(7 \cdot 3 = 21\).
03

Subtract 10

From the result of the multiplication, subtract \(10\). Compute \(21 - 10\) to get \(11\).

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Key Concepts

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

Order of Operations
When dealing with mathematical expressions, the order of operations is crucial. It tells us which operations to perform first to ensure accurate results. This order can often be remembered by the acronym PEMDAS:

  • **P**arentheses (or brackets)
  • **E**xponents (or powers and roots)
  • **M**ultiplication and **D**ivision (from left to right)
  • **A**ddition and **S**ubtraction (from left to right)
In our example, the expression does not include exponents, but it does involve parentheses, multiplication, and subtraction. The first step was to solve the operation within the parentheses: \(8 - 5\), which equals \(3\). After simplifying the brackets, we proceed with multiplication before subtraction, as prescribed by PEMDAS. It's important to always follow this sequence to avoid misinterpretations of calculations.
Basic Arithmetic
Basic arithmetic refers to the four foundational operations: addition, subtraction, multiplication, and division. In the given problem, we employ subtraction and multiplication.

Let's break down what each operation involves:
  • **Subtraction**: Takes away a certain number from another, simplifying our initial brackets, \(8 - 5 = 3\).
  • **Multiplication**: Combines repeated addition. For instance, multiplying \(7\) by \(3\) results in adding \(7\) three times, yielding \(21\).
By grasping these fundamental operations, students build a solid arithmetic foundation. In this scenario, performing operations step-by-step helps reinforce the basic arithmetic skills required for more complex problems.
Prealgebra Expressions
Prealgebra expressions often introduce variables and operations that prepare students for algebra. Even without variables, problems like our task of simplifying \(7 \cdot[8-5]-10\) hone in on those prealgebra skills.

Here's what prealgebra requires you to understand:
  • Breaking down expressions into smaller parts.
  • Using operations systematically to simplify.
  • Learning to trust the method and sequence (like order of operations) to reach the correct solution.
Even though there aren鈥檛 variables here, these skills are relevant. Simplifying expressions in prealgebra builds confidence and skill for transitioning to algebraic expressions with variables. The approach undertaken鈥攊nvolving simplifying brackets, multiplication, and subtraction鈥攎irrors the procedures in algebra but with straightforward arithmetic, laying an excellent foundation.

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