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Chapter 1: Problem 33

Simplify the given expression. $$ (18+10) \div(2+2) $$

Short Answer

Expert verified
The simplified expression is 7.

Step by step solution

01

Simplify the Numerator

The numerator is the expression inside the parentheses: \(18 + 10\). Add these numbers together to get \(28\).
02

Simplify the Denominator

The denominator is the expression inside the second pair of parentheses: \(2 + 2\). Add these numbers together to get \(4\).
03

Divide the Numerator by the Denominator

Now divide the simplified numerator \(28\) by the simplified denominator \(4\). Perform the division: \(28 \div 4 = 7\).

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Key Concepts

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

Simplifying Expressions
In prealgebra, simplifying expressions is a fundamental skill that helps make complex problems easier to understand and solve. An expression may contain numbers, operators, and sometimes parentheses. The goal is to combine like terms and perform any calculations possible to reduce the expression to its simplest form.
To simplify expressions:
  • Look for terms that can be combined: These are usually the terms with the same variable or just plain numbers if you鈥檙e working with constant terms.
  • Perform any addition or subtraction that is straightforward, especially those inside parentheses.
  • Ensure all arithmetic operations within parentheses are completed before moving on to any other operations.
By following these steps, the expression becomes streamlined and ready for any subsequent operations which might need to be performed.
Order of Operations
When simplifying mathematical expressions, it's essential to follow the order of operations. This rule is critical to obtaining the correct result. The order of operations is often remembered by the acronym PEMDAS.
PEMDAS stands for:
  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)
In our example, \( (18+10) \div(2+2) \), following PEMDAS means starting with the operations inside the parentheses first:
  • Add the numbers inside each set of parentheses: \(18 + 10 = 28\) and \(2 + 2 = 4\).
  • Then, move on to division: \(28 \div 4\).
By correctly applying the order of operations, we ensure that we get the right answer when simplifying expressions.
Division in Mathematics
Division is one of the primary operations in mathematics and can sometimes be misunderstood due to its nature as the 'reverse' of multiplication. In the context of simplifying expressions, division helps to solve expressions by breaking them down into smaller parts.
Here's how division works:
  • A division problem consists of the dividend (the number being divided) and the divisor (the number you divide by).
  • The result is called the quotient.
In our example, Understanding division enables us to simplify complex mathematical expressions and solve equations efficiently. Remember, when dividing by a number, you're essentially treating the dividend as a whole and determining how many times the divisor can "fit" into that whole.

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Most popular questions from this chapter

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