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Chapter 9: Problem 59

Simplify. $$ (18+8)-(12+4) $$

Short Answer

Expert verified
The simplified expression is 10.

Step by step solution

01

Simplify inside the parentheses

First, solve the operations inside each pair of parentheses. Begin with the first pair, \[(18+8)\]Calculate this:\[18 + 8 = 26\]Now, calculate the second pair of parentheses:\[(12+4)\]Calculate this:\[12 + 4 = 16\]
02

Subtract the results

After simplifying the expressions inside the parentheses, you subtract the result of the second from the first. This gives you:\[26 - 16\]
03

Calculate the subtraction

Now, perform the subtraction:\[26 - 16 = 10\]

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Key Concepts

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

Simplifying Expressions
Simplifying mathematical expressions involves reducing them to their simplest form. This means eliminating any unnecessary numbers or operations, combining like terms, and performing calculations when possible. In our example,
  • we have the expression \[(18+8)-(12+4)\].
  • The first step is to perform the calculations inside the parentheses.
  • This involves adding 18 and 8, as well as adding 12 and 4.
Breaking down the expression into smaller parts makes it easier to manage and understand. Simpler parts are straightforward to compute, like adding numbers within parentheses or subtracting in the final step.
The goal of simplifying expressions is to make complex problems easier to solve, minimizing the number of steps required.
Order of Operations
The order of operations is crucial in mathematics. It determines the sequence in which calculations are performed to get the correct result.
  • The commonly used acronym for remembering the order is PEMDAS:
    • P for Parentheses
    • E for Exponents
    • M for Multiplication
    • D for Division
    • A for Addition
    • S for Subtraction
In the exercise \[(18+8)-(12+4)\],
  • we addressed the parentheses first,
  • following the rule that operations inside parentheses should be completed before anything else.
This ensures accurate completion of expressions, especially when dealing with complex problems. Remembering the order of operations is essential to correctly approach and solve any mathematical problem without errors.
Basic Arithmetic
Basic arithmetic is the foundation of all mathematics. It includes simple operations like addition, subtraction, multiplication, and division. These fundamental operations are the building blocks for more complex calculations.
In our problem \[(18+8)-(12+4)\],
  • addition and subtraction were used.
  • The first step involves adding numbers within the parentheses.
  • Add 18 and 8 to get 26,
  • and 12 and 4 to get 16.
Next, subtraction is used to find the difference between these sums:
  • 26 minus 16 results in 10.
Understanding basic arithmetic is essential because it is used frequently in daily life and forms the basis for learning more advanced mathematical concepts.

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