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Chapter 1: Problem 80

Perform each indicated operation. $$ (9-3)-15 $$

Short Answer

Expert verified
-9

Step by step solution

01

Evaluate the Expression Inside the Parentheses

First, calculate the expression inside the parentheses. Here we have \[ 9 - 3 = 6 \]
02

Subtract the Result Outside the Parentheses

Next, subtract the number outside the parentheses from the result obtained in Step 1. This means we perform the operation: \[ 6 - 15 = -9 \]

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Key Concepts

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

Subtraction Within Parentheses
In this exercise, we start with the expression \( (9 - 3) - 15 \). The first step is to handle the operation within the parentheses. Parentheses are crucial in math because they tell us which part of the expression to solve first.

In our example, it's \(9 - 3\). We subtract 3 from 9, which equals 6. Thus, the expression inside the parentheses simplifies to 6.
Evaluating Expressions
Once we've simplified the expression inside the parentheses, we can then evaluate the rest of the expression. The original expression \( (9 -3) - 15 \) now becomes \(6 - 15\).

Evaluating this new expression is straightforward because it simply involves subtracting two numbers. Start with the number 6 and subtract 15 from it. This results in -9. The final answer to our expression is -9.

Remember, always perform the simplifications step-by-step to avoid mistakes.
Order of Operations
The order of operations is a fundamental concept in math that dictates the correct sequence to evaluate a mathematical expression. We'll use the mnemonic PEMDAS to remember the right order:
  • P: Parentheses first
  • E: Exponents (powers and roots)
  • MD: Multiplication and Division (from left to right)
  • AS: Addition and Subtraction (from left to right)

In our example, (9 - 3) - 15, we first solved the expression in the parentheses: (9 - 3) to get 6. Following PEMDAS, we moved from parentheses to subtraction, evaluating the simplified expression 6 - 15 to get the final result of -9.

Always sticking to the order of operations ensures consistency and correctness in solving math problems.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 5 if its last digit is divisible by \(5,\) and not otherwise. (a) Is 9,332,123 divisible by \(5 ?\) (b) Is 3,774,595 divisible by \(5 ?\)

Solve each problem. The lowest temperature ever recorded in Arkansas was \(-29^{\circ} \mathrm{F}\). The highest temperature ever recorded there was \(149^{\circ} \mathrm{F}\) more than the lowest. What was this highest temperature? (Data from National Climatic Data Center.)

Find the average of each group of numbers. All integers between -15 and \(-10,\) including both -15 and -10

Write each sentence as an equation, using \(x\) as the variable. Then find the solution of the equation from the set of integers between -12 and \(12,\) inclusive. An integer is divisible by 4 if its last two digits form a number divisible by \(4,\) and not otherwise. (a) Is 2,876,335 divisible by \(4 ?\) (b) Is 6,221,464 divisible by \(4 ?\)

Write each phrase as a mathematical expression using \(x\) as the variable, and simplify. Nine times a number added to \(6,\) subtracted from triple the sum of 12 and 8 times the number
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