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Chapter 1: Problem 72

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

Short Answer

Expert verified
-9

Step by step solution

01

Perform operation inside the parentheses

First, evaluate the expression inside the parentheses (9-3). Subtract 3 from 9 to get 6.
02

Subtract 15 from the result

Next, subtract 15 from the result obtained in Step 1. Therefore, 6 - 15 = -9.

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Key Concepts

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

Order of Operations
In arithmetic, it's essential to perform operations in the correct order to get the right answer. This is called the **Order of Operations**. The order is often remembered by the acronym **PEMDAS**:
  • P: Parentheses
  • E: Exponents
  • M: Multiplication
  • D: Division
  • A: Addition
  • S: Subtraction

According to this rule, you must solve any operations inside parentheses first. In our exercise, we first solve the part inside the parentheses, which is **(9 - 3)**. Only after this, we move to the next step.
Subtraction
Subtraction is one of the basic arithmetic operations. It represents taking away one number from another. When following the order of operations, subtraction is performed after parentheses, exponents, multiplication, and division:
  • First, we subtract inside the parentheses: (9 - 3), which equals 6.
  • Then, we handle the remaining subtraction: 6 - 15.

In our exercise, subtracting 15 from 6 results in -9, showing that we move into the realm of negative numbers.
Negative Numbers
Negative numbers are less than zero. They are used to represent a loss or decrease and are written with a minus sign in front. When you're subtracting a larger number from a smaller one, the result is negative.
  • In our exercise: (9 - 3) - 15, we first find 9 - 3 = 6.
  • Next, we subtract 15 from 6, which gives us -9.

This is because 6 is less than 15, so the subtraction crosses zero and continues into negative territory, ending at -9.

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Most popular questions from this chapter

Write a numerical expression for each phrase and simplify. See Examples 7 and \(8 .\) The product of 12 and the difference between 9 and \(-8\)

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Find each difference. $$ 8-13 $$

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