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Chapter 2: Problem 18

Write as an equivalent addition; then evaluate. $$9-15$$

Short Answer

Expert verified
Question: Rewrite the subtraction 9-15 as an equivalent addition and find the result. Answer: The equivalent addition is 9+(-15), and the result is -6.

Step by step solution

01

Rewrite subtraction as equivalent addition

In order to rewrite this subtraction as an addition, we can change the sign of the second number and proceed with addition. So, we will add the opposite of the second number to the first number, making the subtraction an addition as shown below:$$ 9-15 = 9+(-15) $$
02

Evaluate the addition

Now, we have the equivalent addition, \(9+(-15)\). Let's evaluate the result of the addition:$$ 9+(-15) = -6 $$So the equivalent addition is \(9+(-15)\), and the result of the addition (and thus the original subtraction \(9-15\)) is \(-6\).

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Key Concepts

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

Negative Numbers
Negative numbers are numbers less than zero and are represented with a minus sign, like \(-15\). In mathematics, they can be thought of as numbers that indicate an opposite direction or value. Think of a thermometer: when the temperature is below zero, it is considered negative.
  • Negative numbers can represent things like debts or temperature below freezing.
  • The further a number is from zero on the negative side, the smaller its value actually is (e.g., \(-15\) is less than \(-9\)).
When performing arithmetic operations, it鈥檚 important to remember that two negatives make a positive, which is key to converting subtraction into addition when tackling equations. To grasp negative numbers better, consider them as movements on a number line, heading toward the left for negative, and right for positive numbers.
Integer Operations
Integer operations involve performing arithmetic on whole numbers, including both positive and negative numbers. These operations can be addition, subtraction, multiplication, or division. When working with integers, especially involving both positive and negative numbers, it鈥檚 crucial to follow specific rules:
  • Addition: Adding two positive or two negative integers gives a positive or negative result, respectively.
  • Subtraction: Subtracting a number is the same as adding its opposite. For example, \(9 - 15\) can be seen as \(9 + (-15)\).
  • Multiplication and Division: Multiplying or dividing two integers with the same sign results in a positive number, while different signs yield a negative result.
When transforming subtraction into addition, consider that subtracting a positive integer is equivalent to adding its negative counterpart, which simplifies the calculations.
Basic Arithmetic
Basic arithmetic involves the fundamental mathematical operations: addition, subtraction, multiplication, and division. These operations form the foundation of arithmetic which we use in everyday calculations. Understanding these concepts helps solve various math problems efficiently.
  • Addition: Combining two numbers into a single sum.
  • Subtraction: Finding the difference between two numbers, which can always be reinterpreted as addition of a negative.
  • Multiplication: A shorthand for repeated addition.
  • Division: Determining how many times one number is contained within another.
In this exercise, subtraction was converted to addition using the basic principle of arithmetic: that subtracting a number is the same as adding its opposite. This simple act transforms potentially tricky problems into something more straightforward by using these foundational concepts.

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Most popular questions from this chapter

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