Problem 95
Question
In Exercises 89-96, evaluate the expression. $$ \frac{-144}{-12} $$
Step-by-Step Solution
Verified Answer
The answer to the equation \(\frac{-144}{-12}\) is 12.
1Step 1: Identify the numbers and their signs
Here, two numbers are given: -144 and -12. Both numbers are negative.
2Step 2: Apply the rule of division for negative numbers
The rule of division states that a negative number divided by another negative number will yield a positive result. Apply this rule to the given numbers.
3Step 3: Perform the division
Now divide 144 by 12. The result is 12.
Key Concepts
Elementary AlgebraArithmetic OperationsDivision Rules
Elementary Algebra
Elementary algebra encompasses some of the basic concepts of algebra, one of the main branches of mathematics. It is typically taught in secondary education and includes the study of symbols and the rules for manipulating these symbols to solve problems.
When dealing with negative numbers in algebra, understanding the fundamental rules is crucial. The expression \( \frac{-144}{-12} \) presents a perfect example of how elementary algebra applies these rules. In this case, the symbols \( -144 \) and \( -12 \) represent negative numbers. Elementary algebra tells us that we can manipulate these numbers using division, while following specific arithmetic rules related to negative numbers.
When dealing with negative numbers in algebra, understanding the fundamental rules is crucial. The expression \( \frac{-144}{-12} \) presents a perfect example of how elementary algebra applies these rules. In this case, the symbols \( -144 \) and \( -12 \) represent negative numbers. Elementary algebra tells us that we can manipulate these numbers using division, while following specific arithmetic rules related to negative numbers.
Arithmetic Operations
Arithmetic operations refer to the basic mathematical operations that consist of addition, subtraction, multiplication, and division. These are the building blocks for more advanced mathematics.
Division, the operation in question, is essentially the process of determining how many times one number is contained within another. But when we enter into the realm of negative numbers, students often become confused. To clear up this confusion, it's important to remember that dividing a negative by a negative gives a positive result because the two negative signs cancel each other out. Thus, the operation \( \frac{-144}{-12} \) simplifies to dividing the absolute values of the numbers, giving us a positive answer.
Division, the operation in question, is essentially the process of determining how many times one number is contained within another. But when we enter into the realm of negative numbers, students often become confused. To clear up this confusion, it's important to remember that dividing a negative by a negative gives a positive result because the two negative signs cancel each other out. Thus, the operation \( \frac{-144}{-12} \) simplifies to dividing the absolute values of the numbers, giving us a positive answer.
Division Rules
Division rules are the guidelines followed to correctly divide numbers. These rules become especially handy when dealing with positive and negative numbers in arithmetic operations.
One key division rule to remember is: when you divide two numbers that both have the same sign, whether negative or positive, the result is always positive. Conversely, if you divide two numbers with different signs, the result is always negative.
Therefore, when we divide \( -144 \) by \( -12 \) as seen in the expression \( \frac{-144}{-12} \), we apply this rule and know our result will be positive. After dividing the absolute values, 144 by 12, we affirm the rule by concluding the result as a positive 12. These rules streamline the process of division and help in maintaining consistency and understanding in arithmetic operations.
One key division rule to remember is: when you divide two numbers that both have the same sign, whether negative or positive, the result is always positive. Conversely, if you divide two numbers with different signs, the result is always negative.
Therefore, when we divide \( -144 \) by \( -12 \) as seen in the expression \( \frac{-144}{-12} \), we apply this rule and know our result will be positive. After dividing the absolute values, 144 by 12, we affirm the rule by concluding the result as a positive 12. These rules streamline the process of division and help in maintaining consistency and understanding in arithmetic operations.
Other exercises in this chapter
Problem 94
In Exercises 89-96, evaluate the expression. $$ \frac{-56}{7} $$
View solution Problem 95
Discuss the difference between \((6 x)^{4}\) and \(6 x^{4}\).
View solution Problem 96
Describe and correct the error. $$ \begin{aligned} 4 x-3(x-1) &=4 x-3(x)-3(1) \\ & \Rightarrow 4 x-3 x-3 \\ &=x-3 \end{aligned} $$
View solution Problem 96
In Exercises 89-96, evaluate the expression. $$ 5(-7) $$
View solution