Problem 7
Question
Evaluate the expression. $$ 15+6 \div 3 $$
Step-by-Step Solution
Verified Answer
The result is 17.
1Step 1: Perform Division
In the expression \(15 + 6 \div 3\), the first operation to be done according to the order of operations will be the division. So, \(6 \div 3 = 2\).
2Step 2: Perform Addition
Next, add the quotient obtained from the division operation to 15: \(15 + 2 = 17\).
Key Concepts
Order of OperationsArithmetic OperationsDivision in AlgebraAddition in Algebra
Order of Operations
In mathematics, the order in which operations should be performed is critical. The concept commonly followed is known as PEMDAS/BODMAS, which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
When evaluating expressions like \(15 + 6 \times 3\), it’s important to follow these rules closely to arrive at the correct answer. Division comes before addition, so you must divide 6 by 3 first before adding it to 15. This hierarchy avoids ambiguity and ensures that no matter who calculates the expression, the outcome will be the same.
When evaluating expressions like \(15 + 6 \times 3\), it’s important to follow these rules closely to arrive at the correct answer. Division comes before addition, so you must divide 6 by 3 first before adding it to 15. This hierarchy avoids ambiguity and ensures that no matter who calculates the expression, the outcome will be the same.
Arithmetic Operations
Arithmetic operations are the foundation of basic mathematics and include operations such as addition, subtraction, multiplication, and division.
These operations are not just procedures but also concepts that reveal the relationships between numbers. They are applicable in a wide range of contexts, from simple everyday counting to advanced mathematical theories. Understanding how to execute these operations, both individually and in combination, as governed by the order of operations, allows one to approach and solve algebraic expressions systematically.
These operations are not just procedures but also concepts that reveal the relationships between numbers. They are applicable in a wide range of contexts, from simple everyday counting to advanced mathematical theories. Understanding how to execute these operations, both individually and in combination, as governed by the order of operations, allows one to approach and solve algebraic expressions systematically.
Division in Algebra
Division in algebra is much like division in basic arithmetic, except it involves unknown variables along with known numbers.
When performing division, especially in expressions with multiple terms and operations, it's crucial to divide the numbers accurately and apply the quotient correctly in subsequent steps. For instance, in the expression \(15 + 6 \times 3\), you first divide 6 by 3 to get 2. This division simplifies the expression and makes it easier to progress to the remaining steps in the problem.
When performing division, especially in expressions with multiple terms and operations, it's crucial to divide the numbers accurately and apply the quotient correctly in subsequent steps. For instance, in the expression \(15 + 6 \times 3\), you first divide 6 by 3 to get 2. This division simplifies the expression and makes it easier to progress to the remaining steps in the problem.
Addition in Algebra
Addition is a fundamental operation in algebra, used to combine numbers or variables.
After completing operations like multiplication and division, addition comes into play. In the given expression, once the division is done, you're left with adding the numbers together. Here, \(15 + 2 = 17\). Addition should be performed after any multiplication and division unless grouped by parentheses, which would cue priority running contrary to standard operation order.
After completing operations like multiplication and division, addition comes into play. In the given expression, once the division is done, you're left with adding the numbers together. Here, \(15 + 2 = 17\). Addition should be performed after any multiplication and division unless grouped by parentheses, which would cue priority running contrary to standard operation order.
Other exercises in this chapter
Problem 7
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