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Chapter 2: Problem 25

Compute the exact value of the given expression. \(15 \div 1 \cdot 3\)

Short Answer

Expert verified
The exact value of the expression is 45.

Step by step solution

01

Understanding the Expression

The given expression is \(15 \div 1 \cdot 3\). Here we have two operations: division (\( \div \)) and multiplication (\( \cdot \)). Operations should be performed from left to right, according to the order of operations (PEMDAS/BODMAS rules).
02

Perform the Division

Begin with the division part of the expression: \(15 \div 1\). Dividing 15 by 1 gives 15, so we rewrite the expression as \(15 \cdot 3\).
03

Perform the Multiplication

Now, we perform the multiplication: \(15 \cdot 3\). Multiplying 15 by 3 gives us 45. Therefore, the value of the expression is 45.

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Key Concepts

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

Division
Division is an essential arithmetic operation, symbolized by the division sign \(\div\) or a slash \(/\). In our exercise, we start with \(15 \div 1\). Division is the process of determining how many times one number is contained within another. For instance, when dividing 15 by 1, we are simply calculating how many times 1 fits into 15.
\(15 \div 1 = 15\). Hence, dividing by 1 results in the number itself.
Some key points to remember about division:
  • Any number divided by 1 remains unchanged.
  • Division by 0 is undefined, so we must never attempt it.
  • Dividing by larger numbers results in smaller quotients.
Multiplication
Multiplication is another core arithmetic operation, represented by the symbol \(\cdot\) or sometimes by \(x\). After simplifying the division in our problem, the expression left is \(15 \cdot 3\). Multiplication is essentially repeated addition. In this case, 15 is added to itself 3 times, or:
\(15 \cdot 3 = 15 + 15 + 15 = 45\).
Some useful multiplication tips:
  • Any number multiplied by 1 equals the original number.
  • If multiplied by 0, the result is always 0.
  • Multiplication is commutative, meaning \(a \cdot b = b \cdot a\).
PEMDAS
PEMDAS is an acronym used to remember the order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). It guides us on how to correctly evaluate expressions with multiple operations.
In the exercise, following PEMDAS meant handling the division and multiplication from left to right, even though they seem equally important otherwise.
Here's a breakdown of PEMDAS:
  • Parentheses: Solve expressions within parentheses first.
  • Exponents: Calculate powers and roots next.
  • Multiplication and Division: Perform these operations from left to right as they appear in the expression.
  • Addition and Subtraction: Finally, perform these from left to right.
In our example, the order was crucial in solving \(15 \div 1 \cdot 3\) correctly, by addressing the division before the multiplication.

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