Problem 64 - Prealgebra

Question

Perform the indicated operations. $$2 \times 65+45$$

Step-by-Step Solution

Answer

The result is 175.

Step 1: Multiply First

First, we need to perform the multiplication operation as per order of operations (PEMDAS/BODMAS rules). We have to multiply 2 by 65.\[ 2 \times 65 = 130 \] So, the result of the multiplication is 130.

Step 2: Add the Result

Now we add the result from Step 1 to 45. Thus, we take 130 and add 45. \[ 130 + 45 = 175 \] So, the sum of 130 and 45 gives us the final result of 175.

Key Concepts

Understanding Multiplication

Multiplication is one of the basic arithmetic operations, often considered a quicker way of adding the same number multiple times. For instance, if you want to add 65 twice, you could do it like this: 65 + 65. But with multiplication, you can achieve the same result with less work by calculating \(2 \times 65\). This not only saves time but also reduces the likelihood of making errors in more complex calculations.

• Multiplier: The number that tells you how many times to add.
• Multiplicand: The number to be multiplied.
• Product: The result of the multiplication.

Once you understand these elements, performing multiplication becomes straightforward and efficient.

The Role of Addition

Addition is all about combining numbers to get a sum. It’s like putting pieces together to make a whole. In the exercise, after multiplying \(2 \times 65\), we get 130.
Addition is used to combine this result with another number, which in this case is 45.

• Augend: The number to which another number is added.
• Addend: The number that is added to another.
• Sum: The result of adding two or more numbers.

So, when we add 130 and 45, our purpose is to find out how these two parts make up a bigger whole, resulting in 175.

Order of Operations (PEMDAS)

PEMDAS is an acronym used to remember the order of operations in mathematics. It stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). This order is crucial because it determines how complex expressions are simplified.
In our exercise, "\(2 \times 65 + 45\)", the order of operations helps us decide what to compute first. According to PEMDAS, multiplication should be done before addition:- P: Parentheses- E: Exponents- M/D: Multiplication/Division- A/S: Addition/Subtraction
Following this order ensures consistency and correctness, especially when solving complicated problems, and avoids errors that can occur if operations are performed out of sequence.