Problem 63 - Prealgebra

Question

Perform the indicated operations. $$3 \times 60+15$$

Step-by-Step Solution

Answer

195

Step 1: Identify the Operations

First, identify the mathematical operations involved in the problem. The problem statement is \(3 \times 60 + 15\), which includes a multiplication and an addition operation.

Step 2: Perform the Multiplication

Multiply the first part of the equation: \(3 \times 60\). Calculate this to get \(180\) because multiplying \(3\) by \(60\) results in \(180\).

Step 3: Perform the Addition

Now, add the result of the multiplication to \(15\). So, calculate \(180 + 15\) which equals \(195\).

Key Concepts

Understanding Multiplication

Multiplication is one of the four elementary arithmetic operations; it refers to adding a number to itself a certain number of times. When you multiply two numbers, you're essentially adding copies of one number, as specified by the other number. In our example, the operation \( 3 \times 60 \) requires us to consider this concept:

• Imagine you have three groups of items, and each group contains 60 items.
• Multiplication tells you the total number of items in all groups.

For our specific case, multiplying 3 groups by 60 gives us the product of 180. Thus, \( 3 \times 60 = 180 \). Remember, multiplication is a faster and more efficient way to add equal sets together quickly.

The Role of Addition

Addition is a fundamental arithmetic operation. It involves combining two or more quantities to find their total. In the context of our exercise, once we've computed \( 3 \times 60 = 180 \), we then need to perform an addition operation: \( 180 + 15 \).

• Addition helps us to combine the original result (180) with a standalone number (15).
• This operation increases the total value by the added quantity, which in our case, is 15.

Therefore, when you add 15 to 180, you arrive at a total of 195. The addition process simplifies finding a total when combining different amounts.

Mastering the Order of Operations

The order of operations is crucial in correctly solving mathematical expressions, especially when they involve multiple types of operations. The standard rule to remember is PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). This rule dictates the sequence:

• Perform operations enclosed in Parentheses first.
• Execute Exponents second.
• Proceed with Multiplication and Division from left to right.
• Finish with Addition and Subtraction from left to right.

In our exercise, \( 3 \times 60 + 15 \), we first perform the multiplication \( 3 \times 60 \), according to PEMDAS, because multiplication comes before addition. After we obtain 180, we then add 15 to get 195. Following the order of operations ensures that everyone solves the problem in a consistent way, avoiding incorrect results.