Problem 79 - Prealgebra

Question

Perform the indicated operations. $$3(2)(5)$$

Step-by-Step Solution

Answer

The result of the operation is 30.

Step 1: Multiply the first two numbers

Start by multiplying the first two numbers, which are 3 and 2. Calculate: \(3 \times 2 = 6\).

Step 2: Multiply the result with the third number

Take the result from Step 1, which is 6, and multiply it by the third number, 5. Calculate: \(6 \times 5 = 30\).

Key Concepts

Multiplication

Multiplication is one of the basic mathematical operations and is essential in prealgebra. It involves taking two numbers and combining them to find a total amount. Think of multiplication as a quick way to add numbers repeatedly. For instance, if you want to add the number 3 five times, instead of writing it out as 3 + 3 + 3 + 3 + 3, multiplication makes it easier by expressing it as \(3 \times 5\). This operation tells you to add 3 to itself a total of 5 times, which equals 15.
Understanding multiplication is crucial because it is used in many areas of mathematics and everyday life, such as calculating areas, understanding rates, and working with various arithmetic problems. When you multiply numbers, the numbers being multiplied are called factors, and the result is called the product.

Step-by-step solution

Breaking down an operation into a step-by-step solution is a helpful way to solve problems without feeling overwhelmed. When faced with the expression \(3(2)(5)\), following a series of logical steps can simplify the process.
First, look at the expression and identify the numbers or elements that need to be multiplied together. The step-by-step process begins by multiplying the first two numbers:

• **Step 1:** Multiply 3 and 2, which gives us 6.
• **Step 2:** Take the result, 6, and multiply it by the third number, 5.
• **Step 3:** The result of 6 multiplied by 5 is 30, which is the final product of the entire operation.

This breakdown helps not only in reaching the solution but also in understanding each part of the process, reinforcing the learning of multiplication.

Mathematical operations

Mathematical operations are fundamental actions that we perform on numbers in arithmetic. The primary operations include addition, subtraction, multiplication, and division. Each operation serves a different purpose and helps us manipulate numbers to find desired results.
In the example \(3(2)(5)\), multiplication is the operation used to combine numbers. Understanding how to perform and connect these operations allows us to solve complex mathematical problems in a structured manner.
Remember, performing operations in these steps ensures accuracy:

• Identify what needs to be done; here, it's determining the product by applying multiplication across all given numbers.
• Follow the arithmetic order of operations, known as the PEMDAS/BODMAS rule (Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
• Think of each multiply as a mini add, keeping it simple and straightforward.

These systematic approaches help you tackle not only basic but also more complex arithmetic challenges with confidence.