Problem 75 - Prealgebra

Question

Multiply. $$1 \cdot 3 \cdot 1$$

Step-by-Step Solution

Answer

The product is 3.

Step 1: Identify the Numbers to Multiply

We are given the expression that requires multiplication of three numbers: 1, 3, and 1.

Step 2: Multiply the First Two Numbers

Start by multiplying the first two numbers: 1 multiplied by 3. The result of this calculation is 3.

Step 3: Multiply the Result with the Third Number

Now take the result from Step 2, which is 3, and multiply it by the third number, which is also 1. The calculation is 3 multiplied by 1, which gives us 3 as the result.

Key Concepts

Step-by-step solution

Breaking down problems into small, manageable steps makes learning smoother, especially when dealing with basic arithmetic operations like multiplication. The given exercise asks us to multiply three numbers: 1, 3, and 1. To solve it accurately, follow these clear steps:

1. **Identify the Numbers to Multiply**: We start by listing the numbers involved in the expression. In this case, they are 1, 3, and 1.
2. **Multiply the First Two Numbers**: Begin with the first pair of numbers. Multiply 1 by 3. Since 1 times any number is that number itself, we get 3 as the answer here.
3. **Multiply the Result with the Third Number**: Use the result from the previous step. Multiply 3 by the next number, which is again 1. This step also results in 3, as any number multiplied by 1 remains unchanged.

Following these steps ensures you correctly solve the multiplication problem without missing a number. Each step brings us closer to the final answer.

Multiplication problem solving

Multiplication is one of the fundamental arithmetic operations and is, in essence, repeated addition. Understanding this helps make sense of multiplication problems.

In multiplication, each number in the operation is called a "factor," while the result is the "product." For the expression 1, 3, and 1, these are the steps to solve it proficiently:

• Start with two numbers: 1 (the identity element in multiplication, meaning any number multiplied by 1 remains that number) and 3.
• The product of 1 and 3 is 3. This confirms that multiplying anything by 1 gives the original number.
• The product of this result with the final number 1 is still 3.

Realizing that multiplication can be mentally simplified when involving the number 1 helps in solving similar exercises quickly.

Arithmetic operations

The world of arithmetic operations includes addition, subtraction, multiplication, and division. Each operation has its rules that, when understood, help solve mathematical expressions.

In today’s exercise, we focused on multiplication—especially its characteristic property with the number 1, known as the identity element. Understanding this can demystify many arithmetic puzzles:

• **Addition**: Adds numbers to increase their total.
• **Subtraction**: Deducts numbers to decrease the total.
• **Multiplication**: Repeated addition of the same number.
• **Division**: Splitting a number into equal parts.

In the context of our example, we utilized multiplication. Multiplying 1 by any number maintains that number’s value. This property highlights why it was straightforward to see that 1 multiplied by any sequence of numbers involving 1 yields the non-1 number.