Problem 315 - Prealgebra

Question

In the following exercises, translate and simplify. the product of 12 and 875

Step-by-Step Solution

Answer

The product of 12 and 875 is 10500.

Step 1: Identify the terms

The exercise is asking for the product of 12 and 875. In mathematical terms, 'product' means multiplication.

Step 2: Set up the multiplication

Write the multiplication expression as 12 * 875.

Step 3: Perform the multiplication

Calculate the product of 12 and 875. \[ 12 \times 875 = 10500 \]

Step 4: Verify the result

Double-check the calculation to ensure the result is correct.

Key Concepts

Explaining Mathematical Terms

When tackling any mathematical problem, understanding the key terms is crucial. Here, one important term is 'product'. In mathematical terms, 'product' refers to the result you get when you multiply two numbers. For example, in the exercise, we are asked to find the product of 12 and 875. This simply means we need to multiply the two numbers together: 12 * 875.

Understanding Multiplication

Multiplication is one of the basic arithmetic operations, alongside addition, subtraction, and division. It is a way of adding a number to itself a certain number of times. For instance, when we multiply 12 by 875, we are essentially adding 12 to itself 875 times. 
Here's a simple representation: If we multiply 4 by 3, written as 4 * 3, it means 4+4+4, which equals 12.
In our exercise: 12 * 875 is set up similarly. Instead of adding 12 repeatedly, we perform the calculation in one go:

Verification of Your Calculation

After calculating the product, it is always a good habit to verify the result to ensure accuracy. Verification helps catch any mistakes that might have occurred during the initial calculation. A simple way to verify multiplication results is to use the reverse operation, which is division.
In our exercise, we calculated that 12 times 875 equals 10500. To verify: Divide 10500 by one of the original numbers to see if you get the other number: