Problem 51 - Beginning and Intermediate Algebra

Question

Find each sum or product. $$ 5(47)(2) $$

Step-by-Step Solution

Answer

470

Step 1 - Calculate the product of the first two numbers

Multiply the first two numbers together: \( 5 \times 47 = 235 \)

Step 2 - Multiply the result by the third number

Take the result from Step 1 and multiply it by the third number: \( 235 \times 2 = 470 \)

Key Concepts

Basic Arithmetic

In basic arithmetic, multiplication is a fundamental operation. It's used to find the total amount when you have equal groups. For example, if you have 5 groups of 4 apples, you multiply 5 by 4 to get 20 apples.
In this exercise, we multiply three numbers together: 5, 47, and 2. Understanding multiplication helps in solving not only simple problems but also more complex ones.
Here are a few important points about basic multiplication:

• It involves repeated addition. For instance, 4 × 3 means adding 4 three times: 4 + 4 + 4.
• It's one of the four elementary operations in math, along with addition, subtraction, and division.
• The order of multiplication doesn't matter, meaning 3 × 4 is the same as 4 × 3.

Understanding these principles can help you solve multiplication problems easily.

Step-by-Step Solution

Breaking down a multiplication problem into smaller steps makes it easier to solve. Here's how we solve the given exercise step-by-step:
Step 1: Calculate the product of the first two numbers.

• We start with 5 and 47. We multiply them together.
• The calculation is:
  
  • 5 × 47 = 235

This gives us an intermediate result of 235.
Step 2: Multiply the result by the third number.

• We now take our intermediate result (235) and multiply it by 2.
• The calculation is:
  
  • 235 × 2 = 470

We arrive at the final answer, which is 470.
By following each step, you ensure accuracy and make the problem less overwhelming.

Product Calculation

The final outcome of a multiplication problem is called the product. When you multiply numbers, you get a product that represents the total amount.
For the given problem 5(47)(2), we perform the following calculations:

• First, find the product of 5 and 47, which is 235.
• Next, multiply the result by 2, giving us 470.

The product calculation in this exercise follows these steps:

• Multiply the first two numbers: 5 × 47 = 235
• Then multiply the intermediate product by the third number: 235 × 2 = 470

Understanding product calculation helps in solving various multiplication problems efficiently. It also builds a strong foundation for more advanced math concepts.
Always remember, breaking down problems into smaller steps aids in comprehension and accuracy.