Problem 269 - Prealgebra

Question

In the following exercises, multiply. $$23\cdot 10$$

Step-by-Step Solution

Answer

230

Step 1 - Understand the Problem

We need to multiply two numbers: 23 and 10. Understanding multiplication will help solve this exercise.

Step 2 - Use Basic Multiplication

When multiplying a number by 10, the simplest way is to append a zero to the end of the number. For instance, 23 multiplied by 10 can be visualized as 23 followed by a zero.

Step 3 - Perform the Multiplication

Using the property of multiplication, 23 times 10 equals 230. This is because when you multiply any number by 10, you effectively make it ten times larger.

Key Concepts

Multiplying Numbers

Multiplying numbers is one of the fundamental operations in arithmetic. When you multiply, you are essentially adding a number to itself a certain number of times. For example, if you multiply 4 by 3, you are adding 4 three times: 4 + 4 + 4, which equals 12. This can also be expressed as \(4 \cdot 3 = 12\). Multiplication involves two numbers: the multiplicand (the number to be multiplied) and the multiplier (the number we are multiplying by). Understanding how to multiply numbers is essential for more complex mathematical concepts.

Multiplication by 10

Multiplying by 10 is one of the easiest and quickest operations in math. The reason it's so simple is because of our base-10 number system. When you multiply any number by 10, you just need to add a zero to the end of the number.
For example:

• 1 × 10 = 10
• 5 × 10 = 50
• 23 × 10 = 230

This works because multiplying by 10 moves all digits of the number one place to the left in the place value system, making the number ten times larger.

Basic Multiplication Steps

To multiply numbers, especially using basic methods, follow these simple steps:

1. Identify the numbers to be multiplied. These are your multiplicand and your multiplier.
2. If one number is simpler to work with (like 10), use that to make the multiplication easier.
3. Break down larger multiplications into smaller, more manageable parts if necessary (though this step isn't needed when multiplying by 10).
4. Perform the multiplication operation.

Let's apply this to our example of 23 × 10:

• The numbers to multiply are 23 (multiplicand) and 10 (multiplier).
• Since one of the numbers is 10, we can use the simplify by adding a zero to 23.
• The result is 230.

Following these steps systematically ensures you get the correct result every time.