Problem 568 - Prealgebra

Question

Divide. Then check by multiplying. $$0 \div 52$$

Step-by-Step Solution

Answer

0

Step 1: Understand the Problem

The task is to divide 0 by 52. The division of any number by another number can be understood as distributing the first number into the specified number of groups determined by the second number. Here, we have to distribute 0 into 52 groups.

Step 2: Perform the Division

Divide 0 by 52: Any number divided by a non-zero number is still 0. Therefore, \( 0 \div 52 = 0 \)

Step 3: Check the Result by Multiplying

To verify the division, multiply the result by the divisor. If the result is correct, the product should be equal to the dividend. Here, multiply 0 (the result) by 52 (the divisor): \( 0 \times 52 = 0 \)Since the product is 0, our division is verified as correct.

Key Concepts

division by zero

One of the most important concepts in division is understanding what happens when you try to divide by zero. It is crucial to know that division by zero is undefined. This means that it is not possible to divide any number by zero.
Think of it like this: dividing a number by another number is like splitting it into groups. But if you try to split something into groups of zero, it doesn't make any sense because you can't have zero groups.
Therefore, trying to compute something like \(a \div 0\) does not have a valid answer in mathematics. It's an operation that just doesn't work.

multiplication check

After performing any division, it's a good habit to check your work by reversing the operation with multiplication. This helps to verify that your division was correct.
Here’s how you can do this:

• Take the result of the division.
• Multiply it by the divisor (the number you divided by).
• If the product equals the original number (the dividend), then your division is correct.

For example, in our exercise with \(0 \div 52 \), we divided 0 by 52 and got 0.
To check, we multiplied 0 (the result) by 52 (the divisor), and got \(0 \times 52 = 0\). Since our product matches the original number, the division is verified as correct.

properties of zero

Zero holds unique properties that make it special in arithmetic, especially in operations like addition, subtraction, multiplication, and division.
Some important properties of zero include:

• Addition: Adding zero to any number leaves the number unchanged. \(a + 0 = a\).
• Subtraction: Subtracting zero from any number also leaves the number unchanged. \(a - 0 = a\).
• Multiplication: Multiplying any number by zero results in zero. \(a \times 0 = 0\).
• Division: Dividing zero by any non-zero number always results in zero. \(0 \div a = 0\). However, dividing a number by zero is not defined.

Understanding these properties deeply helps you perform and verify arithmetic operations accurately.