Problem 379 - Prealgebra

Question

Divide. Then check by multiplying. $$0 \div 4$$

Step-by-Step Solution

Answer

0 \div 4 = 0. Checking: 0 \times 4 = 0.

Step 1: Identify the Dividend and Divisor

In the division problem, the number to be divided is called the dividend, and the number by which the dividend is divided is called the divisor. Here, the dividend is 0, and the divisor is 4.

Step 2: Perform the Division

When any number is divided by another non-zero number, the result is zero. Therefore, dividing 0 by 4 gives us 0. Mathematically, this is represented as: \[ 0 \div 4 = 0 \]

Step 3: Check the Result by Multiplying

To check the division, multiply the quotient by the divisor. If the product equals the original dividend, the division is correct. Here, multiply the quotient (which is 0) by the divisor (which is 4): \[ 0 \times 4 = 0 \] Since the product is 0, which is equal to the original dividend, the division is correct.

Key Concepts

division

Division is one of the basic operations in mathematics, along with addition, subtraction, and multiplication. In division, you split a number (called the dividend) into equal parts. You use another number (called the divisor) to determine the size of each part. For example, in the exercise, 0 is the dividend and 4 is the divisor. You're asked to divide 0 by 4.

When you perform this division \(0 \div 4\), the result is zero. This is because dividing zero by any non-zero number always gives zero. It's easy to remember this rule: if there is nothing to share (the dividend is zero), everyone, no matter the number (the divisor), gets nothing.

Always make sure the divisor is not zero. Division by zero is undefined and cannot be performed.

multiplication

Multiplication is another fundamental operation in mathematics. It is often described as repeated addition. For instance, using 4 multiplied by 2 (\( 4 \times 2 = 8 \)), you are adding 4 two times. In short, multiplication finds the total of groups of equal size.

In the context of the exercise, multiplication is used to verify the result of division. Since you got a quotient of 0 when you divided 0 by 4, you'll multiply the quotient by the original divisor (\( 0 \times 4\)). If the product of this multiplication equals the original dividend, the division is confirmed to be correct.

The math works out because 0 multiplied by any number is always 0. This rule helps ensure the accuracy of your division.

zero property

The Zero Property is an important concept in mathematics, and it states that any number multiplied by zero is zero. This property simplifies many calculations and checks in mathematical problems.

Applying this to the exercise, the zero property is why \( 0 \times 4 = 0 \) verifies the division correctly. When you follow the zero property, it makes it easier to check your work and understand why division by any number results in 0 when the dividend is 0.

This property is not just limited to multiplication or division. It holds true in addition as well: Adding zero to any number doesn’t change the number, which further emphasizes how pivotal zero is in arithmetic operations.