Evaluate each expression. 0/7

Verified step by step guidance

1. Identify the expression to evaluate: \( \frac{0}{7} \).
2. Recall the property of division: any number divided by a non-zero number is zero.
3. Apply this property to the expression: since the numerator is 0 and the denominator is 7, the expression evaluates to 0.
4. Understand that division by zero is undefined, but division of zero by any non-zero number is always zero.
5. Conclude that the expression \( \frac{0}{7} \) simplifies to 0.

Key Concepts

Division by Zero

In mathematics, division by zero is undefined. This means that any expression where the divisor is zero does not yield a valid numerical result. For example, in the expression 0/7, the numerator is zero, which is valid, but the denominator is not zero, allowing the division to be performed. However, if the denominator were zero, the expression would be undefined.

Zero as a Numerator

When zero is the numerator in a fraction, the value of the fraction is always zero, provided the denominator is not zero. This is because zero divided by any non-zero number results in zero. In the case of 0/7, the result is 0, illustrating that any number divided by a non-zero number yields zero.

Evaluating Expressions

Evaluating an expression involves calculating its value based on the operations and numbers involved. In the case of 0/7, the evaluation process requires performing the division operation, which leads to the conclusion that the expression equals zero. Understanding how to evaluate expressions is fundamental in algebra, as it allows for the simplification and solving of mathematical problems.