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Chapter 7: Problem 181

Simplify using the properties of zero. \(0 \div \frac{7}{15}\)

Short Answer

Expert verified
0 \div \frac{7}{15} = 0

Step by step solution

01

Understand the division involving zero

When zero is divided by any non-zero number, the result is always zero. This is based on the property that zero divided by any number remains zero.
02

Apply the property of zero

In this exercise, you need to divide zero by the fraction \(\frac{7}{15}\). According to the property of zero, this operation is equal to zero.
03

Write the final answer

Therefore, \(0 \div \frac{7}{15} = 0\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

division involving zero
Division involving zero can seem confusing at first, but it's quite simple. When you divide zero by any non-zero number, the result is always zero. This rule helps simplify many mathematical problems. For example, in the exercise, we have to simplify the expression \(0 \div \frac{7}{15}\). Using the property of zero, we know the result will be zero because zero divided by any fraction (or any non-zero number) remains zero. This concept is essential, and mastering it can make learning math easier.
basic arithmetic operations
Understanding basic arithmetic operations is crucial for solving math problems. The primary operations are addition, subtraction, multiplication, and division. Each operation has properties that make calculations easier. For division, one crucial property is that zero divided by any non-zero number is always zero. For example, in \(0 \div \frac{7}{15}\), we use this property to simplify the expression to zero. By grasping these fundamental operations, you can solve more complex problems with confidence.
zero property in mathematics
The zero property in mathematics is a fundamental concept. It states that when zero is involved in an arithmetic operation, the results follow specific rules:
  • Zero added to or subtracted from any number leaves that number unchanged.
  • Zero multiplied by any number is always zero.
  • Zero divided by any non-zero number is always zero.
These properties of zero help simplify many math problems. For instance, in the given exercise where we have \(0 \div \frac{7}{15}\), we use the zero property to conclude that the result is zero. Understanding these properties makes it easier to solve various arithmetic problems.

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