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Chapter 7: Problem 178

Simplify using the properties of zero. \(0 \div \frac{11}{12}\)

Short Answer

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Step by step solution

01

Understand the Problem

The exercise involves dividing zero by a fraction. We need to use the properties of zero to simplify the expression.
02

Recall the Property of Zero in Division

One of the properties of zero is that any number divided by zero is zero itself. Mathematically, for any number or fraction \(a\), \(0 \div a = 0\).
03

Apply the Property

Using the property mentioned above, divide zero by the given fraction. Therefore, \(0 \div \frac{11}{12} = 0\).
04

Write the Simplified Expression

The simplified value of the expression \(0 \div \frac{11}{12}\) is 0.

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Key Concepts

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

division by zero
Division by zero is a fundamental concept in mathematics that can be tricky to understand at first. It鈥檚 important to know that division by zero is undefined. This means you cannot divide any number by zero. For example, \( \frac{5}{0} \) or \( 7 \div \ 0 \) does not result in a valid number. Instead, it causes a mathematical contradiction.

Zero divided by any number, on the other hand, is always zero. If you take zero and divide it by any non-zero number, the result is zero. For example, \( 0 \div \ 7 \) equals 0. This concept is crucial because it helps ensure calculations stay accurate and meaningful.

Remember:
  • Any number divided by zero is undefined.
  • Zero divided by any number is always zero.
fraction division
Fraction division might seem complicated, but it follows simple rules. Dividing fractions involves multiplying by the reciprocal. For example, instead of dividing by \( \frac{11}{12} \), you multiply by its reciprocal, \( \frac{12}{11} \).

Here are the steps:
  • Take the reciprocal of the second fraction.
  • Multiply the first fraction by this reciprocal.
Using these steps, \( 0 \div \frac{11}{12}\) becomes \( 0 \times \frac{12}{11} = 0 \).
Since zero multiplied by any number or fraction remains zero, the result is 0.
Remember these points for fraction division:
  • Use the reciprocal of the dividing fraction.
  • Multiply instead of dividing.
simplifying expressions
Simplifying expressions is key to making math problems easier to solve. One way to simplify expressions is by using known properties of numbers, like the properties of zero.
Simplify by:
  • Identifying special properties like the zero property.
  • Applying these properties to the numbers or fractions involved.

In the example \( 0 \div \frac{11}{12} \), knowing that zero divided by any number is zero makes the simplification straightforward.
By understanding and using these steps, we can easily simplify \( 0 \div \frac{11}{12} \) to just 0. This practice helps avoid unnecessary complexity.
Simplifying expressions involves:
  • Breaking the problem into smaller parts.
  • Applying mathematical properties like the zero property.
  • Combining the simplified parts for the final answer.

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Most popular questions from this chapter

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