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Chapter 4: Problem 598

In the following exercises, find the reciprocal. $$\frac{2}{9}$$

Short Answer

Expert verified
The reciprocal of \(\frac{2}{9}\) is \(\frac{9}{2}\).

Step by step solution

01

Understand the Reciprocal

The reciprocal of a fraction is found by swapping the numerator and the denominator. For a fraction \(\frac{a}{b}\), its reciprocal is \(\frac{b}{a}\).
02

Identify Numerator and Denominator

In the given fraction \(\frac{2}{9}\), the numerator is 2 and the denominator is 9.
03

Swap Numerator and Denominator

To find the reciprocal, swap the numerator and the denominator. Therefore, the reciprocal of \(\frac{2}{9}\) is \(\frac{9}{2}\).

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Key Concepts

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

Numerator and Denominator
The terms 'numerator' and 'denominator' are crucial parts of any fraction. Understanding them can make fraction operations much easier. The numerator is the top number of a fraction. It shows how many parts of the whole we have. In the fraction \(\frac{2}{9}\), 2 is the numerator.
The denominator is the bottom number. It represents the total number of equal parts that make up the whole. In the fraction \(\frac{2}{9}\), 9 is the denominator.
Remembering that the numerator is on top, and the denominator is on the bottom will help you handle fractions more smoothly in various math problems.
Fraction Operations
Being able to perform different operations with fractions is a fundamental math skill. Here, we will focus on finding the reciprocal, a simple yet important operation.
To find the reciprocal of a fraction, we swap its numerator and denominator. For example, for the fraction \(\frac{2}{9}\), the reciprocal would be \(\frac{9}{2}\).
This operation is vital in division of fractions. Dividing by a fraction is the same as multiplying by its reciprocal. For instance, \(\frac{2}{9} \div \frac{1}{4}\) is the same as \(\frac{2}{9} \times 4\) (here, 4 is the reciprocal of \(\frac{1}{4}\)).
Basic Arithmetic
Basic arithmetic is the foundation of all mathematical operations. It includes addition, subtraction, multiplication, and division.
When working with fractions, these operations follow specific rules. For example, to add fractions, they must have a common denominator. Similarly, for multiplication and division, knowing how to handle numerators and denominators is essential.
Finding the reciprocal is a part of basic arithmetic. It involves a simple swap of the numerator and denominator. Understanding reciprocals helps in performing more complex fraction problems and equations. Always keep the properties of numerators and denominators in mind for simple and quick computations.

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