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Chapter 1: Problem 68

\(-\frac{5}{9}\)

Short Answer

Expert verified
The fraction \(-\frac{5}{9}\) is in its simplest form.

Step by step solution

01

Identifying the fraction

The given fraction is \(-\frac{5}{9}\). This fraction is negative, meaning it is less than zero. The numerator, which is the top section of the fraction, is 5. The denominator, the bottom section, is 9.
02

Simplifying the fraction

To simplify a fraction, you need to find a number that both the numerator and the denominator can be divided evenly by. However, 5 and 9 don't have any common divisors other than 1. Therefore, the fraction \(-\frac{5}{9}\) is already in its simplest form.

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Key Concepts

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

Understanding Negative Fractions
Negative fractions are fractions that represent values less than zero. They have a negative sign either in front of the numerator, the denominator, or the entire fraction itself. All these forms indicate the same negative value, such as -\(\frac{5}{9}\), \(\frac{-5}{9}\), or \(\frac{5}{-9}\). Here are key points to consider:
  • Any fraction with a negative numerator or a negative denominator is considered negative. But both cannot be negative, as they would cancel each other out to make a positive fraction.
  • When multiplying or dividing negative fractions, remember that multiplying two negative fractions results in a positive product, while multiplying a negative fraction by a positive fraction results in a negative product.
Always be mindful of the placement of the negative sign to ensure the correct interpretation.
Numerators and Denominators Explained
A fraction consists of two parts: the numerator and the denominator. Let's break down what each part signifies:
  • Numerator: This is the top number in a fraction. It tells you how many parts of a whole you have. In the fraction \(\frac{5}{9}\), 5 is the numerator, indicating five parts out of the whole.
  • Denominator: This is the bottom number in a fraction and represents the total number of equal parts the whole is divided into. In our example, 9 is the denominator, showing that the whole is divided into nine equal parts.
Understanding the roles of the numerator and denominator helps in comparing fractions, performing arithmetic operations, and simplifying fractions. They are fundamental building blocks in learning how fractions work.
What is the Simplest Form of a Fraction?
Simplifying a fraction means expressing it in the simplest form, where the numerator and denominator have no common factors other than 1. Here are steps to simplify any fraction:
  • Find the greatest common divisor (GCD) of the numerator and denominator.
  • Divide both the numerator and the denominator by their GCD.
However, not all fractions can be simplified. For example, \(-\frac{5}{9}\) cannot be reduced as 5 and 9 have no common divisors other than 1. This means \(-\frac{5}{9}\) is already in its simplest form.
When simplifying, always check for the highest number that divides both values evenly. If you find none, then you're already as simple as can be! This process not only makes numbers easier to work with but also enhances clarity in mathematical operations.

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Most popular questions from this chapter

Sales Tax You purchase a sweater for \(\$ 35.95\). There is a \(6 \%\) sales tax, which means that the total amount you must pay is \(35.95+0.06(35.95)\). (a) Use the Distributive Property to rewrite the expression. (b) How much must you pay for the sweater including sales tax?

\(\frac{3+[15 \div(-3)]}{16}\)

Cereal A grocery store has a cereal display that is 8 boxes high, 8 boxes wide, and 8 boxes long. How many cereal boxes are in the display?

\(17-|2-(6+5)|\)

\((-3)^{3}+\left(12 \div 2^{2}\right)\)
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