Problem 54 Determine whether the statement ... [FREE SOLUTION]

Chapter 0: Problem 54

Determine whether the statement is true or false. $$-\frac{5}{3}<-\frac{9}{5}$$

Short Answer

Expert verified

False

Step by step solution

- Understand the Inequality

We need to determine if the statement $-\frac{5}{3} < -\frac{9}{5}$ is true or false. This can be done by comparing the values of $-\frac{5}{3}$ and $-\frac{9}{5}$.

- Find the Decimal Values

Convert both fractions to their decimal forms. For $-\frac{5}{3}$, divide 5 by 3 to get approximately -1.67. For $-\frac{9}{5}$, divide 9 by 5 to get -1.8.

- Compare the Decimal Values

Compare $-1.67$ and $-1.8$. Notice that $-1.67$ is greater than $-1.8$.

- Conclude the Inequality

Since $-1.67$ is greater than $-1.8$, we have $-\frac{5}{3} > -\frac{9}{5}$. Therefore, the statement $-\frac{5}{3} < -\frac{9}{5}$ is false.

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Key Concepts

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

Inequalities

Inequalities are mathematical expressions used to compare the sizes of two values. They tell us if one value is bigger, smaller, or equal to another.

For instance, we use symbols like < (less than), > (greater than), 鈮� (less than or equal to), and 鈮� (greater than or equal to). In the exercise provided, the inequality $-\frac{5}{3} < -\frac{9}{5}$ is an example of using the < symbol to see if one fraction is smaller than the other.

When you're dealing with negative numbers in an inequality, remember that the inequality sign flips. For example, comparing -2 and -3, we have -2 > -3 because -2 is closer to zero.

Decimal Conversion

Decimal conversion involves changing numbers from one form to another, particularly from fractions to decimal numbers.

Let's take the given fractions $-\frac{5}{3}$ and $-\frac{9}{5}$. You convert them to decimals by dividing the numerator by the denominator.

To convert $-\frac{5}{3}$, you divide 5 by 3 to get approximately -1.67. To convert $-\frac{9}{5}$, divide 9 by 5 to get -1.8.

Decimals make it easier to compare values, especially when the fractions have different denominators.

Negative Numbers

Negative numbers are numbers less than zero, and they come with their own unique set of rules, especially when comparing them.

When two negative numbers are compared, the farther a number is from zero, the smaller it is. For example, between -1 and -2, -2 is smaller because it is farther from zero.

Looking at the exercise, you compare -1.67 and -1.8. Here, -1.67 is closer to zero than -1.8, which means -1.67 is greater. That鈥檚 why $-\frac{5}{3}$ is greater than $-\frac{9}{5}$. So, the statement $-\frac{5}{3}<-\frac{9}{5}$ is false.

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91影视

Determine whether the statement is true or false. $$-\frac{5}{3}<-\frac{9}{5}$$

Short Answer

Step by step solution

- Understand the Inequality

- Find the Decimal Values

- Compare the Decimal Values

- Conclude the Inequality

Key Concepts

Inequalities

Decimal Conversion

Negative Numbers

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