Comparing numbers and understanding inequalities is a fundamental concept in mathematics. In this blog post, we will explore the inequality -3/3 < 5/6, discuss the principles of comparing fractions and integers, provide step-by-step explanations, and offer practical examples of when such comparisons are important.

## Is-3-3-Smaller-than-5-6 ?

*Yes, -3/3 is indeed smaller than 5/6. When simplified, -3/3 equals -1, which is less than 5/6. In this comparison, -1 is on the left side of the number line, indicating that it is smaller than 5/6, which falls on the right side of the number line.*

### Understanding Inequalities

An inequality is a mathematical expression that compares two values and shows their relationship. Common inequality symbols include:

- Less than (<)
- Greater than (>)
- Less than or equal to (≤)
- Greater than or equal to (≥)
- Not equal to (≠)

In the context of comparing numbers, we will focus on the less than (<) symbol.

## Comparing Fractions

To compare fractions, consider the following principles:

#### 1. Common Denominator

For fractions with different denominators, it is helpful to find a common denominator. This allows for easier comparison.

#### 2. Cross-Multiplication

After finding a common denominator, you can cross-multiply to compare fractions. For fractions A/B and C/D, if AD < BC, then A/B < C/D.

## Comparing Integers and Fractions

When comparing integers (whole numbers) and fractions, you can convert the integers to fractions with denominators of 1. This allows you to compare them using the principles mentioned earlier.

### Evaluating -3/3 < 5/6

Now, let’s apply these principles to the inequality -3/3 < 5/6:

#### 1. Common Denominator

Both fractions already share a common denominator, which is 3.

#### 2. Cross-Multiplication

- For -3/3, we have -3/3 = (-3) × (1/3) = -1.
- For 5/6, we have 5/6 = (5) × (1/6) = 5/6.

Now, we have the inequality -1 < 5/6.

## Practical Examples

Understanding inequalities is crucial for various real-life scenarios:

#### 1. Finance and Budgeting

When budgeting, you may need to compare your expenses (in dollars) to your income (in dollars and cents).

#### 2. Grades and Assessments

Teachers use inequalities to compare students’ scores or grades to determine their academic performance.

#### 3. Time Management

In scheduling and time management, you might compare the time required for different tasks or events to prioritize effectively.

#### 4. Measurement and Quantities

In scientific experiments or construction projects, comparing measurements or quantities helps make informed decisions.

## Conclusion

Inequalities are a fundamental concept in mathematics used to compare numbers and values. Understanding how to compare fractions, integers, and mixed numbers is essential for various applications in everyday life and across different fields of study. In the case of the inequality -3/3 < 5/6, it is indeed true because -1 is less than 5/6. Being proficient in inequalities enables individuals to make informed decisions, analyze data, and solve problems efficiently.

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