Addition and Subtraction of Rational Numbers - Operation on Rational Numbers

Summary

In this instructional video, Teacher explains how to add and subtract rational numbers, which are numbers expressed as fractions with non-zero denominators. The video covers both cases: fractions with the same denominator and fractions with different denominators, demonstrating step-by-step methods including finding the least common denominator (LCD) and performing the necessary arithmetic operations. Four clear examples illustrate these concepts, showing how to simplify answers correctly and handle negative results. The lesson provides practical tips for mastering these operations and prepares viewers for future tutorials on multiplying and dividing rational numbers, making it a helpful guide for learners of all levels.

Takeaways

• 😀 Rational numbers are numbers that can be written in the form p/q, where q ≠ 0.
• 😀 Rational numbers can be expressed as fractions.
• 😀 When adding or subtracting rational numbers with the same denominator, keep the denominator and add or subtract the numerators.
• 😀 Always simplify your final answer after performing addition or subtraction of rational numbers.
• 😀 When adding or subtracting rational numbers with different denominators, find the Least Common Denominator (LCD) first.
• 😀 The Least Common Denominator (LCD) is the least common multiple (LCM) of the denominators.
• 😀 To convert fractions to the same denominator, divide the LCD by the original denominator and multiply by the numerator.
• 😀 For addition with different denominators, add the converted numerators after finding the LCD.
• 😀 For subtraction with different denominators, subtract the converted numerators after finding the LCD.
• 😀 If the result of subtraction is negative, place the negative sign in front of the fraction.
• 😀 Understanding the process of adding and subtracting rational numbers is essential before moving on to multiplying and dividing rational numbers.
• 😀 Using step-by-step conversion and simplification ensures accurate results in all operations involving rational numbers.

Q & A

What is the definition of a rational number?

A rational number is a number that can be written in the form p/q, where q is not equal to zero. In other words, it is a number that can be expressed as a fraction.

How do you add two rational numbers with the same denominator?

To add rational numbers with the same denominator, keep the denominator the same and add the numerators. Then simplify the fraction if possible.

What is the result of adding 2/9 and 3/9?

The sum of 2/9 and 3/9 is 5/9.

What is the first step when adding rational numbers with different denominators?

The first step is to find the least common multiple (LCM) of the denominators to determine the least common denominator (LCD).

How do you convert fractions to have the same denominator before adding or subtracting?

Divide the LCD by the original denominator of each fraction and then multiply the result by the numerator. This gives the equivalent fractions with the same denominator.

What is the sum of 4/3 and 5/2?

The sum of 4/3 and 5/2 is 23/6.

How do you subtract two rational numbers with the same denominator?

To subtract rational numbers with the same denominator, keep the denominator the same and subtract the numerators. Simplify the result if possible.

What is the difference between 7/3 and 5/3?

The difference between 7/3 and 5/3 is 2/3.

How do you subtract rational numbers with different denominators?

First, find the least common denominator (LCD), convert each fraction to an equivalent fraction with the LCD as the denominator, then subtract the numerators and simplify the result.

What is the result of subtracting 5/2 from 4/3?

The result of subtracting 5/2 from 4/3 is -7/6.

Why is it important to simplify the final answer when performing operations with rational numbers?

Simplifying the final answer ensures the fraction is in its simplest form, making it easier to understand, compare, and use in further calculations.

What are the main steps to follow when adding or subtracting rational numbers?

The main steps are: (1) Ensure the fractions have a common denominator, (2) Convert fractions if necessary using the LCD, (3) Add or subtract the numerators, (4) Keep the common denominator, and (5) Simplify the result.