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The sum of two rational numbers is always:
- a)A natural number
- b)A whole number
- c)A rational number
- d)An irrational number
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The sum of two rational numbers is always:a)A natural numberb)A whole ...
The sum of two rational numbers is always a rational number because the sum of two fractions (where the denominator is not zero) always results in another fraction, which remains rational.
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The sum of two rational numbers is always:a)A natural numberb)A whole ...
Understanding Rational Numbers
Rational numbers are defined as numbers that can be expressed in the form of a fraction, where both the numerator and the denominator are integers, and the denominator is not zero. Examples include 1/2, -3/4, and 5.
Sum of Two Rational Numbers
When we add two rational numbers, the result is also a rational number. Here's why:
1. Definition of Addition
- When we add two fractions, we find a common denominator and then sum the numerators.
- For example, to add 1/2 and 3/4, we convert them to the same denominator:
- 1/2 = 2/4
- Now, add: 2/4 + 3/4 = 5/4.
2. Closure Property
- Rational numbers exhibit a closure property under addition. This means that if you take any two rational numbers and add them together, you will always get another rational number.
- For instance, if you take 2/3 and 4/5, their sum is (2*5 + 4*3) / (3*5) = 22/15, which is also rational.
3. Real-World Implications
- This property is essential in various fields, such as finance, physics, and engineering, where calculations involving rational numbers are common.
Conclusion
Thus, the correct answer to the question is option 'C': the sum of two rational numbers is always a rational number. Understanding this property helps in solving mathematical problems more effectively.
Rational numbers are defined as numbers that can be expressed in the form of a fraction, where both the numerator and the denominator are integers, and the denominator is not zero. Examples include 1/2, -3/4, and 5.
Sum of Two Rational Numbers
When we add two rational numbers, the result is also a rational number. Here's why:
1. Definition of Addition
- When we add two fractions, we find a common denominator and then sum the numerators.
- For example, to add 1/2 and 3/4, we convert them to the same denominator:
- 1/2 = 2/4
- Now, add: 2/4 + 3/4 = 5/4.
2. Closure Property
- Rational numbers exhibit a closure property under addition. This means that if you take any two rational numbers and add them together, you will always get another rational number.
- For instance, if you take 2/3 and 4/5, their sum is (2*5 + 4*3) / (3*5) = 22/15, which is also rational.
3. Real-World Implications
- This property is essential in various fields, such as finance, physics, and engineering, where calculations involving rational numbers are common.
Conclusion
Thus, the correct answer to the question is option 'C': the sum of two rational numbers is always a rational number. Understanding this property helps in solving mathematical problems more effectively.
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