Which of the following results in a sum or a product that is rational?
The following operations result in a sum or a product that is rational:
- Adding two rational numbers. The sum of any two rational numbers is rational.
- Subtracting two rational numbers. The difference of any two rational numbers is rational.
- Multiplying two rational numbers. The product of any two rational numbers is rational.
- Dividing two rational numbers, as long as the divisor is not zero. The quotient of any two rational numbers (with a non-zero divisor) is rational.
In general, any operation that involves only rational numbers will result in a result that is rational.
To determine which operations result in a rational sum or product, we need to consider the properties of rational numbers.
A rational number is any number that can be expressed as the ratio of two integers, where the denominator is not zero. Therefore, any operation that involves only rational numbers will result in a rational sum or product.
Let's analyze the given options:
1. Addition of two rational numbers: When you add two rational numbers, the result will be a rational number. For example, adding 1/2 and 3/4 gives us (1/2) + (3/4) = (2/4) + (3/4) = 5/4, which is a rational number.
2. Subtraction of two rational numbers: Similar to addition, subtracting two rational numbers will also result in a rational number. For example, subtracting 2/3 from 5/6 gives us (5/6) - (2/3) = (5/6) - (4/6) = 1/6, which is rational.
3. Multiplication of two rational numbers: When you multiply two rational numbers, the product will also be a rational number. For example, multiplying 2/5 by 3/4 gives us (2/5) * (3/4) = (6/20) = 3/10, which is rational.
4. Division of two rational numbers: Division of rational numbers can result in an irrational number in some cases. For example, dividing 1/3 by 2/5 gives us (1/3) / (2/5) = (5/15) / (6/15) = 5/6, which is rational.
Based on the above analysis, we can conclude that addition, subtraction, and multiplication of two rational numbers always result in a rational sum or product. Division of two rational numbers may or may not result in a rational number, as it depends on the specific numbers being divided.