Points to Remember:
- The question involves basic arithmetic operations with rational numbers.
- The core concept is finding an unknown number given its product with a known rational number.
- The solution requires understanding of fractions and their multiplication.
Introduction:
Rational numbers are numbers that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Operations on rational numbers, such as addition, subtraction, multiplication, and division, follow specific rules. This question involves finding an unknown rational number given its product with a known rational number. The product of two rational numbers is obtained by multiplying their numerators and denominators separately.
Body:
Finding the Unknown Rational Number:
Let the two rational numbers be denoted as a and b. We are given that their product is -14, i.e., a * b = -14. We are also given that one of the numbers, say a, is 25/7. Therefore, we can write the equation as:
(25/7) * b = -14
To find b, we need to isolate it by dividing both sides of the equation by 25/7. Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of 25/7 is 7/25. Therefore:
b = -14 * (7/25)
b = -98/25
Therefore, the other rational number is -98/25.
Verification:
To verify our answer, we can multiply the two rational numbers:
(25/7) * (-98/25) = -2450/175 = -14
The product is indeed -14, confirming our solution.
Conclusion:
In conclusion, by applying the basic rules of multiplication of rational numbers and solving a simple algebraic equation, we found that the other rational number is -98/25. This problem highlights the importance of understanding fundamental arithmetic operations with rational numbers, a crucial skill in various mathematical and scientific applications. The solution demonstrates a clear and systematic approach to solving such problems, emphasizing accuracy and verification. Further development of mathematical skills builds a strong foundation for more complex problem-solving in various fields.