The Product Of Two Rational Number Is -5 Upon 7 If One Of Them Number Is 2 Upon 9 Find The Other
Introduction
In mathematics, rational numbers are a type of number that can be expressed as the ratio of two integers. When we multiply two rational numbers together, we get another rational number. In this article, we will explore how to find the product of two rational numbers, with a specific example where one of the numbers is given as 2/9 and the product is -5/7.
Understanding Rational Numbers
Before we dive into the example, let's quickly review what rational numbers are. A rational number is a number that can be expressed as the ratio of two integers, i.e., a fraction. Rational numbers can be positive or negative, and they can be expressed in the form of a/b, where a and b are integers and b is not equal to zero.
The Product of Two Rational Numbers
When we multiply two rational numbers together, we get another rational number. The product of two rational numbers can be found by multiplying the numerators (the numbers on top) and multiplying the denominators (the numbers on the bottom), and then simplifying the resulting fraction.
Example: Finding the Other Rational Number
Let's say we have two rational numbers, x and y, and we know that their product is -5/7. We are also given that one of the numbers, let's say x, is equal to 2/9. Our goal is to find the other number, y.
To find y, we can use the formula for the product of two rational numbers:
xy = (a/b) × (c/d) = (ac)/(bd)
where a, b, c, and d are integers.
In this case, we know that xy = -5/7 and x = 2/9. We can plug these values into the formula:
(-5/7) = (2/9) × y
To find y, we can multiply both sides of the equation by the reciprocal of (2/9), which is (9/2). This will give us:
y = (-5/7) × (9/2)
Now, we can simplify the right-hand side of the equation by multiplying the numerators and denominators:
y = (-5 × 9) / (7 × 2)
y = -45 / 14
Conclusion
In this article, we explored how to find the product of two rational numbers, with a specific example where one of the numbers is given as 2/9 and the product is -5/7. We used the formula for the product of two rational numbers and simplified the resulting fraction to find the other number. We hope this article has provided you with a clear understanding of how to find the product of two rational numbers.
Additional Examples
Here are a few more examples of finding the product of two rational numbers:
- If the product of two rational numbers is 3/4 and one of the numbers is 5/6, find the other number.
- If the product of two rational numbers is -2/3 and one of the numbers is 7/8, find the other number.
- If the product of two rational numbers is 1/2 and one of the numbers is 3/4, find the other number.
Solving Rational Number Problems
When solving rational number problems, it's essential to remember the following steps:
- Identify the problem and the given information.
- Use the formula for the product of two rational numbers to set up an equation.
- Simplify the equation by multiplying the numerators and denominators.
- Solve for the unknown variable.
By following these steps, you can confidently solve rational number problems and find the product of two rational numbers.
Common Mistakes to Avoid
When solving rational number problems, it's easy to make mistakes. Here are a few common mistakes to avoid:
- Not simplifying the equation before solving for the unknown variable.
- Not using the correct formula for the product of two rational numbers.
- Not checking the answer to ensure it is in simplest form.
By avoiding these common mistakes, you can ensure that your answers are accurate and complete.
Conclusion
Introduction
In our previous article, we explored how to find the product of two rational numbers, with a specific example where one of the numbers is given as 2/9 and the product is -5/7. In this article, we will provide a Q&A guide to help you better understand the concept of the product of two rational numbers.
Q: What is the product of two rational numbers?
A: The product of two rational numbers is the result of multiplying two rational numbers together. It can be expressed as a fraction, where the numerator is the product of the numerators and the denominator is the product of the denominators.
Q: How do I find the product of two rational numbers?
A: To find the product of two rational numbers, you can use the formula:
xy = (a/b) × (c/d) = (ac)/(bd)
where a, b, c, and d are integers.
Q: What if one of the rational numbers is a negative number?
A: If one of the rational numbers is a negative number, the product will also be a negative number. For example, if the product of two rational numbers is -5/7 and one of the numbers is -2/9, the other number will also be a negative number.
Q: Can I simplify the product of two rational numbers?
A: Yes, you can simplify the product of two rational numbers by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Q: What is the greatest common divisor (GCD)?
A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.
Q: How do I find the GCD of two numbers?
A: To find the GCD of two numbers, you can use the Euclidean algorithm or list the factors of each number and find the greatest common factor.
Q: Can I use a calculator to find the product of two rational numbers?
A: Yes, you can use a calculator to find the product of two rational numbers. However, it's essential to ensure that the calculator is set to display the result as a fraction.
Q: What if I get a decimal result when finding the product of two rational numbers?
A: If you get a decimal result when finding the product of two rational numbers, it means that the result is not in simplest form. You can simplify the result by dividing both the numerator and the denominator by their GCD.
Q: Can I use the product of two rational numbers to solve real-world problems?
A: Yes, you can use the product of two rational numbers to solve real-world problems. For example, if you are a carpenter and you need to find the area of a rectangle with a length of 2/3 and a width of 3/4, you can use the product of two rational numbers to find the area.
Conclusion
In conclusion, the product of two rational numbers is a fundamental concept in mathematics that can be used to solve a wide range of problems. By understanding how to find the product of two rational numbers and simplifying the result, you can confidently solve rational number problems and apply the concept to real-world situations.
Additional Resources
For more information on the product of two rational numbers, you can refer to the following resources:
- Khan Academy: Rational Numbers
- Mathway: Rational Numbers
- Wolfram Alpha: Rational Numbers
Practice Problems
Here are a few practice problems to help you reinforce your understanding of the product of two rational numbers:
- Find the product of 2/3 and 3/4.
- Find the product of -2/3 and 3/4.
- Find the product of 2/3 and -3/4.
- Find the product of -2/3 and -3/4.
Answer Key
Here are the answers to the practice problems:
- 6/12 = 1/2
- -6/12 = -1/2
- -6/12 = -1/2
- 6/12 = 1/2