The Product Of Two Rational Number Is -4/5 If One Of Them Is 8/35, Find The Other.​

by ADMIN 84 views

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, we get another rational number. In this article, we will explore how to find the product of two rational numbers and use this concept to solve a problem involving a given product and one of the rational numbers.

What are Rational Numbers?

Rational numbers are numbers that can be expressed as the ratio of two integers. They can be written in the form of a fraction, where the numerator is an integer and the denominator is a non-zero integer. For example, 3/4, 5/6, and 7/8 are all rational numbers.

The Product of Two Rational Numbers

When we multiply two rational numbers, we get another rational number. The product of two rational numbers can be found by multiplying the numerators and denominators separately. For example, if we have two rational numbers 1/2 and 3/4, their product is:

(1/2) × (3/4) = (1 × 3) / (2 × 4) = 3/8

Finding the Other Rational Number

Now, let's move on to the problem at hand. We are given that the product of two rational numbers is -4/5, and one of the rational numbers is 8/35. We need to find the other rational number.

Let's assume that the other rational number is x. We can set up an equation based on the given information:

(8/35) × x = -4/5

To solve for x, we can start by multiplying both sides of the equation by the reciprocal of 8/35, which is 35/8.

x = (-4/5) × (35/8)

Simplifying the Equation

Now, let's simplify the equation by multiplying the numerators and denominators separately.

x = (-4 × 35) / (5 × 8) x = -140 / 40 x = -7 / 2

Conclusion

In this article, we explored the concept of rational numbers and how to find the product of two rational numbers. We then used this concept to solve a problem involving a given product and one of the rational numbers. By following the steps outlined in this article, you should be able to find the other rational number in a similar problem.

Key Takeaways

  • Rational numbers are numbers that can be expressed as the ratio of two integers.
  • The product of two rational numbers can be found by multiplying the numerators and denominators separately.
  • To find the other rational number in a problem involving a given product and one of the rational numbers, we can set up an equation and solve for the unknown variable.

Frequently Asked Questions

  • What is the product of two rational numbers? The product of two rational numbers is another rational number that can be found by multiplying the numerators and denominators separately.
  • How do I find the other rational number in a problem involving a given product and one of the rational numbers? To find the other rational number, you can set up an equation based on the given information and solve for the unknown variable.

Additional Resources

  • Khan Academy: Rational Numbers
  • Math Is Fun: Rational Numbers
  • Wolfram MathWorld: Rational Numbers
    The Product of Two Rational Numbers: Q&A =============================================

Introduction

In our previous article, we explored the concept of rational numbers and how to find the product of two rational numbers. We also used this concept to solve a problem involving a given product and one of the rational numbers. In this article, we will answer some frequently asked questions related to the product of two rational numbers.

Q&A

Q: What is the product of two rational numbers?

A: The product of two rational numbers is another rational number that can be found by multiplying the numerators and denominators separately.

Q: How do I find the product of two rational numbers?

A: To find the product of two rational numbers, you can multiply the numerators and denominators separately. For example, if you have two rational numbers 1/2 and 3/4, their product is:

(1/2) × (3/4) = (1 × 3) / (2 × 4) = 3/8

Q: What if the product of two rational numbers is a negative number?

A: If the product of two rational numbers is a negative number, it means that one or both of the rational numbers are negative. For example, if you have two rational numbers 2/3 and -4/5, their product is:

(2/3) × (-4/5) = (-2 × 4) / (3 × 5) = -8/15

Q: Can I find the product of two rational numbers with different denominators?

A: Yes, you can find the product of two rational numbers with different denominators. To do this, you need to find the least common multiple (LCM) of the denominators and then multiply the numerators and denominators separately. For example, if you have two rational numbers 1/2 and 3/4, their product is:

(1/2) × (3/4) = (1 × 3) / (2 × 4) = 3/8

Q: How do I find the other rational number in a problem involving a given product and one of the rational numbers?

A: To find the other rational number, you can set up an equation based on the given information and solve for the unknown variable. For example, if you are given that the product of two rational numbers is -4/5 and one of the rational numbers is 8/35, you can set up the equation:

(8/35) × x = -4/5

To solve for x, you can multiply both sides of the equation by the reciprocal of 8/35, which is 35/8.

x = (-4/5) × (35/8) x = (-4 × 35) / (5 × 8) x = -140 / 40 x = -7 / 2

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 always a good idea to double-check your work by multiplying the numerators and denominators separately.

Q: What if I make a mistake when finding the product of two rational numbers?

A: If you make a mistake when finding the product of two rational numbers, don't worry! You can always go back and recheck your work. Make sure to multiply the numerators and denominators separately and simplify the fraction if necessary.

Conclusion

In this article, we answered some frequently asked questions related to the product of two rational numbers. We hope that this article has been helpful in clarifying any confusion you may have had about this topic. Remember to always multiply the numerators and denominators separately and simplify the fraction if necessary.

Key Takeaways

  • The product of two rational numbers is another rational number that can be found by multiplying the numerators and denominators separately.
  • To find the product of two rational numbers with different denominators, you need to find the least common multiple (LCM) of the denominators and then multiply the numerators and denominators separately.
  • To find the other rational number in a problem involving a given product and one of the rational numbers, you can set up an equation based on the given information and solve for the unknown variable.

Frequently Asked Questions

  • What is the product of two rational numbers? The product of two rational numbers is another rational number that can be found by multiplying the numerators and denominators separately.
  • How do I find the product of two rational numbers? To find the product of two rational numbers, you can multiply the numerators and denominators separately.
  • What if the product of two rational numbers is a negative number? If the product of two rational numbers is a negative number, it means that one or both of the rational numbers are negative.
  • Can I find the product of two rational numbers with different denominators? Yes, you can find the product of two rational numbers with different denominators.
  • How do I find the other rational number in a problem involving a given product and one of the rational numbers? To find the other rational number, you can set up an equation based on the given information and solve for the unknown variable.

Additional Resources

  • Khan Academy: Rational Numbers
  • Math Is Fun: Rational Numbers
  • Wolfram MathWorld: Rational Numbers