If 3/4 = A/8 = 15/b, Then A+B = ​

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Introduction

Mathematical equations and proportions are essential concepts in mathematics that help us solve various problems and understand the relationships between different quantities. In this article, we will explore a mathematical equation involving proportions and solve for the unknown values. The equation given is 3/4 = a/8 = 15/b, and we need to find the value of A+B.

Understanding the Equation

The given equation is a proportion, which means that the ratios of the quantities are equal. We can write the equation as:

3/4 = a/8 = 15/b

This equation tells us that the ratio of 3 to 4 is equal to the ratio of a to 8, and also equal to the ratio of 15 to b.

Solving the Equation

To solve the equation, we can start by cross-multiplying the ratios. Cross-multiplying means multiplying the numerator of one ratio by the denominator of the other ratio.

3/4 = a/8 3 × 8 = 4 × a 24 = 4a a = 24/4 a = 6

Now that we have found the value of a, we can substitute it into the second ratio:

a/8 = 15/b 6/8 = 15/b 6 × b = 8 × 15 6b = 120 b = 120/6 b = 20

Finding the Value of A+B

Now that we have found the values of a and b, we can find the value of A+B.

A = 6 B = 20 A + B = 6 + 20 A + B = 26

Conclusion

In this article, we have solved a mathematical equation involving proportions and found the value of A+B. We started by understanding the equation and then solved it by cross-multiplying the ratios. We found the values of a and b, and then used them to find the value of A+B. The final answer is A+B = 26.

Frequently Asked Questions

  • What is a proportion? A proportion is a statement that two ratios are equal.
  • How do you solve a proportion? To solve a proportion, you can cross-multiply the ratios and then solve for the unknown values.
  • What is the value of A+B? The value of A+B is 26.

Tips and Tricks

  • When solving a proportion, make sure to cross-multiply the ratios correctly.
  • Use the correct order of operations to solve for the unknown values.
  • Check your work by plugging the values back into the original equation.

Real-World Applications

Proportions are used in many real-world applications, such as:

  • Cooking: Recipes often involve proportions of ingredients.
  • Building: Architects use proportions to design buildings.
  • Finance: Investors use proportions to calculate interest rates.

Final Thoughts

Mathematical equations and proportions are essential concepts in mathematics that help us solve various problems and understand the relationships between different quantities. In this article, we have solved a mathematical equation involving proportions and found the value of A+B. We hope that this article has helped you understand the concept of proportions and how to solve them.

Introduction

Proportions are a fundamental concept in mathematics that help us understand the relationships between different quantities. In our previous article, we solved a mathematical equation involving proportions and found the value of A+B. In this article, we will answer some frequently asked questions about proportions and provide additional information to help you understand this concept better.

Q&A

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is a way of expressing the relationship between two quantities in the form of a ratio.

Q: How do you solve a proportion?

A: To solve a proportion, you can cross-multiply the ratios and then solve for the unknown values. This involves multiplying the numerator of one ratio by the denominator of the other ratio.

Q: What is the difference between a proportion and a ratio?

A: A ratio is a comparison of two quantities, while a proportion is a statement that two ratios are equal. For example, 2:3 is a ratio, while 2/3 = 4/6 is a proportion.

Q: How do you simplify a proportion?

A: To simplify a proportion, you can cross-multiply the ratios and then simplify the resulting equation. This involves dividing both sides of the equation by the greatest common divisor (GCD) of the two numbers.

Q: What is the value of A+B?

A: In our previous article, we solved a mathematical equation involving proportions and found the value of A+B to be 26.

Q: How do you use proportions in real-world applications?

A: Proportions are used in many real-world applications, such as cooking, building, and finance. For example, a recipe may involve proportions of ingredients, while an architect may use proportions to design a building.

Q: What are some common mistakes to avoid when solving proportions?

A: Some common mistakes to avoid when solving proportions include:

  • Not cross-multiplying the ratios correctly
  • Not simplifying the resulting equation
  • Not checking the work by plugging the values back into the original equation

Q: How do you check your work when solving proportions?

A: To check your work when solving proportions, you can plug the values back into the original equation and verify that the proportion is still true.

Q: What are some real-world examples of proportions?

A: Some real-world examples of proportions include:

  • The ratio of the length of a rectangle to its width
  • The ratio of the area of a circle to its circumference
  • The ratio of the volume of a cube to its surface area

Conclusion

In this article, we have answered some frequently asked questions about proportions and provided additional information to help you understand this concept better. We hope that this article has helped you understand the concept of proportions and how to solve them.

Tips and Tricks

  • When solving a proportion, make sure to cross-multiply the ratios correctly.
  • Use the correct order of operations to solve for the unknown values.
  • Check your work by plugging the values back into the original equation.

Real-World Applications

Proportions are used in many real-world applications, such as:

  • Cooking: Recipes often involve proportions of ingredients.
  • Building: Architects use proportions to design buildings.
  • Finance: Investors use proportions to calculate interest rates.

Final Thoughts

Proportions are a fundamental concept in mathematics that help us understand the relationships between different quantities. In this article, we have answered some frequently asked questions about proportions and provided additional information to help you understand this concept better. We hope that this article has helped you understand the concept of proportions and how to solve them.