Solve For $h$ In The Proportion.$\[ \frac{2}{7} = \frac{20}{h} \\]$h = \square$

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Introduction

In mathematics, proportions are used to describe the relationship between two or more quantities. A proportion is a statement that two ratios are equal. In this article, we will focus on solving for h in a proportion using the given equation: 27=20h\frac{2}{7} = \frac{20}{h}. We will break down the solution step by step and provide a clear explanation of each step.

Understanding the Equation

The given equation is a proportion, which can be written as: 27=20h\frac{2}{7} = \frac{20}{h}. This equation states that the ratio of 2 to 7 is equal to the ratio of 20 to h. Our goal is to solve for h, which means we need to find the value of h that makes the equation true.

Step 1: Cross-Multiplication

To solve for h, we can use the method of cross-multiplication. This involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa. In this case, we multiply 2 by h and 7 by 20.

27=20h\frac{2}{7} = \frac{20}{h}

2h=20×72h = 20 \times 7

Step 2: Simplifying the Equation

Now that we have the equation 2h=1402h = 140, we can simplify it by dividing both sides by 2.

2h=1402h = 140

h=1402h = \frac{140}{2}

Step 3: Solving for h

Finally, we can solve for h by dividing 140 by 2.

h=1402h = \frac{140}{2}

h=70h = 70

Conclusion

In this article, we solved for h in the proportion 27=20h\frac{2}{7} = \frac{20}{h}. We used the method of cross-multiplication to simplify the equation and then solved for h by dividing 140 by 2. The final answer is h = 70.

Why is Solving for h Important?

Solving for h in a proportion is an important skill in mathematics, as it allows us to describe the relationship between two or more quantities. This skill is used in a variety of real-world applications, such as finance, science, and engineering. By understanding how to solve for h, we can make informed decisions and solve complex problems.

Real-World Applications of Solving for h

Solving for h in a proportion has many real-world applications. For example:

  • In finance, solving for h can help us calculate interest rates and investment returns.
  • In science, solving for h can help us understand the relationship between variables in a scientific experiment.
  • In engineering, solving for h can help us design and build complex systems, such as bridges and buildings.

Tips and Tricks for Solving for h

Here are some tips and tricks for solving for h in a proportion:

  • Make sure to read the equation carefully and understand what is being asked.
  • Use the method of cross-multiplication to simplify the equation.
  • Solve for h by dividing both sides of the equation by the coefficient of h.
  • Check your answer by plugging it back into the original equation.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving for h in a proportion:

  • Not reading the equation carefully and understanding what is being asked.
  • Not using the method of cross-multiplication to simplify the equation.
  • Not solving for h by dividing both sides of the equation by the coefficient of h.
  • Not checking your answer by plugging it back into the original equation.

Conclusion

Introduction

In our previous article, we discussed how to solve for h in a proportion using the equation 27=20h\frac{2}{7} = \frac{20}{h}. We provided a step-by-step guide on how to solve for h and explained the importance of this skill in mathematics. In this article, we will answer some frequently asked questions about solving for h in a proportion.

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It can be written as a fraction, such as ab=cd\frac{a}{b} = \frac{c}{d}, where a, b, c, and d are numbers.

Q: How do I know if I have a proportion?

A: To determine if you have a proportion, look for the following characteristics:

  • The equation is written as a fraction, such as ab=cd\frac{a}{b} = \frac{c}{d}.
  • The two ratios are equal.
  • The equation can be solved for a variable, such as h.

Q: What is cross-multiplication?

A: Cross-multiplication is a method used to solve for a variable in a proportion. It involves multiplying the numerator of the first ratio by the denominator of the second ratio, and vice versa.

Q: How do I use cross-multiplication to solve for h?

A: To use cross-multiplication to solve for h, follow these steps:

  1. Multiply the numerator of the first ratio by the denominator of the second ratio.
  2. Multiply the numerator of the second ratio by the denominator of the first ratio.
  3. Set the two products equal to each other.
  4. Solve for h.

Q: What is the coefficient of h?

A: The coefficient of h is the number that is multiplied by h in the equation. In the equation 27=20h\frac{2}{7} = \frac{20}{h}, the coefficient of h is 20.

Q: How do I solve for h by dividing both sides of the equation by the coefficient of h?

A: To solve for h by dividing both sides of the equation by the coefficient of h, follow these steps:

  1. Divide both sides of the equation by the coefficient of h.
  2. Simplify the equation.
  3. Solve for h.

Q: Why is it important to check my answer by plugging it back into the original equation?

A: It is important to check your answer by plugging it back into the original equation to ensure that it is correct. This is because solving for h can be a complex process, and it is easy to make mistakes.

Q: What are some common mistakes to avoid when solving for h in a proportion?

A: Some common mistakes to avoid when solving for h in a proportion include:

  • Not reading the equation carefully and understanding what is being asked.
  • Not using the method of cross-multiplication to simplify the equation.
  • Not solving for h by dividing both sides of the equation by the coefficient of h.
  • Not checking your answer by plugging it back into the original equation.

Q: How can I practice solving for h in a proportion?

A: You can practice solving for h in a proportion by working through examples and exercises. You can also use online resources, such as math websites and apps, to practice solving for h in a proportion.

Conclusion

In conclusion, solving for h in a proportion is an important skill in mathematics that has many real-world applications. By understanding how to solve for h, we can make informed decisions and solve complex problems. We hope this article has provided a clear and concise guide to solving for h in a proportion and has answered some frequently asked questions about this topic.