Solve The Following Proportion For $u$.$\frac{u}{4} = \frac{8}{7}$Round Your Answer To The Nearest Tenth.$u =$

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What is a Proportion?

A proportion is a statement that two ratios are equal. It is often written in the form of a fraction, where the numerator and denominator of the first fraction are equal to the numerator and denominator of the second fraction, respectively. In this article, we will focus on solving proportions, specifically the proportion u4=87\frac{u}{4} = \frac{8}{7}.

Why Solve Proportions?

Solving proportions is an essential skill in mathematics, particularly in algebra and geometry. It is used to solve problems involving ratios, rates, and proportions. In real-life situations, proportions are used to compare quantities, such as the ratio of the length of a rectangle to its width, or the ratio of the cost of a product to its weight.

Step 1: Write the Proportion

The given proportion is u4=87\frac{u}{4} = \frac{8}{7}. To solve for uu, we need to isolate uu on one side of the equation.

Step 2: Cross-Multiply

To solve the proportion, we can cross-multiply, which means multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. This gives us:

uâ‹…7=4â‹…8u \cdot 7 = 4 \cdot 8

Step 3: Simplify the Equation

Now, we can simplify the equation by multiplying the numbers:

7u=327u = 32

Step 4: Solve for uu

To solve for uu, we need to isolate uu on one side of the equation. We can do this by dividing both sides of the equation by 7:

u=327u = \frac{32}{7}

Step 5: Round the Answer

The problem asks us to round our answer to the nearest tenth. To do this, we can divide 32 by 7 and round the result to the nearest tenth:

u≈4.6u \approx 4.6

Conclusion

In this article, we solved the proportion u4=87\frac{u}{4} = \frac{8}{7} for uu. We used the steps of cross-multiplication, simplification, and division to isolate uu on one side of the equation. Finally, we rounded our answer to the nearest tenth.

Real-World Applications

Solving proportions has many real-world applications, such as:

  • Finance: Calculating interest rates, investment returns, and loan payments.
  • Science: Measuring the concentration of a solution, the speed of a chemical reaction, and the distance traveled by an object.
  • Engineering: Designing bridges, buildings, and other structures that require precise calculations of proportions.

Tips and Tricks

Here are some tips and tricks to help you solve proportions:

  • Use cross-multiplication: Cross-multiplication is a powerful tool for solving proportions. It allows you to eliminate the fractions and work with whole numbers.
  • Simplify the equation: Simplifying the equation can make it easier to solve for the variable.
  • Check your answer: Always check your answer to make sure it is reasonable and makes sense in the context of the problem.

Common Mistakes

Here are some common mistakes to avoid when solving proportions:

  • Forgetting to cross-multiply: Failing to cross-multiply can lead to incorrect solutions.
  • Not simplifying the equation: Failing to simplify the equation can make it difficult to solve for the variable.
  • Rounding incorrectly: Rounding incorrectly can lead to incorrect solutions.

Conclusion

Frequently Asked Questions

Q: What is a proportion?

A: A proportion is a statement that two ratios are equal. It is often written in the form of a fraction, where the numerator and denominator of the first fraction are equal to the numerator and denominator of the second fraction, respectively.

Q: Why do we need to solve proportions?

A: Solving proportions is an essential skill in mathematics, particularly in algebra and geometry. It is used to solve problems involving ratios, rates, and proportions. In real-life situations, proportions are used to compare quantities, such as the ratio of the length of a rectangle to its width, or the ratio of the cost of a product to its weight.

Q: How do I solve a proportion?

A: To solve a proportion, you need to follow these steps:

  1. Write the proportion as an equation.
  2. Cross-multiply by multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa.
  3. Simplify the equation by multiplying the numbers.
  4. Solve for the variable by dividing both sides of the equation by the coefficient of the variable.
  5. Check your answer to make sure it is reasonable and makes sense in the context of the problem.

Q: What is cross-multiplication?

A: Cross-multiplication is a technique used to solve proportions. It involves multiplying the numerator of the first fraction by the denominator of the second fraction, and vice versa. This allows you to eliminate the fractions and work with whole numbers.

Q: Why do I need to simplify the equation?

A: Simplifying the equation makes it easier to solve for the variable. By simplifying the equation, you can eliminate any unnecessary numbers and make the equation more manageable.

Q: How do I round my answer?

A: To round your answer, you need to look at the digit to the right of the digit you are rounding to. If the digit to the right is 5 or greater, you round up. If the digit to the right is less than 5, you round down.

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

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

  • Forgetting to cross-multiply
  • Not simplifying the equation
  • Rounding incorrectly
  • Not checking your answer

Q: How do I apply proportions to real-world problems?

A: Proportions are used to compare quantities in real-world problems. For example, you might use proportions to calculate the cost of a product, the speed of a chemical reaction, or the distance traveled by an object.

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

A: Some real-world applications of proportions include:

  • Finance: Calculating interest rates, investment returns, and loan payments.
  • Science: Measuring the concentration of a solution, the speed of a chemical reaction, and the distance traveled by an object.
  • Engineering: Designing bridges, buildings, and other structures that require precise calculations of proportions.

Q: How do I check my answer?

A: To check your answer, you need to make sure it is reasonable and makes sense in the context of the problem. You can do this by:

  • Checking the units of the answer
  • Checking the magnitude of the answer
  • Checking the sign of the answer

Conclusion

Solving proportions is an essential skill in mathematics, particularly in algebra and geometry. By following the steps of cross-multiplication, simplification, and division, you can solve proportions and apply them to real-world problems. Remember to check your answer and avoid common mistakes to ensure accurate solutions.