What Is The Value Of $p$ In The Proportion Below?$\frac{20}{6} = \frac{p}{12}$A. 2 B. 10 C. 40 D. 72

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Understanding the Concept of Proportions

A proportion is a mathematical statement that two ratios are equal. It is often represented as a fraction or a decimal, and it can be used to solve a wide range of problems in mathematics and real-life situations. In this article, we will focus on solving a proportion problem to find the value of $p$.

The Given Proportion

The given proportion is 206=p12\frac{20}{6} = \frac{p}{12}. This proportion states that the ratio of 20 to 6 is equal to the ratio of $p$ to 12.

Solving the Proportion

To solve the proportion, we need to find the value of $p$. We can do this by cross-multiplying the two ratios. Cross-multiplying means multiplying the numerator of the first ratio by the denominator of the second ratio, and multiplying the numerator of the second ratio by the denominator of the first ratio.

Cross-Multiplying the Ratios

Cross-multiplying the ratios gives us:

20×12=6×p20 \times 12 = 6 \times p

Simplifying the Equation

Simplifying the equation gives us:

240=6p240 = 6p

Solving for $p$

To solve for $p$, we need to isolate $p$ on one side of the equation. We can do this by dividing both sides of the equation by 6.

2406=p\frac{240}{6} = p

Simplifying the Fraction

Simplifying the fraction gives us:

40=p40 = p

Conclusion

Therefore, the value of $p$ in the proportion 206=p12\frac{20}{6} = \frac{p}{12} is 40.

Real-Life Applications of Proportions

Proportions have many real-life applications, including:

  • Finance: Proportions are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Proportions are used to calculate the concentration of solutions, the amount of a substance in a mixture, and other scientific measurements.
  • Engineering: Proportions are used to design and build structures, such as bridges, buildings, and roads.
  • Cooking: Proportions are used to measure ingredients and calculate cooking times.

Tips for Solving Proportions

Here are some tips for solving proportions:

  • Read the problem carefully: Make sure you understand what the problem is asking for.
  • Identify the ratios: Identify the two ratios in the proportion.
  • Cross-multiply: Cross-multiply the two ratios to eliminate the fractions.
  • Simplify the equation: Simplify the equation to isolate the variable.
  • Check your answer: Check your answer to make sure it is reasonable and makes sense in the context of the problem.

Common Mistakes to Avoid

Here are some common mistakes to avoid when solving proportions:

  • Not reading the problem carefully: Make sure you understand what the problem is asking for.
  • Not identifying the ratios: Identify the two ratios in the proportion.
  • Not cross-multiplying: Cross-multiplying is a crucial step in solving proportions.
  • Not simplifying the equation: Simplifying the equation is essential to isolate the variable.
  • Not checking your answer: Check your answer to make sure it is reasonable and makes sense in the context of the problem.

Conclusion

In conclusion, solving proportions is a crucial skill in mathematics and real-life situations. By following the steps outlined in this article, you can solve proportions and find the value of $p$. Remember to read the problem carefully, identify the ratios, cross-multiply, simplify the equation, and check your answer. With practice and patience, you can become proficient in solving proportions and apply this skill to a wide range of problems.