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Chapter 6: Problem 309

In the following exercises, translate to a proportion. What percent of 92 is 46\(?\)

Short Answer

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Step by step solution

01

- Identify the required proportion

To find what percent of 92 is 46, we need to set up a proportion. Suppose the unknown percent is represented by x.
02

- Set up the proportion equation

A percentage can be expressed as a fraction of 100. So, we set up the equation: \[\frac{x}{100} = \frac{46}{92}\]
03

- Solve the equation

To find x, cross-multiply and then solve the resulting equation: \[x \cdot 92 = 46 \cdot 100 \] This simplifies to: \[92x = 4600 \]
04

- Isolate the variable x

Divide both sides of the equation by 92 to solve for x: \[x = \frac{4600}{92}\] This simplifies to: \[x = 50\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

percent calculations
Understanding percent calculations is crucial in pre-algebra and beyond. A percentage represents a part of a whole, typically out of 100. If you want to find what percentage one number is of another, you set it up as an equation.
For instance, finding what percent of 92 is 46 involves comparing 46 directly to 92.
Here鈥檚 a simple structure
  • Let the unknown percent be x.
  • Set up the proportion: \(\frac{x}{100} = \frac{46}{92}\).
A percentage provides a clear, proportional comparison, which is why it's widely used in various fields like finance, statistics, and everyday scenarios.
fraction to percent
To convert a fraction into a percent, follow these simple steps:
  • Start with your fraction, in this case, \(\frac{46}{92}\).
  • Divide the numerator by the denominator - \(\frac{46}{92} = 0.5\).

Now that you have 0.5, which is a decimal, convert it to a percent by multiplying by 100.
\(0.5 \times 100 = 50\)%.
You now know that 46 is 50% of 92.
Converting fractions to percentages makes it easier to understand the ratio as a part of 100, which is often more intuitive to grasp.
cross-multiplication
Cross-multiplication is a method used to solve proportions easily. Let's look at the equation from our problem:

\(\frac{x}{100} = \frac{46}{92}\)

To solve this, you multiply the numerator of one fraction by the denominator of the other fraction.
Here鈥檚 what happens: \(x \times 92 = 46 \times 100\).
This results in \(92x = 4600\).

Now, isolate x by dividing both sides by 92: \(x = \frac{4600}{92} \).
Performing this division, you get \(x = 50\).
So, 46 is 50% of 92.
Cross-multiplication is a reliable and straightforward method to solve ratios and proportions in algebra.

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