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Chapter 6: Problem 13

Translate to a proportion. Do not solve. $$ 4.8 \% \text { of } 60 \text { is what? } $$

Short Answer

Expert verified
Set up the proportion: \( \frac{4.8}{100} = \frac{x}{60} \).

Step by step solution

01

- Understand the given percentage

The problem states 4.8% of 60. This means you need to understand how to represent 4.8% in a fraction form. Remember that percent means per hundred, so 4.8% can be written as the fraction \( \frac{4.8}{100} \).
02

- Set up the proportion

Translate the problem '4.8% of 60 is what?' into a mathematical equation using a proportion. The structure of a proportion for this type of problem is: \( \frac{4.8}{100} = \frac{x}{60} \). Here, \( x \) is the unknown value you need to find.

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Key Concepts

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

Percentage
A percentage is a way to express a number as a fraction of 100. It is often used to compare proportions. In this problem, we are given 4.8%. The symbol '%' means 'per hundred,' so 4.8% can also be written as 4.8 out of 100 or \( \frac{4.8}{100} \).
  • To convert a percentage to a decimal, simply divide the percentage by 100. Hence, 4.8% becomes 0.048.
  • Percentages are useful when comparing different quantities on a common scale.
Remember, if you have a percentage, you always divide by 100 to turn it into a decimal or fraction.
Fraction
Fractions represent parts of a whole and are shown using a numerator and a denominator. For example, the fraction \( \frac{4.8}{100} \) means 4.8 parts out of 100.
  • The numerator is the number above the line (4.8).
  • The denominator is the number below the line (100).
Fractions can be converted into decimals by dividing the numerator by the denominator. In this case, \( \frac{4.8}{100} = 0.048 \).
Fractions are crucial for representing parts of any quantity, and they are particularly useful in proportions and percentages.
Proportion
A proportion is an equation that states that two ratios are equivalent. In simpler words, it shows that two fractions or ratios are equal.
In this exercise, you are asked to set up a proportion to solve a problem involving a percentage. Here's how:
The problem states, '4.8% of 60 is what?' This can be translated into a proportion:
\( \frac{4.8}{100} = \frac{x}{60} \), where \( x \) is the unknown value.
  • The left side of the equation \( \frac{4.8}{100} \) represents the given percentage as a fraction.
  • The right side \( \frac{x}{60} \) represents the part of 60 that we need to find.
Solving the proportion will give us the value for \( x \), showing the part of 60 that corresponds to 4.8%.

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